ENA, Section 1.4, Exercise 4d
Time bar (total: 7.8s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 12.8% | 87.2% | 0% | 0% | 0% | 0 |
| 0% | 0% | 12.8% | 87.2% | 0% | 0% | 0% | 1 |
| 0% | 0% | 12.8% | 87.2% | 0% | 0% | 0% | 2 |
| 50% | 6.4% | 6.4% | 87.2% | 0% | 0% | 0% | 3 |
| 57.1% | 6.4% | 4.8% | 87.2% | 0% | 1.6% | 0% | 4 |
| 69.2% | 7.2% | 3.2% | 87.2% | 0% | 2.4% | 0% | 5 |
| 75% | 7.2% | 2.4% | 87.2% | 0% | 3.2% | 0% | 6 |
| 82.6% | 7.6% | 1.6% | 87.2% | 0% | 3.6% | 0% | 7 |
| 86.4% | 7.6% | 1.2% | 87.2% | 0% | 4% | 0% | 8 |
| 90.7% | 7.8% | 0.8% | 87.2% | 0% | 4.2% | 0% | 9 |
| 92.6% | 7.8% | 0.6% | 87.2% | 0% | 4.4% | 0% | 10 |
| 95% | 7.9% | 0.4% | 87.2% | 0% | 4.5% | 0% | 11 |
| 96.3% | 8% | 0.3% | 87.2% | 0% | 4.5% | 0% | 12 |
Compiled 24 to 18 computations (25% saved)
| 522.0ms | 4 889× | 0 | valid |
| 398.0ms | 2 805× | 1 | valid |
| 103.0ms | 562× | 2 | valid |
| 13.0ms | 165× | 0 | invalid |
ival-mult: 194.0ms (25.6% of total)ival-<=: 153.0ms (20.2% of total)ival-sub: 141.0ms (18.6% of total)ival-sqrt: 137.0ms (18.1% of total)adjust: 90.0ms (11.9% of total)ival-and: 22.0ms (2.9% of total)exact: 18.0ms (2.4% of total)ival-assert: 4.0ms (0.5% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 102 | 0 | - | 0 | - | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (sqrt.f64 (-.f64 (*.f64 x x) eps)) |
| 0 | 0 | - | 0 | - | (-.f64 (*.f64 x x) eps) |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) | cancellation | 102 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 102 | 0 |
| - | 0 | 154 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 102 | 0 | 0 |
| - | 0 | 0 | 154 |
| number | freq |
|---|---|
| 0 | 154 |
| 1 | 102 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 54.0ms | 324× | 0 | valid |
| 37.0ms | 152× | 1 | valid |
| 10.0ms | 36× | 2 | valid |
Compiled 84 to 28 computations (66.7% saved)
adjust: 8.0ms (29.9% of total)ival-sub: 7.0ms (26.1% of total)ival-sqrt: 6.0ms (22.4% of total)ival-mult: 5.0ms (18.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 46 |
| 1 | 55 | 42 |
| 2 | 164 | 41 |
| 3 | 535 | 41 |
| 4 | 1383 | 41 |
| 5 | 1804 | 41 |
| 6 | 2153 | 41 |
| 7 | 4196 | 41 |
| 8 | 4816 | 41 |
| 9 | 5286 | 41 |
| 10 | 5812 | 41 |
| 11 | 6190 | 41 |
| 12 | 6666 | 41 |
| 13 | 6952 | 41 |
| 14 | 7734 | 41 |
| 0 | 6 | 8 |
| 0 | 10 | 8 |
| 1 | 19 | 8 |
| 2 | 43 | 8 |
| 3 | 152 | 8 |
| 4 | 517 | 8 |
| 5 | 903 | 8 |
| 6 | 1504 | 8 |
| 7 | 3467 | 8 |
| 8 | 4220 | 8 |
| 9 | 5006 | 8 |
| 10 | 5358 | 8 |
| 11 | 5712 | 8 |
| 12 | 6253 | 8 |
| 13 | 6510 | 8 |
| 0 | 8051 | 8 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 64.5% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (-.f64 (*.f64 x x) eps) | |
| cost-diff | 0 | (sqrt.f64 (-.f64 (*.f64 x x) eps)) | |
| cost-diff | 0 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 24 |
| 0 | 10 | 24 |
| 1 | 19 | 24 |
| 2 | 43 | 24 |
| 3 | 152 | 24 |
| 4 | 517 | 24 |
| 5 | 903 | 24 |
| 6 | 1504 | 24 |
| 7 | 3467 | 24 |
| 8 | 4220 | 24 |
| 9 | 5006 | 24 |
| 10 | 5358 | 24 |
| 11 | 5712 | 24 |
| 12 | 6253 | 24 |
| 13 | 6510 | 24 |
| 0 | 8051 | 24 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(-.f64 (*.f64 x x) eps) |
(*.f64 x x) |
eps |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(-.f64 (*.f64 x x) eps) |
(*.f64 x x) |
eps |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0 | (*.f64 x x) | |
| accuracy | 0.015625 | (sqrt.f64 (-.f64 (*.f64 x x) eps)) | |
| accuracy | 0.01953125 | (-.f64 (*.f64 x x) eps) | |
| accuracy | 22.739072900172633 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 8.0ms | 162× | 0 | valid |
| 8.0ms | 76× | 1 | valid |
| 3.0ms | 18× | 2 | valid |
Compiled 50 to 14 computations (72% saved)
ival-sub: 4.0ms (36.4% of total)ival-mult: 3.0ms (27.3% of total)ival-sqrt: 3.0ms (27.3% of total)adjust: 2.0ms (18.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(-.f64 (*.f64 x x) eps) |
(*.f64 x x) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(pow x 2) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 2 x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* -1 eps) (pow x 2)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | eps | @ | 0 | ((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x)) |
| 2.0ms | eps | @ | inf | ((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x)) |
| 1.0ms | x | @ | inf | ((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x)) |
| 1.0ms | x | @ | 0 | ((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x)) |
| 1.0ms | eps | @ | -inf | ((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 257 | 1067 |
| 0 | 842 | 1017 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(pow x 2) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 2 x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* -1 eps) (pow x 2)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(* -1 eps) |
(neg.f64 eps) |
(- (pow x 2) eps) |
(fma.f64 x x (neg.f64 eps)) |
(pow x 2) |
(*.f64 x x) |
(* 1/2 (/ eps x)) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(* 2 x) |
(*.f64 #s(literal 2 binary64) x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64) #s(literal -2 binary64))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(*.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) |
(+ x (* -1/2 (/ eps x))) |
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) eps x) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) eps x) |
(+ (* -1 eps) (pow x 2)) |
(fma.f64 x x (neg.f64 eps)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 x eps)) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) eps) #s(literal -1 binary64) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 22 |
| 0 | 10 | 22 |
| 1 | 47 | 22 |
| 2 | 378 | 22 |
| 3 | 4841 | 22 |
| 0 | 9913 | 19 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(-.f64 (*.f64 x x) eps) |
(*.f64 x x) |
| Outputs |
|---|
(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) #s(literal 1 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps)))) |
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x eps)) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) (pow.f64 x #s(literal 4 binary64)))) |
(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (fma.f64 x x (fma.f64 x x eps))) (-.f64 x (sqrt.f64 (fma.f64 x x eps)))) |
(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64)))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps)))) |
(*.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64)))) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal -1 binary64)))) |
(*.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x eps)))) |
(*.f64 (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64)))) |
(*.f64 (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64)) (fma.f64 x x (fma.f64 x x eps))) |
(*.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x eps)))) |
(*.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal 1 binary64)) |
(*.f64 (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64))) |
(*.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))))) |
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(+.f64 (*.f64 x x) (neg.f64 (neg.f64 eps))) |
(+.f64 (*.f64 x x) (neg.f64 eps)) |
(+.f64 (*.f64 x x) eps) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x)) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x))) |
(*.f64 #s(literal -1 binary64) (*.f64 x x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 x #s(literal 2 binary64)) |
(neg.f64 (*.f64 x x)) |
(sqrt.f64 (pow.f64 x #s(literal 4 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 x x)) |
(fabs.f64 (*.f64 x x)) |
(exp.f64 (+.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))) |
(exp.f64 (+.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1 binary64)))) |
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))) |
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (*.f64 (log.f64 x) #s(literal 1 binary64)))) |
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (/.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) |
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))) |
Compiled 8 544 to 1 400 computations (83.6% saved)
11 alts after pruning (11 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 386 | 11 | 397 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 387 | 11 | 398 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 64.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| 25.8% | (-.f64 x (sqrt.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))))))) | |
| 63.7% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x)) eps))) | |
| 25.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) | |
| 59.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) | |
| 7.1% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) | |
| ▶ | 3.4% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
| ▶ | 39.5% | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
| 22.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| ▶ | 38.2% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
| ▶ | 41.9% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
Compiled 470 to 282 computations (40% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 eps (pow.f64 x #s(literal 3 binary64))) | |
| cost-diff | 0 | (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) | |
| cost-diff | 0 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| cost-diff | 0 | (/.f64 (*.f64 eps eps) (*.f64 x x)) | |
| cost-diff | 0 | (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) | |
| cost-diff | 0 | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) | |
| cost-diff | 2 | (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) | |
| cost-diff | 0 | (/.f64 eps x) | |
| cost-diff | 0 | (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | (neg.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) | |
| cost-diff | 0 | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) | |
| cost-diff | 0 | (neg.f64 eps) | |
| cost-diff | 0 | (fma.f64 x x (neg.f64 eps)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) | |
| cost-diff | 0 | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 199 |
| 0 | 53 | 203 |
| 1 | 102 | 203 |
| 2 | 292 | 194 |
| 3 | 1625 | 194 |
| 4 | 6167 | 194 |
| 0 | 8355 | 193 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
x |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
x |
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) |
(neg.f64 x) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(/.f64 eps x) |
eps |
x |
#s(literal 1/2 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
(/.f64 (*.f64 eps eps) (*.f64 x x)) |
(*.f64 eps eps) |
eps |
(*.f64 x x) |
x |
#s(literal 1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
eps |
(pow.f64 x #s(literal 3 binary64)) |
x |
#s(literal 3 binary64) |
#s(literal 1/8 binary64) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
x |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
x |
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) |
(neg.f64 x) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 eps x) |
eps |
x |
#s(literal 1/2 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) x) eps #s(literal 1/2 binary64)) eps) |
(/.f64 (*.f64 eps eps) (*.f64 x x)) |
(*.f64 (/.f64 (/.f64 eps x) x) eps) |
(*.f64 eps eps) |
eps |
(*.f64 x x) |
x |
#s(literal 1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) eps) |
#s(literal 1/2 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
eps |
(pow.f64 x #s(literal 3 binary64)) |
x |
#s(literal 3 binary64) |
#s(literal 1/8 binary64) |
(/.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.01953125 | (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) | |
| accuracy | 7.648738771805154 | (/.f64 eps (pow.f64 x #s(literal 3 binary64))) | |
| accuracy | 7.874408237474952 | (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) | |
| accuracy | 38.45565858237369 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| accuracy | 0.12109375 | (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) | |
| accuracy | 0.216247051415032 | (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) | |
| accuracy | 28.38057029974741 | (/.f64 (*.f64 eps eps) (*.f64 x x)) | |
| accuracy | 38.45565858237369 | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) | |
| accuracy | 0.0 | (/.f64 eps x) | |
| accuracy | 0.0 | (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) | |
| accuracy | 37.158430897348445 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) | |
| accuracy | 0.0 | (neg.f64 x) | |
| accuracy | 22.739072900172633 | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) | |
| accuracy | 62.41235305867127 | #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) | |
| accuracy | 0.0 | (fma.f64 x x (neg.f64 eps)) | |
| accuracy | 0.0 | (neg.f64 eps) | |
| accuracy | 0.015625 | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) | |
| accuracy | 22.739072900172633 | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| 44.0ms | 162× | 0 | valid |
| 34.0ms | 76× | 1 | valid |
| 9.0ms | 18× | 2 | valid |
Compiled 367 to 62 computations (83.1% saved)
ival-neg: 14.0ms (21.1% of total)adjust: 13.0ms (19.6% of total)ival-mult: 12.0ms (18.1% of total)ival-div: 9.0ms (13.6% of total)ival-sub: 5.0ms (7.5% of total)ival-sqrt: 5.0ms (7.5% of total)ival-add: 5.0ms (7.5% of total)ival-pow: 3.0ms (4.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) |
(neg.f64 x) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(/.f64 eps x) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(/.f64 (*.f64 eps eps) (*.f64 x x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(* -1 x) |
(* 1/2 (/ eps x)) |
(/ eps x) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2)) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/ (pow eps 2) (pow x 2)) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/ eps (pow x 3)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 1/2 eps) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(* 2 x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* -1 eps) (pow x 2)) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | eps | @ | -inf | ((- x (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/ (* eps eps) (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3))) |
| 4.0ms | eps | @ | inf | ((- x (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/ (* eps eps) (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3))) |
| 4.0ms | x | @ | inf | ((- x (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/ (* eps eps) (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3))) |
| 3.0ms | x | @ | 0 | ((- x (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/ (* eps eps) (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3))) |
| 3.0ms | eps | @ | 0 | ((- x (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (neg eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x) (/ (* eps eps) (* x x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 296 | 1303 |
| 0 | 965 | 1243 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| Inputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(* -1 x) |
(* 1/2 (/ eps x)) |
(/ eps x) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2)) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/ (pow eps 2) (pow x 2)) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/ eps (pow x 3)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 1/2 eps) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(* 2 x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* -1 eps) (pow x 2)) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (*.f64 x x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(* -1 eps) |
(neg.f64 eps) |
(- (pow x 2) eps) |
(fma.f64 x x (neg.f64 eps)) |
(* -1 x) |
(neg.f64 x) |
(* 1/2 (/ eps x)) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(/ eps x) |
(/.f64 eps x) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) (*.f64 x x)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2)) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 3 binary64))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64))) |
(/ (pow eps 2) (pow x 2)) |
(/.f64 (*.f64 eps eps) (*.f64 x x)) |
(* 1/8 (/ eps (pow x 3))) |
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64))) |
(/ eps (pow x 3)) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) eps (fma.f64 #s(literal -1/16 binary64) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(*.f64 (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64)) x) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(* 1/2 eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) |
(* 2 x) |
(*.f64 #s(literal 2 binary64) x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64) #s(literal -2 binary64))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(*.f64 (neg.f64 x) (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(*.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1 binary64))) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) eps)) x)) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(neg.f64 (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps) |
(+ x (* -1/2 (/ eps x))) |
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) eps x) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (neg.f64 (/.f64 #s(literal 1/2 binary64) x))) eps x) |
(+ (* -1 eps) (pow x 2)) |
(fma.f64 x x (neg.f64 eps)) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 x eps)) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) eps)) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps eps)) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) eps) #s(literal -1 binary64) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))) |
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 32 | 169 |
| 0 | 53 | 169 |
| 1 | 218 | 161 |
| 2 | 1685 | 161 |
| 0 | 8852 | 161 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x)) |
(neg.f64 x) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) |
(/.f64 eps x) |
(fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x) |
(/.f64 (*.f64 eps eps) (*.f64 x x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
| Outputs |
|---|
(*.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64))) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 x x (neg.f64 eps)) (-.f64 (*.f64 x x) (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x)))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps)))) (neg.f64 (-.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps)))) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))))) |
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (-.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) |
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(fma.f64 (fabs.f64 (/.f64 eps (pow.f64 x #s(literal 3/2 binary64)))) (fabs.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (fabs.f64 (*.f64 #s(literal 1/8 binary64) eps)) (fabs.f64 (pow.f64 x #s(literal -3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 (fabs.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 eps (pow.f64 x #s(literal -2 binary64))) (fabs.f64 (/.f64 #s(literal 1/8 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 eps (pow.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal -3 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/8 binary64) (fabs.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64))) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1 binary64)) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(fma.f64 (/.f64 eps x) (fabs.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) x)) |
(fma.f64 eps (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal -1 binary64)))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64))))) |
(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(+.f64 (/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 (*.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) eps)) (*.f64 (*.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))))) |
(+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (neg.f64 x) (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 4 binary64)))) |
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 x (*.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 4 binary64)))) |
(+.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 4 binary64))))))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal -2 binary64)) (-.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 4 binary64))))))) |
(+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 x #s(literal 2 binary64)))) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 x #s(literal 2 binary64))))) |
(+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) (neg.f64 x)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 4 binary64)))) |
(+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) x) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 4 binary64)))) |
(+.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64))))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64))))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (*.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/2 binary64) x)) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))) (-.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)))) |
(+.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) x)) |
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64))) |
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) eps) #s(literal -1 binary64))) |
(*.f64 #s(literal -1 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 eps x)) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (*.f64 eps (pow.f64 x #s(literal -2 binary64)))) |
(*.f64 (pow.f64 x #s(literal -3 binary64)) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -3 binary64)) eps) |
(*.f64 #s(literal 1 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (neg.f64 eps) (pow.f64 x #s(literal -3 binary64))) |
(*.f64 eps (pow.f64 x #s(literal -3 binary64))) |
(pow.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (/.f64 eps (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64)))) |
(/.f64 (neg.f64 (*.f64 eps (pow.f64 x #s(literal -2 binary64)))) (neg.f64 x)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps)) (pow.f64 x #s(literal 6 binary64))) |
(/.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (pow.f64 x #s(literal 3 binary64))) |
(/.f64 (/.f64 eps (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) |
(/.f64 (/.f64 (neg.f64 eps) x) (*.f64 (neg.f64 x) x)) |
(/.f64 (/.f64 eps (neg.f64 x)) (*.f64 (neg.f64 x) x)) |
(/.f64 (neg.f64 (neg.f64 eps)) (pow.f64 x #s(literal 3 binary64))) |
(/.f64 (neg.f64 (/.f64 eps x)) (*.f64 (neg.f64 x) x)) |
(/.f64 (*.f64 eps (pow.f64 x #s(literal -2 binary64))) x) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) eps)) |
(/.f64 (/.f64 eps x) (*.f64 x x)) |
(/.f64 (neg.f64 eps) (pow.f64 x #s(literal 3 binary64))) |
(/.f64 eps (pow.f64 x #s(literal 3 binary64))) |
(neg.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) |
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (*.f64 x x)) (/.f64 (/.f64 eps (neg.f64 x)) (*.f64 x x))) |
(-.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps)) #s(literal -1 binary64))) |
(+.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) |
Compiled 28 529 to 3 985 computations (86% saved)
20 alts after pruning (17 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 950 | 13 | 963 |
| Fresh | 2 | 4 | 6 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 0 | 0 |
| Total | 954 | 20 | 974 |
| Status | Accuracy | Program |
|---|---|---|
| 64.2% | (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) | |
| ▶ | 51.4% | (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
| 64.1% | (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| 51.4% | (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) | |
| 64.0% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))))) | |
| ✓ | 64.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ▶ | 25.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
| ▶ | 59.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
| 7.1% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) | |
| ✓ | 3.4% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
| ▶ | 64.4% | (+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
| 38.2% | #s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) eps))) | |
| 39.8% | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) | |
| 22.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) (*.f64 x x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| ▶ | 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
| 37.8% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 x x (*.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))) eps)) | |
| ✓ | 41.9% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
| 41.8% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| 15.9% | #s(approx (- x (sqrt (- (* x x) eps))) (exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -1 binary64)))) |
Compiled 865 to 522 computations (39.7% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) | |
| cost-diff | 0 | (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) | |
| cost-diff | 1 | (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))) | |
| cost-diff | 1 | (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) | |
| cost-diff | 0 | (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) | |
| cost-diff | 0 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) | |
| cost-diff | 2 | (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) | |
| cost-diff | 4 | (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) | |
| cost-diff | 0 | #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) | |
| cost-diff | 0 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) | |
| cost-diff | 1 | (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | (neg.f64 eps) | |
| cost-diff | 0 | #s(approx (- (* x x) eps) (neg.f64 eps)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) | |
| cost-diff | 0 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) | |
| cost-diff | 0 | (*.f64 x x) | |
| cost-diff | 0 | (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| cost-diff | 9 | (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) | |
| cost-diff | 17 | (+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 44 | 428 |
| 0 | 76 | 419 |
| 1 | 153 | 387 |
| 2 | 475 | 368 |
| 3 | 2538 | 356 |
| 4 | 7817 | 356 |
| 0 | 8888 | 352 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
x |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) |
#s(approx (- (* x x) eps) (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) |
#s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) |
(/.f64 eps (*.f64 x x)) |
eps |
(*.f64 x x) |
#s(literal -1 binary64) |
#s(literal 1 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) |
(*.f64 #s(literal 1/8 binary64) eps) |
#s(literal 1/8 binary64) |
eps |
(*.f64 x x) |
x |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
(-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
x |
#s(literal 3 binary64) |
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
#s(literal 3/2 binary64) |
(fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) |
(fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
| Outputs |
|---|
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 eps (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
x |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 (-.f64 eps (*.f64 x x)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(-.f64 eps (*.f64 x x)) |
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) |
#s(approx (- (* x x) eps) (neg.f64 eps)) |
(neg.f64 eps) |
eps |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
#s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) |
(-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) |
(/.f64 eps (*.f64 x x)) |
eps |
(*.f64 x x) |
#s(literal -1 binary64) |
#s(literal 1 binary64) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps)) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) |
(*.f64 (/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) eps) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) |
(/.f64 (fma.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) x)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) |
(*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) |
(*.f64 #s(literal 1/8 binary64) eps) |
#s(literal 1/8 binary64) |
eps |
(*.f64 x x) |
x |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 (+.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x (neg.f64 eps))) |
(-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
x |
#s(literal 3 binary64) |
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) |
(fma.f64 x x (neg.f64 eps)) |
(neg.f64 eps) |
eps |
#s(literal 3/2 binary64) |
(fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) |
(fma.f64 (+.f64 (+.f64 x x) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x (neg.f64 eps)) |
(fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))) |
(fma.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) x (neg.f64 eps)) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.0390625 | (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) | |
| accuracy | 0.1484375 | (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) | |
| accuracy | 13.475692288745583 | (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) | |
| accuracy | 17.337386318520863 | (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) | |
| accuracy | 7.874408237474952 | (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) | |
| accuracy | 11.492859404369032 | (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) | |
| accuracy | 12.60166856548385 | (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) | |
| accuracy | 38.45565858237369 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) | |
| accuracy | 0.015625 | (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) | |
| accuracy | 12.573345578872425 | (/.f64 eps (*.f64 x x)) | |
| accuracy | 22.739072900172633 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) | |
| accuracy | 24.350187504206165 | (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) | |
| accuracy | 0.0 | (neg.f64 eps) | |
| accuracy | 0.015625 | (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) | |
| accuracy | 22.739072900172633 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) | |
| accuracy | 25.004749659725487 | #s(approx (- (* x x) eps) (neg.f64 eps)) | |
| accuracy | 0.31087875976844204 | (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) | |
| accuracy | 0.328125 | (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| accuracy | 5.760214467372504 | (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| accuracy | 22.706005348866682 | (+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
| 133.0ms | 162× | 0 | valid |
| 45.0ms | 76× | 1 | valid |
| 16.0ms | 18× | 2 | valid |
Compiled 826 to 85 computations (89.7% saved)
ival-add: 47.0ms (40.8% of total)ival-pow: 19.0ms (16.5% of total)ival-mult: 15.0ms (13% of total)ival-div: 12.0ms (10.4% of total)adjust: 9.0ms (7.8% of total)ival-sub: 5.0ms (4.3% of total)ival-sqrt: 5.0ms (4.3% of total)ival-neg: 3.0ms (2.6% of total)exact: 1.0ms (0.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) |
#s(approx (- (* x x) eps) (neg.f64 eps)) |
(neg.f64 eps) |
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) |
#s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) |
(fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) |
(fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
(-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 eps (*.f64 x x)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) |
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) |
| Outputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
eps |
(+ eps (* -1 (pow x 2))) |
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) |
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(pow x 2) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(* -1 (/ eps (pow x 2))) |
(/ (+ (* -1 eps) (pow x 2)) (pow x 2)) |
(* 1/8 (/ eps x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(- (* (sqrt eps) (* x (sqrt -1))) eps) |
(- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ (* x (+ 2 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ x (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1))) |
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* (pow x 2) (- x (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* (pow x 2) (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(+ (* x (- (* -1 (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* x (+ (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* -1 eps) (pow x 2)) |
(/ eps (pow x 2)) |
(* 1/8 (/ eps (pow x 2))) |
(* (sqrt (pow eps 3)) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))))) |
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (sqrt -1))))))))) |
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ eps (pow x 2)) 1)) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
1 |
(+ 1 (* -1 (/ eps (pow x 2)))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(* 3 (pow x 2)) |
(* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2)))) |
(* 2 (pow x 2)) |
(* (pow x 2) (- (+ 2 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2)))) |
(* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x)) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x) |
(* -1/2 (* x (+ (* -2 eps) (* -1 eps)))) |
(* x (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/2 (+ (* -2 eps) (* -1 eps))))) |
(* x (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))))) |
(* x (- (* 1/2 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))))) |
(* -1/2 x) |
(* x (- (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) 1/2)) |
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (* -1/32 (/ (pow eps 2) (pow x 4))))) 1/2)) |
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 4))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6)))))))) 1/2)) |
(pow x 3) |
(* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))) |
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))) |
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))) |
(* 2 x) |
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))))))) |
(* 2 (/ (pow x 3) eps)) |
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2))) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* (pow x 2) (- (+ 1 (* 1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 1 (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 1 (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))) (/ eps (pow x 2)))) |
(- (* 1/2 eps) eps) |
(- (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) eps) |
(- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) eps) |
(- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) eps) |
(* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 2))) |
(* 2 (pow x 3)) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) 2))) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))) (+ 2 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (+ 2 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))) |
(* -2 (/ (pow x 3) eps)) |
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 6))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))) |
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))) |
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))) |
(+ (* -1/2 x) (* 1/2 x)) |
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x)))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))) |
(+ (* 1/8 (/ eps x)) (* 1/2 x)) |
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 2 (pow x 2)) (pow x 2)) |
(+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)) (pow x 2))) |
(+ (* -3/2 eps) (* 2 (pow x 2))) |
(+ (* 2 (pow x 2)) (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2))) |
(+ (* 2 (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2))) |
(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) |
(* eps (- (* -1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(* eps (- (* eps (- (* 1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(* eps (- (* eps (- (* eps (- (* 1/2 (/ (* eps (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6))))) (pow x 3))) (* -1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(+ (* -1/2 x) (* 3/8 (/ eps x))) |
(+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))) |
(+ (* -1/2 x) (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x))))) |
(+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3)) |
(+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3)) |
(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3)) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) |
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) |
(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) |
(* eps (- (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) 1)) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) 1)) |
(* eps (- (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)) 1)) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps))) 1)) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)))) 1)) |
(* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) |
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))))) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))) |
(+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(* -1 (* eps (- (/ (pow x 2) eps) 1))) |
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) |
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (- (/ 1 (pow x 2)) (/ 1 eps)))) |
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) |
(* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) |
(* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))) |
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps))))) |
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps))))) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x)) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps))) eps))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 64.0ms | eps | @ | -inf | ((+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (+ (* (/ eps (* x x)) -1) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps)))) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))) (/ (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))))) (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x)) (* (+ (* (/ eps (* x x)) -1) 1) (* x x)) (/ eps (* x x)) (/ (* 1/8 eps) (* x x)) (pow (+ (* x x) (neg eps)) 3/2)) |
| 22.0ms | x | @ | -inf | ((+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (+ (* (/ eps (* x x)) -1) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps)))) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))) (/ (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))))) (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x)) (* (+ (* (/ eps (* x x)) -1) 1) (* x x)) (/ eps (* x x)) (/ (* 1/8 eps) (* x x)) (pow (+ (* x x) (neg eps)) 3/2)) |
| 16.0ms | eps | @ | 0 | ((+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (+ (* (/ eps (* x x)) -1) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps)))) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))) (/ (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))))) (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x)) (* (+ (* (/ eps (* x x)) -1) 1) (* x x)) (/ eps (* x x)) (/ (* 1/8 eps) (* x x)) (pow (+ (* x x) (neg eps)) 3/2)) |
| 11.0ms | eps | @ | inf | ((+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (+ (* (/ eps (* x x)) -1) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps)))) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))) (/ (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))))) (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x)) (* (+ (* (/ eps (* x x)) -1) 1) (* x x)) (/ eps (* x x)) (/ (* 1/8 eps) (* x x)) (pow (+ (* x x) (neg eps)) 3/2)) |
| 10.0ms | x | @ | inf | ((+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (+ (* (/ eps (* x x)) -1) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (- x (sqrt (- (* x x) eps))) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps)))) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))) (/ (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (+ (* x x) (+ (* (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg eps))))) (- (pow x 3) (pow (+ (* x x) (neg eps)) 3/2)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x)) (* (+ (* (/ eps (* x x)) -1) 1) (* x x)) (/ eps (* x x)) (/ (* 1/8 eps) (* x x)) (pow (+ (* x x) (neg eps)) 3/2)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1522 | 10312 |
| 0 | 5489 | 9809 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
eps |
(+ eps (* -1 (pow x 2))) |
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) |
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(pow x 2) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
(* -1 (/ eps (pow x 2))) |
(/ (+ (* -1 eps) (pow x 2)) (pow x 2)) |
(* 1/8 (/ eps x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(- (* (sqrt eps) (* x (sqrt -1))) eps) |
(- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ (* x (+ 2 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ x (* (sqrt eps) (sqrt -1)))) eps) |
(- (* x (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1))) |
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* (pow x 2) (- x (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(- (* (pow x 2) (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(+ (* x (- (* -1 (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* x (+ (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* -1 eps) (pow x 2)) |
(/ eps (pow x 2)) |
(* 1/8 (/ eps (pow x 2))) |
(* (sqrt (pow eps 3)) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (+ (* 2 (pow eps 2)) (pow eps 2))) (sqrt -1)))) (* (sqrt (pow eps 3)) (sqrt -1))) |
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))))) |
(+ (* (sqrt (pow eps 3)) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (- 1 (* 1/2 (/ (* (+ (* 2 (pow eps 2)) (pow eps 2)) (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2)))))) (* (pow eps 3) (pow (sqrt -1) 2)))))) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (- (+ (* -2 eps) (* -1 eps)) (* 1/4 (/ (pow (+ (* 2 (pow eps 2)) (pow eps 2)) 2) (* (pow eps 3) (pow (sqrt -1) 2))))) (sqrt -1))))))))) |
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ eps (pow x 2)) 1)) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
1 |
(+ 1 (* -1 (/ eps (pow x 2)))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(* 3 (pow x 2)) |
(* (pow x 2) (- (+ 3 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 3 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2)))) |
(* 2 (pow x 2)) |
(* (pow x 2) (- (+ 2 (* -1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))) (/ eps (pow x 2)))) |
(* -1/6 (/ (+ (* -2 eps) (* -1 eps)) x)) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))) (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2)))) x) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4)))))) x) |
(/ (- (+ (* -1/6 (+ (* -2 eps) (* -1 eps))) (+ (* -1/6 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* -1/6 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/6 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6)))))) (+ (* -1/18 (/ (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps)) (pow x 2))) (+ (* -1/24 (/ (* (pow eps 2) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 6))) (+ (* 1/288 (/ (* (pow eps 3) (+ (* -2 eps) (* -1 eps))) (pow x 6))) (+ (* 1/144 (/ (* (pow eps 2) (+ (* -2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/144 (* (pow eps 2) (+ (* -2 eps) (* -1 eps)))) (* 1/3 (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))))))) (pow x 6))) (* 1/3 (/ (* (- (* -1/2 eps) eps) (- (* -1/6 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (* -1/18 (* (+ (* -2 eps) (* -1 eps)) (- (* -1/2 eps) eps))))) (pow x 4))))))))) x) |
(* -1/2 (* x (+ (* -2 eps) (* -1 eps)))) |
(* x (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))) (* 1/2 (+ (* -2 eps) (* -1 eps))))) |
(* x (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2)))))) |
(* x (- (* 1/2 (/ (+ (* 1/4 (pow (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) 2)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))))) (pow x 6))) (+ (* 1/2 (+ (* -2 eps) (* -1 eps))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 4))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 2))))))) |
(* -1/2 x) |
(* x (- (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) 1/2)) |
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (* -1/32 (/ (pow eps 2) (pow x 4))))) 1/2)) |
(* x (- (+ (* -1 (/ (- (* -1/2 eps) (* -1/8 eps)) (pow x 2))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 4))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6)))))))) 1/2)) |
(pow x 3) |
(* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))) |
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))) |
(* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))) |
(* 2 x) |
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))))))) |
(* 2 (/ (pow x 3) eps)) |
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2))) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* (pow x 2) (- (+ 1 (* 1/2 (/ eps (pow x 2)))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 1 (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) (/ eps (pow x 2)))) |
(* (pow x 2) (- (+ 1 (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))))) (/ eps (pow x 2)))) |
(- (* 1/2 eps) eps) |
(- (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) eps) |
(- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) eps) |
(- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) eps) |
(* -1 (* x (- (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) 2))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4)))) 2))) |
(* -1 (* x (- (+ (* -1 (/ (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))) (pow x 2))) (+ (* -1 (/ (- (* 1/2 (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))))))) (+ (* 1/8 (* (pow eps 2) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps))))) (+ (* 1/8 (pow eps 3)) (* (- (* 1/2 eps) eps) (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))))))) (pow x 6))) (* -1 (/ (- (* 1/2 (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))) (+ (* 1/4 (pow eps 2)) (* (- (* 1/2 eps) eps) (- (* 1/2 (+ (* -2 eps) (* -1 eps))) (* 2 (- (* 1/2 eps) eps)))))) (pow x 4))))) 2))) |
(* 2 (pow x 3)) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) 2))) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))) (+ 2 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))))))) |
(* -1 (* (pow x 3) (- (* -1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (+ 2 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))) |
(* -2 (/ (pow x 3) eps)) |
(* -1 (* (pow x 3) (- (* 2 (/ 1 eps)) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (* (pow x 3) (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 6)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 6))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) (* 5/2 (/ 1 (pow x 2)))))) |
(* -1 (pow x 3)) |
(* -1 (* (pow x 3) (+ 1 (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2)))))) |
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4))))))) |
(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))) |
(+ (* -1/2 x) (* 1/2 x)) |
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x)))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))) |
(+ (* 1/8 (/ eps x)) (* 1/2 x)) |
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 2 (pow x 2)) (pow x 2)) |
(+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2)) (pow x 2))) |
(+ (* -3/2 eps) (* 2 (pow x 2))) |
(+ (* 2 (pow x 2)) (* eps (- (* -1/8 (/ eps (pow x 2))) 3/2))) |
(+ (* 2 (pow x 2)) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2))))) 3/2))) |
(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) |
(* eps (- (* -1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(* eps (- (* eps (- (* 1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(* eps (- (* eps (- (* eps (- (* 1/2 (/ (* eps (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6))))) (pow x 3))) (* -1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
(+ (* -1/2 x) (* 3/8 (/ eps x))) |
(+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))) |
(+ (* -1/2 x) (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x))))) |
(+ (* 1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) (pow x 3)) |
(+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3)) |
(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3)) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) |
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) |
(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) |
(* eps (- (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) 1)) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) 1)) |
(* eps (- (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)) 1)) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps))) 1)) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)))) 1)) |
(* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) |
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))))) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))) |
(+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(* -1 (* eps (- (/ (pow x 2) eps) 1))) |
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) |
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (- (/ 1 (pow x 2)) (/ 1 eps)))) |
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* eps (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) |
(* -1 (* eps (+ 1 (+ (* -2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (* 2 (pow x 2))) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* -1 (* eps (+ 1 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 5) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 3) (sqrt -1))))) eps)) (pow x 2)) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) |
(* (sqrt eps) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) |
(* -1 (* eps (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2)))) (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))))))) |
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps))))) |
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps))))) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x)) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps))) eps))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
| Outputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.f64 (neg.f64 x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) x (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) #s(literal -1 binary64) (fma.f64 (-.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
eps |
(+ eps (* -1 (pow x 2))) |
(fma.f64 (*.f64 x x) #s(literal -1 binary64) eps) |
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) |
(*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) |
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (neg.f64 x) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps))) (*.f64 x x)) |
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(*.f64 (fma.f64 (fma.f64 (neg.f64 x) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps)))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x)) |
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64)))) x (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps)))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x)) |
(pow x 2) |
(*.f64 x x) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(* -1 eps) |
(neg.f64 eps) |
(- (pow x 2) eps) |
(-.f64 (*.f64 x x) eps) |
(* -1 (/ eps (pow x 2))) |
(/.f64 (neg.f64 eps) (*.f64 x x)) |
(/ (+ (* -1 eps) (pow x 2)) (pow x 2)) |
(/.f64 (-.f64 (*.f64 x x) eps) (*.f64 x x)) |
(* 1/8 (/ eps x)) |
(*.f64 (/.f64 eps x) #s(literal 1/8 binary64)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) x) |
(* 1/8 (/ eps (pow x 3))) |
(*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) eps (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 3 binary64))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 3 binary64))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (pow.f64 x #s(literal 3 binary64))) |
(- (* (sqrt eps) (* x (sqrt -1))) eps) |
(fma.f64 (*.f64 (sqrt.f64 eps) x) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 eps)) |
(- (* x (+ (* 2 x) (* (sqrt eps) (sqrt -1)))) eps) |
(fma.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (*.f64 #s(literal 2 binary64) x)) x (neg.f64 eps)) |
(- (* x (+ (* x (+ 2 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) #s(literal 2 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) x (neg.f64 eps)) |
(- (* x (+ x (* (sqrt eps) (sqrt -1)))) eps) |
(-.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) x) x) eps) |
(- (* x (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))) eps) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) #s(literal 1 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) x (neg.f64 eps)) |
(+ (* x (pow (sqrt -1) 2)) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) x (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* x (- (* x (- (+ (* -1 (* x (+ (* -2 (/ (pow (sqrt -1) 2) eps)) (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1)))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 eps)))))) (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* 2 (pow eps 2)) (pow eps 2)) (sqrt -1))))) (+ (* -2 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) (* -1 (pow (sqrt -1) 2)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps) #s(literal -2 binary64) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) eps))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 #s(literal 3 binary64) (*.f64 eps eps)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -2 binary64) (neg.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) x (*.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(* -1 (* (sqrt (pow eps 3)) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) |
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(pow x 3) |
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(* -1 (pow x 3)) |
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(* -1 (* (pow x 3) (+ 1 (+ (* 1/2 (/ (+ (* -2 eps) (* -1 eps)) (pow x 2))) (+ (* 1/2 (/ (- (* -1 (pow eps 3)) (* 1/2 (* (+ (* -2 eps) (* -1 eps)) (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2)))))) (pow x 6))) (* 1/2 (/ (- (+ (* 2 (pow eps 2)) (pow eps 2)) (* 1/4 (pow (+ (* -2 eps) (* -1 eps)) 2))) (pow x 4)))))))) |
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(*.f64 x #s(literal 0 binary64)) |
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(fma.f64 #s(literal -3/2 binary64) eps (*.f64 (*.f64 x x) #s(literal 2 binary64))) |
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(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) |
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(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
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(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
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(* eps (+ (* -1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (+ (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* eps (- (* 1/2 (/ (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* 1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))) (+ (* 2 (pow x 2)) (pow x 2)))) (+ (* -1/8 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (* (pow x 2) (+ (* 2 (pow x 2)) (pow x 2))))) (* 1/32 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 7) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))))) (+ (* -3/2 (/ (- (* -1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (* (pow x 3) (+ (* 2 (pow x 2)) (pow x 2))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))) (+ (* 2 (pow x 2)) (pow x 2)))) (* 1/16 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 5) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) (* 3/4 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (pow x 3) (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)))))))) |
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(* -1/2 (/ (* eps (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 3))) |
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(* eps (- (* -1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
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(* eps (- (* eps (- (* 1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
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(* eps (- (* eps (- (* eps (- (* 1/2 (/ (* eps (+ (* -1/2 (/ (* (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (+ (* -2 (pow x 4)) (* -1 (pow x 4)))) (pow x 6))) (* 1/4 (/ (pow (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) 2) (pow x 6))))) (pow x 3))) (* -1/2 (/ (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) |
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(+ (* -1/2 x) (* 3/8 (/ eps x))) |
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(+ (* -1/2 x) (* eps (+ (* eps (+ (* 3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 3/128 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 3/8 binary64) x)) eps (*.f64 #s(literal -1/2 binary64) x)) |
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(+ (* eps (+ (* 1/2 (/ (* eps (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 3))) (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))))) (pow x 3)) |
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(+ (* eps (+ (* 1/2 (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (pow x 3))) (* eps (+ (* -1/2 (/ (* eps (+ 1 (* 1/2 (/ (* (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6))))) (pow x 6))))) (pow x 3))) (* 1/2 (/ (- (+ (* 2 (pow x 2)) (pow x 2)) (* 1/4 (/ (pow (+ (* -2 (pow x 4)) (* -1 (pow x 4))) 2) (pow x 6)))) (pow x 3))))))) (pow x 3)) |
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(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) |
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(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) |
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(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) |
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 x (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 x (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps))) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (*.f64 x (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))) |
(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) |
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps) |
(/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.f64 (neg.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
(/.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (neg.f64 (/.f64 (*.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (*.f64 eps eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps) |
(/.f64 (-.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) (*.f64 eps eps)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 x (/.f64 (*.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))))) (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) eps) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 x eps)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps) |
(* eps (- (/ 1 eps) (/ 1 (pow x 2)))) |
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (*.f64 x x))) eps) |
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) eps) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps eps)) |
(* eps (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) eps) |
(* eps (- (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 1)) |
(*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) eps) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) 1)) |
(*.f64 (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)))) eps) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* 2 (/ (pow x 2) eps)) (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) 1)) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal 2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))))) eps) |
(* eps (- (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)) 1)) |
(*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))) eps) |
(* eps (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps))) 1)) |
(*.f64 (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)))) eps) |
(* eps (- (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 5) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* x (sqrt -1))) (/ (pow x 2) eps)))) 1)) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))))) eps) |
(* -1 (* (sqrt eps) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) |
(neg.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) (sqrt.f64 eps))) |
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) (neg.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) eps) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3))))))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (*.f64 eps eps)))) (fma.f64 (*.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))) eps) |
(* eps (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (/ (pow x 3) (* (pow eps 2) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* -2 (* (sqrt (/ 1 (pow eps 3))) (/ (* (pow x 2) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* -1/2 (/ (pow x 3) (* (pow eps 2) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)) (+ (* -1/2 (/ (pow x 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 2))) (+ (* 1/2 (* (sqrt eps) (/ (+ (* 2 (pow x 2)) (pow x 2)) (* (sqrt -1) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))) (* (pow eps 3) (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1)))) (+ (* 4 (* (sqrt (/ 1 (pow eps 5))) (/ (* (pow x 4) (sqrt -1)) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))) (/ (pow x 5) (* (pow eps 3) (pow (- (* (sqrt (/ 1 eps)) (* x (sqrt -1))) 1) 3)))))))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (*.f64 eps eps))))) (fma.f64 (*.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (pow.f64 eps #s(literal 3 binary64))) (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 4 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)))) #s(literal 2 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) #s(literal 3 binary64))) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1 binary64)) eps) #s(literal 3 binary64))))))))) eps) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (-.f64 (fma.f64 (*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 2 binary64)) eps)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) eps))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))) |
(fma.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 x (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))) |
(+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))))))) |
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 x (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 x (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 eps))) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 eps eps)) (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64) (fma.f64 (*.f64 x (/.f64 (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))))))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (+ (* 2 (pow x 2)) (pow x 2)) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (+ (* -2 (pow x 4)) (* -1 (pow x 4))) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (- (pow x 6) (* 1/4 (/ (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2)) (pow (sqrt -1) 2)))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 2 binary64)) eps)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))) |
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(*.f64 (neg.f64 eps) (*.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)))))))) eps) #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) eps)))) |
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (/ (sqrt -1) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (+ (* 2 (/ (* (pow x 2) (- (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))))))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (/ (pow x 5) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3)))) eps)) (/ (pow x 3) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))))) (+ (* -1/2 (/ (pow x 3) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))) (+ (* 1/2 (* (sqrt eps) (/ (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))) (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))))) (* 4 (* (sqrt (/ 1 eps)) (/ (* (pow x 4) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 3))))))) eps)) (* -2 (* (sqrt (/ 1 eps)) (/ (* (pow x 2) (sqrt -1)) (pow (+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) 2))))) eps))))) |
(*.f64 (neg.f64 eps) (*.f64 #s(literal -1 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))))) (fma.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)))))))) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)))) #s(literal 2 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))))) eps) #s(literal -1 binary64) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (fma.f64 (*.f64 #s(literal 4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 3 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64))))))))) eps) #s(literal -1 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) eps)))) |
(* (pow eps 2) (- (/ (pow x 3) (pow eps 2)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)) |
(* (pow eps 2) (- (+ (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (/ (pow x 3) (pow eps 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 2 binary64)) eps) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 eps eps)) |
(- (+ (* -1 (* (sqrt eps) (sqrt -1))) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) (* -1 x)) |
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))) (neg.f64 x)) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps))) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x))) (sqrt.f64 #s(literal -1 binary64))))) eps) #s(literal -1 binary64) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x))))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps))) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) eps) (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x)))) #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x))) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))) eps) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x))) (sqrt.f64 #s(literal -1 binary64)))))) eps) #s(literal -1 binary64) (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 #s(literal 1 binary64) (*.f64 eps x))))) eps))) |
(* (pow eps 2) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4))))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps)) |
(* (pow eps 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (- (pow x 6) (* -1/4 (* eps (pow (+ (* 2 (pow x 2)) (pow x 2)) 2))))))) (* 1/2 (* (sqrt eps) (* (sqrt -1) (+ (* 2 (pow x 4)) (pow x 4)))))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (sqrt -1) (+ (* 2 (pow x 2)) (pow x 2))))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 2 binary64)) eps) #s(literal -1/4 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (pow.f64 eps #s(literal 3 binary64))) #s(literal -1 binary64) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 eps eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 44 | 356 |
| 0 | 76 | 346 |
| 1 | 347 | 281 |
| 2 | 3391 | 273 |
| 0 | 8360 | 269 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) |
#s(approx (- (* x x) eps) (neg.f64 eps)) |
(neg.f64 eps) |
(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))) |
#s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))) |
(fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps) |
(fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) |
(fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
(-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) |
(/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 eps (*.f64 x x)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) |
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) |
| Outputs |
|---|
(*.f64 (pow.f64 (/.f64 (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64))) |
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(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))) (/.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps))))) |
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(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
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(-.f64 (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (*.f64 (neg.f64 x) x) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))) |
(-.f64 (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (neg.f64 x) (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (fma.f64 x x (neg.f64 eps)) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(-.f64 x (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64))) #s(literal -1 binary64))) |
(+.f64 (/.f64 (*.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (/.f64 (fma.f64 x x (neg.f64 eps)) (fabs.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 (neg.f64 x) x) (fma.f64 x x (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps))) #s(literal -3 binary64)) (fma.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (/.f64 (fma.f64 x x (neg.f64 eps)) (fabs.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 (neg.f64 x) x) (fma.f64 x x (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal 2 binary64))))))) |
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(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))))) |
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps)))) (/.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps))))) |
(+.f64 (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(+.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x) |
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(+.f64 x (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(*.f64 #s(literal -1 binary64) (fma.f64 x x (neg.f64 eps))) |
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(neg.f64 (fma.f64 x x (neg.f64 eps))) |
(-.f64 #s(literal 0 binary64) (fma.f64 x x (neg.f64 eps))) |
(*.f64 (/.f64 (*.f64 x x) (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (fma.f64 x x (neg.f64 eps)))) |
(*.f64 (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) x) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)) (*.f64 x x)) |
(*.f64 (*.f64 (neg.f64 x) x) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) #s(literal -1 binary64))) |
(*.f64 (neg.f64 x) (/.f64 (neg.f64 x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))) |
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(*.f64 (*.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64))) |
(*.f64 x (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(pow.f64 (/.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64))))) |
(/.f64 (*.f64 x x) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(neg.f64 (/.f64 (*.f64 (neg.f64 x) x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(neg.f64 (/.f64 (*.f64 x x) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 x #s(literal -2 binary64)))) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x)))) |
(*.f64 (sqrt.f64 (*.f64 (neg.f64 x) x)) (sqrt.f64 (*.f64 (neg.f64 x) x))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (neg.f64 x))) |
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) |
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x))) |
(*.f64 (neg.f64 x) (neg.f64 x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 x x) |
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (neg.f64 x) #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 x #s(literal 2 binary64)) |
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(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
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(*.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (pow.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x) #s(literal -1 binary64))) |
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(literal -1 binary64))) |
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(pow.f64 (/.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps))))) |
(/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 (fma.f64 x x (neg.f64 eps)) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(neg.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))) |
(neg.f64 (*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
(neg.f64 (/.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (neg.f64 x)) (neg.f64 x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x)) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x)) |
(/.f64 (*.f64 (-.f64 (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 x x)) (fma.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 2 binary64)))) |
(/.f64 (*.f64 (*.f64 x x) (-.f64 (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))) |
(/.f64 (*.f64 (*.f64 x x) (+.f64 (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 2 binary64)))) |
(fma.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (sqrt.f64 (*.f64 (neg.f64 x) x)) (sqrt.f64 (*.f64 (neg.f64 x) x)) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (neg.f64 x)) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x) (*.f64 x x)) |
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(fma.f64 (*.f64 x x) (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (*.f64 (*.f64 x x) (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))))) |
(fma.f64 x x (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(+.f64 (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x)) (*.f64 x x)) |
(+.f64 (*.f64 (*.f64 x x) (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64)))) (*.f64 (*.f64 x x) #s(literal 1 binary64))) |
(+.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (*.f64 (*.f64 x x) (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))))) |
(+.f64 (*.f64 x x) (*.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64))) (*.f64 x x))) |
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (/.f64 (neg.f64 x) eps) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 eps x)) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) eps) |
(*.f64 (/.f64 eps x) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) |
(*.f64 #s(literal -1 binary64) (/.f64 eps (*.f64 (neg.f64 x) x))) |
(*.f64 (neg.f64 eps) (pow.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))) |
(*.f64 eps (pow.f64 x #s(literal -2 binary64))) |
(pow.f64 (/.f64 x (/.f64 eps x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)) |
(/.f64 (*.f64 eps #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 (/.f64 eps (neg.f64 x)) (neg.f64 x)) |
(/.f64 (neg.f64 (/.f64 eps x)) (neg.f64 x)) |
(/.f64 (neg.f64 (neg.f64 eps)) (*.f64 x x)) |
(/.f64 (/.f64 eps x) x) |
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) eps))) |
(/.f64 (neg.f64 eps) (*.f64 (neg.f64 x) x)) |
(/.f64 eps (*.f64 x x)) |
(neg.f64 (/.f64 eps (*.f64 (neg.f64 x) x))) |
(neg.f64 (*.f64 (neg.f64 eps) (pow.f64 x #s(literal -2 binary64)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) x)) (/.f64 eps (*.f64 (neg.f64 x) x))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) eps)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (neg.f64 x) #s(literal 1/8 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (neg.f64 x) eps) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (neg.f64 x) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 (neg.f64 x) #s(literal 1/8 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (/.f64 (neg.f64 x) (*.f64 #s(literal 1/8 binary64) eps)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) |
(*.f64 (/.f64 #s(literal 1/8 binary64) (neg.f64 x)) (/.f64 eps (neg.f64 x))) |
(*.f64 (/.f64 eps (neg.f64 x)) (/.f64 #s(literal 1/8 binary64) (neg.f64 x))) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal -1 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 x #s(literal -2 binary64)) (*.f64 #s(literal 1/8 binary64) eps)) |
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 eps x)) |
(*.f64 (*.f64 #s(literal -1/8 binary64) eps) (pow.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) (pow.f64 x #s(literal -1 binary64))) |
(*.f64 (*.f64 #s(literal 1/8 binary64) eps) (pow.f64 x #s(literal -2 binary64))) |
(*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x))) |
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)))) |
(*.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64)) |
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(*.f64 eps (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -2 binary64)))) |
(pow.f64 (/.f64 x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps)) #s(literal -1 binary64)) |
(/.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) eps) x) |
(/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) eps) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (neg.f64 x)) (neg.f64 x)) |
(/.f64 (neg.f64 (*.f64 #s(literal -1/8 binary64) eps)) (*.f64 x x)) |
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) (neg.f64 x)) |
(/.f64 (*.f64 #s(literal -1/8 binary64) eps) (*.f64 (neg.f64 x) x)) |
(/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) x) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) |
(/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x x) eps)) |
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps)))) |
(neg.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) eps) (*.f64 x x))) |
(neg.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 (neg.f64 x) x))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 x #s(literal 1/8 binary64)) (/.f64 x eps))) #s(literal -1 binary64))) |
(*.f64 (neg.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))))) |
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 1/4 binary64)) #s(literal 3 binary64))) |
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x eps) #s(literal -1 binary64)) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) #s(literal 3/2 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))) |
(*.f64 (pow.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/4 binary64)) (pow.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/4 binary64))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/2 binary64))) |
(*.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))) (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64)))) |
(*.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64)) (pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) #s(literal 3/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (fma.f64 x x (neg.f64 eps))) |
(*.f64 (fma.f64 x x (neg.f64 eps)) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(pow.f64 (exp.f64 #s(literal 3/2 binary64)) (log.f64 (fma.f64 x x (neg.f64 eps)))) |
(pow.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64)) #s(literal 3/4 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3 binary64)) |
(pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)) |
(/.f64 (pow.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (fma.f64 x x eps)) #s(literal 3 binary64))) |
(/.f64 (pow.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) |
(/.f64 (pow.f64 (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) |
(sqrt.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3 binary64))) |
(fabs.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) |
(fabs.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) |
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/4 binary64) (*.f64 (log.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/4 binary64)))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 3/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 3/4 binary64))) |
(exp.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) |
(+.f64 (cosh.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64)))) (sinh.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) |
Compiled 48 136 to 5 049 computations (89.5% saved)
27 alts after pruning (23 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 162 | 17 | 1 179 |
| Fresh | 6 | 6 | 12 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 3 | 3 |
| Total | 1 172 | 27 | 1 199 |
| Status | Accuracy | Program |
|---|---|---|
| 37.3% | (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (neg.f64 eps)) #s(literal 2 binary64)))) (-.f64 (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) (fma.f64 x x (neg.f64 eps))) (/.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps))))) | |
| ▶ | 64.4% | (fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
| 64.1% | (fma.f64 (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) x (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) | |
| 64.2% | (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) | |
| 51.0% | (/.f64 (fma.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 x x))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) | |
| 38.0% | (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 (-.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (neg.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64)) (*.f64 x x))) | |
| 38.0% | (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (/.f64 (-.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (neg.f64 (fma.f64 x x (neg.f64 eps))))))) | |
| 64.1% | (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| 59.0% | (/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) | |
| ▶ | 64.0% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
| ✓ | 64.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ▶ | 25.8% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
| ✓ | 59.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
| 7.1% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) | |
| ✓ | 3.4% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
| 62.6% | (*.f64 (/.f64 (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| 39.8% | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) | |
| 31.7% | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) eps)))) | |
| 22.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) (/.f64 eps (*.f64 x x)))) | |
| 37.1% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))) eps)) | |
| 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))) (*.f64 x x)) eps)) | |
| ▶ | 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
| ✓ | 41.9% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
| 41.8% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| 15.9% | #s(approx (- x (sqrt (- (* x x) eps))) (exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -1 binary64)))) | |
| ▶ | 4.2% | #s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
Compiled 1 518 to 778 computations (48.7% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) | |
| cost-diff | 0 | (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) | |
| cost-diff | 0 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) | |
| cost-diff | 10 | (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) | |
| cost-diff | 0 | (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) | |
| cost-diff | 1 | (neg.f64 (fma.f64 x x (neg.f64 eps))) | |
| cost-diff | 2 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) | |
| cost-diff | 7 | (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) | |
| cost-diff | 0 | (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) | |
| cost-diff | 0 | #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) | |
| cost-diff | 0 | (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) | |
| cost-diff | 0 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) | |
| cost-diff | 0 | #s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) | |
| cost-diff | 2 | (*.f64 x #s(literal 0 binary64)) | |
| cost-diff | 0 | (fma.f64 x x (neg.f64 eps)) | |
| cost-diff | 0 | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) | |
| cost-diff | 0 | (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| cost-diff | 25 | (fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 532 |
| 0 | 94 | 510 |
| 1 | 174 | 478 |
| 2 | 449 | 414 |
| 3 | 2023 | 414 |
| 0 | 8519 | 410 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
x |
(neg.f64 eps) |
eps |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(*.f64 x #s(literal 0 binary64)) |
x |
#s(literal 0 binary64) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) |
(-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) |
#s(literal 1 binary64) |
(/.f64 eps (*.f64 x x)) |
eps |
(*.f64 x x) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
#s(literal 1 binary64) |
(/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
x |
(neg.f64 eps) |
eps |
(fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) |
(neg.f64 (fma.f64 x x (neg.f64 eps))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) |
(/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) |
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) |
(*.f64 #s(literal 1/8 binary64) eps) |
#s(literal 1/8 binary64) |
eps |
x |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)) |
(/.f64 eps x) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(*.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
#s(literal 1/4 binary64) |
(*.f64 x x) |
| Outputs |
|---|
(fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 eps (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
x |
(neg.f64 eps) |
eps |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(*.f64 x x) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(literal 0 binary64)) |
(*.f64 x #s(literal 0 binary64)) |
#s(literal 0 binary64) |
x |
#s(literal 0 binary64) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
x |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) |
(-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) |
#s(literal 1 binary64) |
(/.f64 eps (*.f64 x x)) |
eps |
(*.f64 x x) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
(/.f64 eps (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
#s(literal 1 binary64) |
(/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) |
(/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) eps) |
(+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
x |
(neg.f64 eps) |
eps |
(fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) |
eps |
(neg.f64 (fma.f64 x x (neg.f64 eps))) |
(-.f64 eps (*.f64 x x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) (/.f64 eps (*.f64 x x)))) |
(*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) |
(*.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) (/.f64 eps (*.f64 x x))) |
(/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) |
(/.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) (*.f64 x x)) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 #s(literal -1/4 binary64) x) x (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64))) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) |
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) |
(pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) |
(*.f64 #s(literal 1/8 binary64) eps) |
#s(literal 1/8 binary64) |
eps |
x |
#s(literal 2 binary64) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)) |
(fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) |
(/.f64 eps x) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(*.f64 (*.f64 (/.f64 x (fma.f64 #s(literal -1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) #s(literal 1/4 binary64)) x) |
(*.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
#s(literal 1/4 binary64) |
(*.f64 x x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 1.2910511769785578 | (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) | |
| accuracy | 7.2599374902576415 | (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) | |
| accuracy | 7.874408237474952 | (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) | |
| accuracy | 38.45565858237369 | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) | |
| accuracy | 0.015625 | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) | |
| accuracy | 0.15234375 | (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) | |
| accuracy | 0.31640625 | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) | |
| accuracy | 22.660079549684827 | (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) | |
| accuracy | 0.0625 | (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) | |
| accuracy | 11.506461753981599 | (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) | |
| accuracy | 12.573345578872425 | (/.f64 eps (*.f64 x x)) | |
| accuracy | 22.739072900172633 | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) | |
| accuracy | 0.0 | (*.f64 x #s(literal 0 binary64)) | |
| accuracy | 61.3214111276013 | #s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) | |
| accuracy | 0.015625 | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) | |
| accuracy | 0.03125 | (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| accuracy | 5.760214467372504 | (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| accuracy | 22.749367547294458 | (fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
| 50.0ms | 162× | 0 | valid |
| 46.0ms | 76× | 1 | valid |
| 16.0ms | 18× | 2 | valid |
Compiled 1 029 to 104 computations (89.9% saved)
ival-div: 22.0ms (26.3% of total)ival-mult: 20.0ms (23.9% of total)adjust: 11.0ms (13.2% of total)ival-add: 10.0ms (12% of total)ival-sub: 6.0ms (7.2% of total)ival-neg: 5.0ms (6% of total)ival-sqrt: 5.0ms (6% of total)ival-pow2: 3.0ms (3.6% of total)exact: 1.0ms (1.2% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
(fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(*.f64 x #s(literal 0 binary64)) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
(neg.f64 (fma.f64 x x (neg.f64 eps))) |
(/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) |
(/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 eps (*.f64 x x)) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) |
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
| Outputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
1 |
(+ 1 (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2))))))))) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt eps) (* (sqrt -1) (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))))))))))))))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
0 |
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(+ (* -1 eps) (pow x 2)) |
eps |
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ eps (* -1 (pow x 2))) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)) |
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ x (sqrt -1)))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* x (+ (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(* 1/8 (/ eps x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) |
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(/ eps (pow x 2)) |
(* -1 (/ eps x)) |
(/ (+ (* -1 eps) (pow x 2)) x) |
(/ (+ (* 1/8 eps) (* (pow x 2) (+ 1/2 (* 2 (/ (pow x 2) eps))))) x) |
(/ (+ (* 1/8 eps) (* (pow x 2) (+ 1/2 (* (pow x 2) (+ (* 8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))))) x) |
(* 2 (/ (pow x 3) eps)) |
(* (pow x 3) (+ (* 8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps)))) |
(* (pow x 3) (+ (* (pow x 2) (+ (* 32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) |
(* (pow x 3) (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) |
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x) |
1/2 |
(+ 1/2 (+ (* -1/4 (/ eps (pow x 2))) (* 1/8 (/ eps (pow x 2))))) |
(+ 1/2 (+ (* -1/4 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))) |
(+ 1/2 (+ (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6))) (+ (* -1/4 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x) |
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ eps (pow x 2)) 1)) |
(* 2 (/ x eps)) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (+ (* -1/16 (/ (pow eps 2) (pow x 6))) (* 2 (/ 1 eps)))) (* 1/2 (/ 1 (pow x 2))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (* -1 (/ eps (pow x 2))))) |
(* -1/32 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* -1/32 (pow eps 2)) (* -1/128 (/ (pow eps 3) (pow x 2)))) (pow x 3)) |
(/ (+ (* -1/32 (pow eps 2)) (+ (* -1/128 (/ (pow eps 3) (pow x 2))) (* -1/512 (/ (pow eps 4) (pow x 4))))) (pow x 3)) |
(/ (+ (* -1/32 (pow eps 2)) (+ (* -1/128 (/ (pow eps 3) (pow x 2))) (+ (* -1/512 (/ (pow eps 4) (pow x 4))) (* -1/2048 (/ (pow eps 5) (pow x 6)))))) (pow x 3)) |
(* -1/2 x) |
(* x (- (* -1/8 (/ eps (pow x 2))) 1/2)) |
(* x (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2)))))) |
(* x (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))) |
(* 2 x) |
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))))))) |
(* -2 (/ (pow x 2) eps)) |
(* (pow x 2) (- (* 3/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))) |
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 3/2 (/ 1 (pow x 2)))))) (* 2 (/ 1 eps)))) |
(* (pow x 2) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/16 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 6))) (+ (* 1/4 (/ eps (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (* 3/2 (/ 1 (pow x 2)))))))))) (* 2 (/ 1 eps)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4))))))))) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x)) |
(* -1 (/ (- (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))) 1/2) x)) |
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2))) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) |
(* -1 (* x (- (/ eps (pow x 2)) 1))) |
(* -1 (/ (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2))) (pow x 3))) |
(* -1 (/ (+ (* 1/512 (/ (pow eps 4) (pow x 4))) (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2)))) (pow x 3))) |
(* -1 (/ (+ (* 1/2048 (/ (pow eps 5) (pow x 6))) (+ (* 1/512 (/ (pow eps 4) (pow x 4))) (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2))))) (pow x 3))) |
(* -1 (* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))) |
(* -1 (* x (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))) |
(* -1 (* x (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))))) |
(+ (* -1/2 x) (* 1/2 x)) |
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x)))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))) |
(+ 1/2 (* -1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))) |
(+ 1/2 (* eps (- (* eps (- (* -5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2)))))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(- eps (pow x 2)) |
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps) |
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps) |
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps) |
(- (* 1/8 (/ eps x)) (* -1/2 x)) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 1/8 (/ eps x)) (* 1/2 x)) |
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(+ x (* -1 (/ eps x))) |
(* (pow eps 2) (- (* -1/128 (/ eps (pow x 5))) (* 1/32 (/ 1 (pow x 3))))) |
(* (pow eps 2) (- (* eps (- (* -1/512 (/ eps (pow x 7))) (* 1/128 (/ 1 (pow x 5))))) (* 1/32 (/ 1 (pow x 3))))) |
(* (pow eps 2) (- (* eps (- (* eps (- (* -1/2048 (/ eps (pow x 9))) (* 1/512 (/ 1 (pow x 7))))) (* 1/128 (/ 1 (pow x 5))))) (* 1/32 (/ 1 (pow x 3))))) |
(+ (* -1/2 x) (* -1/8 (/ eps x))) |
(+ (* -1/2 x) (* eps (- (* -1/32 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* -1/2 x) (* eps (- (* eps (- (* -1/128 (/ eps (pow x 5))) (* 1/32 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) |
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) |
(+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))))) (* 1/2 (/ (pow x 2) (* eps (pow (sqrt -1) 2))))))) |
(+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 7))) (* (sqrt -1) (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow x 2) (* eps (pow (sqrt -1) 2))))))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) |
(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))) |
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps) |
(* eps (- (/ x eps) (/ 1 x))) |
(* eps (- (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 1/8 (/ 1 x))) (* -1/2 (/ x eps)))) |
(* eps (- (+ (* 8 (/ (pow x 5) (pow eps 3))) (* 1/8 (/ 1 x))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (* -1/2 (/ x eps))))) |
(/ (+ (* 2 (pow x 3)) (* 8 (/ (pow x 5) eps))) eps) |
(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (* 32 (/ (pow x 7) (pow eps 2))))) eps) |
(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (+ (* 32 (/ (pow x 7) (pow eps 2))) (* 128 (/ (pow x 9) (pow eps 3)))))) eps) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) |
(+ 1 (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* -1/2 (* eps (pow x 2)))) eps))) eps))) |
(+ 1 (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3))))))) (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1))))) eps)) (* -1/2 (* eps (pow x 2))))) eps))) eps))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) |
(* -1 (* eps (- (/ (pow x 2) eps) 1))) |
(* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))) |
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) |
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (* eps (+ (* -1 (/ x eps)) (/ 1 x)))) |
(* -1 (* eps (- (* -1 (/ (- (* 2 (/ (pow x 3) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -8 (/ (pow x 5) eps)) (* 2 (pow x 3))) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(* -1 (/ (+ (* -8 (/ (pow x 5) eps)) (* -2 (pow x 3))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* 8 (pow x 5)) (* 32 (/ (pow x 7) eps))) eps))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* -1 (/ (+ (* -128 (/ (pow x 9) eps)) (* -32 (pow x 7))) eps)) (* 8 (pow x 5))) eps))) eps)) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 36.0ms | eps | @ | inf | ((+ (* (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (neg (sqrt (+ (* x x) (neg eps))))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x))) (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (* x 0) (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (* (- 1 (/ eps (* x x))) x) x) (+ (* x x) (neg (+ (* x x) (neg eps)))) (/ 1 (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps)))))) (neg (+ (* x x) (neg eps))) (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (- x (sqrt (- (* x x) eps))) (* (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) eps) (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ eps (* x x)) (* (- 1 (/ eps (* x x))) x) (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) |
| 11.0ms | x | @ | inf | ((+ (* (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (neg (sqrt (+ (* x x) (neg eps))))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x))) (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (* x 0) (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (* (- 1 (/ eps (* x x))) x) x) (+ (* x x) (neg (+ (* x x) (neg eps)))) (/ 1 (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps)))))) (neg (+ (* x x) (neg eps))) (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (- x (sqrt (- (* x x) eps))) (* (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) eps) (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ eps (* x x)) (* (- 1 (/ eps (* x x))) x) (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) |
| 10.0ms | eps | @ | 0 | ((+ (* (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (neg (sqrt (+ (* x x) (neg eps))))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x))) (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (* x 0) (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (* (- 1 (/ eps (* x x))) x) x) (+ (* x x) (neg (+ (* x x) (neg eps)))) (/ 1 (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps)))))) (neg (+ (* x x) (neg eps))) (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (- x (sqrt (- (* x x) eps))) (* (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) eps) (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ eps (* x x)) (* (- 1 (/ eps (* x x))) x) (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) |
| 8.0ms | eps | @ | -inf | ((+ (* (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (neg (sqrt (+ (* x x) (neg eps))))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x))) (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (* x 0) (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (* (- 1 (/ eps (* x x))) x) x) (+ (* x x) (neg (+ (* x x) (neg eps)))) (/ 1 (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps)))))) (neg (+ (* x x) (neg eps))) (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (- x (sqrt (- (* x x) eps))) (* (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) eps) (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ eps (* x x)) (* (- 1 (/ eps (* x x))) x) (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) |
| 6.0ms | x | @ | -inf | ((+ (* (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (neg (sqrt (+ (* x x) (neg eps))))) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x))) (/ (sqrt (+ (* x x) (neg eps))) (+ (sqrt (+ (* x x) (neg eps))) x)) (sqrt (+ (* x x) (neg eps))) (+ (* x x) (neg eps)) (* x 0) (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* (* (- 1 (/ eps (* x x))) x) x) (+ (* x x) (neg (+ (* x x) (neg eps)))) (/ 1 (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps)))))) (neg (+ (* x x) (neg eps))) (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (- x (sqrt (- (* x x) eps))) (* (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) eps) (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ eps (* x x)) (* (- 1 (/ eps (* x x))) x) (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 1215 | 6099 |
| 0 | 4389 | 5811 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
1 |
(+ 1 (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2))))))))) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt eps) (* (sqrt -1) (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))))))))))))))) |
(* (sqrt eps) (sqrt -1)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(* -1 eps) |
(- (pow x 2) eps) |
0 |
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(+ (* -1 eps) (pow x 2)) |
eps |
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ eps (* -1 (pow x 2))) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)) |
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ x (sqrt -1)))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* x (+ (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(* 1/8 (/ eps x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) |
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) |
(/ eps (pow x 2)) |
(* -1 (/ eps x)) |
(/ (+ (* -1 eps) (pow x 2)) x) |
(/ (+ (* 1/8 eps) (* (pow x 2) (+ 1/2 (* 2 (/ (pow x 2) eps))))) x) |
(/ (+ (* 1/8 eps) (* (pow x 2) (+ 1/2 (* (pow x 2) (+ (* 8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps))))))) x) |
(* 2 (/ (pow x 3) eps)) |
(* (pow x 3) (+ (* 8 (/ (pow x 2) (pow eps 2))) (* 2 (/ 1 eps)))) |
(* (pow x 3) (+ (* (pow x 2) (+ (* 32 (/ (pow x 2) (pow eps 3))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) |
(* (pow x 3) (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 128 (/ (pow x 2) (pow eps 4))) (* 32 (/ 1 (pow eps 3))))) (* 8 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))) |
(/ (- (* -1 (- (* -1/2 eps) (* -1/8 eps))) (* -1/8 eps)) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 2))))) (+ (* -1/8 eps) (* -1/16 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4)))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* -1/128 (/ (pow eps 3) (pow x 4))))))) x) |
(/ (- (+ (* -1 (- (* -1/2 eps) (* -1/8 eps))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 2))) (+ (* -1/16 (/ (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/32 (/ (* (pow eps 3) (- (* -1/2 eps) (* -1/8 eps))) (pow x 6))) (+ (* -1/32 (/ (pow eps 2) (pow x 2))) (+ (* -1/64 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (* (pow eps 2) (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 6))) (+ (* 1/4 (/ (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))) (pow x 4))) (* 1/4 (/ (* eps (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2)))))))) (pow x 6))))))))))) (+ (* -1/8 eps) (+ (* -1/16 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 3) (pow x 4))) (+ (* -1/128 (/ (pow eps 4) (pow x 6))) (* 1/4 (/ (* eps (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3)))) (pow x 6))))))))) x) |
1/2 |
(+ 1/2 (+ (* -1/4 (/ eps (pow x 2))) (* 1/8 (/ eps (pow x 2))))) |
(+ 1/2 (+ (* -1/4 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))) |
(+ 1/2 (+ (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6))) (+ (* -1/4 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* -1/64 (/ (pow eps 3) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))))))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* 1/2 (/ eps x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x) |
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x) |
(* -1 (pow x 2)) |
(* (pow x 2) (- (/ eps (pow x 2)) 1)) |
(* 2 (/ x eps)) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1/8 (/ eps (pow x 4))) (+ (* -1/16 (/ (pow eps 2) (pow x 6))) (* 2 (/ 1 eps)))) (* 1/2 (/ 1 (pow x 2))))) |
(* 1/2 x) |
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2))))) |
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 1 (* -1 (/ eps (pow x 2))))) |
(* -1/32 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* -1/32 (pow eps 2)) (* -1/128 (/ (pow eps 3) (pow x 2)))) (pow x 3)) |
(/ (+ (* -1/32 (pow eps 2)) (+ (* -1/128 (/ (pow eps 3) (pow x 2))) (* -1/512 (/ (pow eps 4) (pow x 4))))) (pow x 3)) |
(/ (+ (* -1/32 (pow eps 2)) (+ (* -1/128 (/ (pow eps 3) (pow x 2))) (+ (* -1/512 (/ (pow eps 4) (pow x 4))) (* -1/2048 (/ (pow eps 5) (pow x 6)))))) (pow x 3)) |
(* -1/2 x) |
(* x (- (* -1/8 (/ eps (pow x 2))) 1/2)) |
(* x (- (* -1/32 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2)))))) |
(* x (- (* -1/128 (/ (pow eps 3) (pow x 6))) (+ 1/2 (+ (* 1/32 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))) |
(* 2 x) |
(* -1 (* x (- (* 5/8 (/ eps (pow x 2))) (+ 2 (* 1/8 (/ eps (pow x 2))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (* 5/8 (/ eps (pow x 2))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))))))) |
(* -1 (* x (- (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 5/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 5/8 eps))) (pow x 6))) (+ (* 5/16 (/ (pow eps 2) (pow x 4))) (+ (* 5/8 (/ eps (pow x 2))) (* 5/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))) (+ 2 (+ (* -1/4 (/ (* eps (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2))))) (pow x 6))) (+ (* -1/4 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 4))) (+ (* -1/8 (/ (* (pow eps 2) (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (+ (* 1/8 (/ eps (pow x 2))) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6))))))))))))) |
(* -2 (/ (pow x 2) eps)) |
(* (pow x 2) (- (* 3/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))) |
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 3/2 (/ 1 (pow x 2)))))) (* 2 (/ 1 eps)))) |
(* (pow x 2) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* -1/16 (/ (pow eps 2) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 6))) (+ (* 1/4 (/ eps (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1/4 eps) (* 1/8 eps))) (pow x 6))) (* 3/2 (/ 1 (pow x 2)))))))))) (* 2 (/ 1 eps)))) |
(* -1 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4))))))))) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x)) |
(* -1 (/ (- (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))) 1/2) x)) |
(* -1 (* x (- (* -1/8 (/ eps (pow x 2))) 1/2))) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps))))) |
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps))))))) |
(* -1 (* x (- (/ eps (pow x 2)) 1))) |
(* -1 (/ (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2))) (pow x 3))) |
(* -1 (/ (+ (* 1/512 (/ (pow eps 4) (pow x 4))) (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2)))) (pow x 3))) |
(* -1 (/ (+ (* 1/2048 (/ (pow eps 5) (pow x 6))) (+ (* 1/512 (/ (pow eps 4) (pow x 4))) (+ (* 1/128 (/ (pow eps 3) (pow x 2))) (* 1/32 (pow eps 2))))) (pow x 3))) |
(* -1 (* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))) |
(* -1 (* x (- (+ 1/2 (* 1/32 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))) |
(* -1 (* x (- (+ 1/2 (* 1/128 (/ (pow eps 3) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4))))))) |
(+ (* -1/2 x) (* 1/2 x)) |
(+ (* -1/2 x) (+ (* 1/2 x) (* 1/2 (/ eps x)))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))) |
(+ (* -1/2 x) (+ (* 1/2 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))) |
(+ 1/2 (* -1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* eps (- (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))) |
(+ 1/2 (* eps (- (* eps (- (* -5/128 (/ eps (pow x 6))) (* 1/16 (/ 1 (pow x 4))))) (* 1/8 (/ 1 (pow x 2)))))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(- eps (pow x 2)) |
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps) |
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps) |
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps) |
(- (* 1/8 (/ eps x)) (* -1/2 x)) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 1/8 (/ eps x)) (* 1/2 x)) |
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(+ x (* -1 (/ eps x))) |
(* (pow eps 2) (- (* -1/128 (/ eps (pow x 5))) (* 1/32 (/ 1 (pow x 3))))) |
(* (pow eps 2) (- (* eps (- (* -1/512 (/ eps (pow x 7))) (* 1/128 (/ 1 (pow x 5))))) (* 1/32 (/ 1 (pow x 3))))) |
(* (pow eps 2) (- (* eps (- (* eps (- (* -1/2048 (/ eps (pow x 9))) (* 1/512 (/ 1 (pow x 7))))) (* 1/128 (/ 1 (pow x 5))))) (* 1/32 (/ 1 (pow x 3))))) |
(+ (* -1/2 x) (* -1/8 (/ eps x))) |
(+ (* -1/2 x) (* eps (- (* -1/32 (/ eps (pow x 3))) (* 1/8 (/ 1 x))))) |
(+ (* -1/2 x) (* eps (- (* eps (- (* -1/128 (/ eps (pow x 5))) (* 1/32 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))) |
(+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) |
(- (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (+ (* -1 (/ (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))) eps)) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (* (pow eps 2) (pow (sqrt -1) 2)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (* eps (pow (sqrt -1) 2)))))) |
(+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))))) (* 1/2 (/ (pow x 2) (* eps (pow (sqrt -1) 2))))))) |
(+ 1 (+ (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 (pow eps 5))) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 7))) (* (sqrt -1) (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow x 2) (* eps (pow (sqrt -1) 2))))))))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) |
(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))) |
(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps) |
(* eps (- (/ x eps) (/ 1 x))) |
(* eps (- (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 1/8 (/ 1 x))) (* -1/2 (/ x eps)))) |
(* eps (- (+ (* 8 (/ (pow x 5) (pow eps 3))) (* 1/8 (/ 1 x))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (* -1/2 (/ x eps))))) |
(/ (+ (* 2 (pow x 3)) (* 8 (/ (pow x 5) eps))) eps) |
(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (* 32 (/ (pow x 7) (pow eps 2))))) eps) |
(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (+ (* 32 (/ (pow x 7) (pow eps 2))) (* 128 (/ (pow x 9) (pow eps 3)))))) eps) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (+ (* -1 (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))) (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* eps (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) |
(+ 1 (* (sqrt (/ 1 eps)) (* x (sqrt -1)))) |
(+ 1 (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* -1/2 (* eps (pow x 2)))) eps))) eps))) |
(+ 1 (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3))))))) (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1))))) eps)) (* -1/2 (* eps (pow x 2))))) eps))) eps))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) |
(* -1 (* eps (- (/ (pow x 2) eps) 1))) |
(* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))) |
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) |
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(* -1 (* eps (+ (* -1 (/ x eps)) (/ 1 x)))) |
(* -1 (* eps (- (* -1 (/ (- (* 2 (/ (pow x 3) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -8 (/ (pow x 5) eps)) (* 2 (pow x 3))) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(* -1 (/ (+ (* -8 (/ (pow x 5) eps)) (* -2 (pow x 3))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* 8 (pow x 5)) (* 32 (/ (pow x 7) eps))) eps))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* -1 (/ (+ (* -128 (/ (pow x 9) eps)) (* -32 (pow x 7))) eps)) (* 8 (pow x 5))) eps))) eps)) |
| Outputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (/.f64 (neg.f64 x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) x (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
(+ (* x (- (* x (+ (* -1 (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (+ (* x (- (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) #s(literal -1 binary64) (fma.f64 (-.f64 (fma.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) (/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps))) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* -1 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))) |
(fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1 binary64) #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64))) #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps))) x (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) |
(+ 1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (+ (* -1 (* (sqrt eps) (* (sqrt -1) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))))) (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt eps) (* (sqrt -1) (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1))))))))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (fma.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 eps eps) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) #s(literal -1/2 binary64))) x (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)) eps)))) x (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))))) |
(fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5))))))))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))))) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(* -1 eps) |
(neg.f64 eps) |
(- (pow x 2) eps) |
(fma.f64 x x (neg.f64 eps)) |
0 |
#s(literal 0 binary64) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x #s(literal 1 binary64)) x (*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 eps) (pow x 2)) |
(fma.f64 x x (neg.f64 eps)) |
eps |
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (neg.f64 x) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 (fma.f64 (fma.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (neg.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64)))) x (neg.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))) |
(+ eps (* -1 (pow x 2))) |
(-.f64 eps (*.f64 x x)) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)) |
(+ (* x (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ x (sqrt -1)))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) eps)) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* x (+ (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))) (/ 1 eps))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
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(/ eps (pow x 2)) |
(/.f64 eps (*.f64 x x)) |
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(* 2 (/ (pow x 3) eps)) |
(*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 2 binary64)) |
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1/2 |
#s(literal 1/2 binary64) |
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x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) x) |
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(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
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(pow x 2) |
(*.f64 x x) |
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(* 1/2 (/ eps x)) |
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(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
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(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) eps (neg.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/16 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(* -1 (pow x 2)) |
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
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(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) eps) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
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(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
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(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
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(* eps (+ 1 (* -1 (/ (pow x 2) eps)))) |
(*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64)) eps) |
(+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
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(* eps (+ (* 1/2 (/ x eps)) (* 1/8 (/ 1 x)))) |
(*.f64 (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) eps) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 eps eps)) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) |
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(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps) |
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(* eps (- (/ x eps) (/ 1 x))) |
(*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1 binary64) x)) eps) |
(* eps (- (+ (* 2 (/ (pow x 3) (pow eps 2))) (* 1/8 (/ 1 x))) (* -1/2 (/ x eps)))) |
(*.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 eps eps)) #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 (/.f64 x eps) #s(literal -1/2 binary64))) eps) |
(* eps (- (+ (* 8 (/ (pow x 5) (pow eps 3))) (* 1/8 (/ 1 x))) (+ (* -2 (/ (pow x 3) (pow eps 2))) (* -1/2 (/ x eps))))) |
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(/ (+ (* 2 (pow x 3)) (* 8 (/ (pow x 5) eps))) eps) |
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(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (* 32 (/ (pow x 7) (pow eps 2))))) eps) |
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(/ (+ (* 2 (pow x 3)) (+ (* 8 (/ (pow x 5) eps)) (+ (* 32 (/ (pow x 7) (pow eps 2))) (* 128 (/ (pow x 9) (pow eps 3)))))) eps) |
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(fma.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) x) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x x) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))))) eps))) eps) #s(literal -1 binary64) #s(literal 1 binary64)) |
(+ 1 (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (sqrt -1)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3))))))) (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 3) (sqrt -1))))) eps)) (* -1/2 (* eps (pow x 2))))) eps))) eps))) |
(fma.f64 (/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (sqrt.f64 eps) x) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (*.f64 x x) (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 3 binary64)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))))))))) eps)))) eps))) eps) #s(literal -1 binary64) #s(literal 1 binary64)) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(*.f64 (neg.f64 eps) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64) #s(literal 1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps) #s(literal -1 binary64) x) eps)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(-.f64 x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (neg.f64 eps) x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 1/2 binary64) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps)) (*.f64 eps x)) eps))) |
(* -1 (* eps (- (/ (pow x 2) eps) 1))) |
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))) |
(* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) |
(neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)) |
(-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x)) eps))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ (* -1 x) (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps))) |
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (*.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) eps) #s(literal -1 binary64) (neg.f64 x)) eps))) |
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x))))) |
(*.f64 (neg.f64 eps) (-.f64 (*.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))) |
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) |
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (neg.f64 (pow.f64 x #s(literal 3 binary64)))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(neg.f64 (/.f64 (fma.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)) #s(literal -1/2 binary64) (*.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps))) eps))) eps)) |
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps)) |
(neg.f64 (/.f64 (fma.f64 (*.f64 (sqrt.f64 eps) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 #s(literal -1 binary64) (-.f64 (/.f64 (-.f64 (fma.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) eps) #s(literal -1/2 binary64) (neg.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) x) (*.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 (*.f64 (*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) eps) (*.f64 (pow.f64 x #s(literal 3 binary64)) eps))) eps))) eps)) |
(* -1 (* eps (+ (* -1 (/ x eps)) (/ 1 x)))) |
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))) |
(* -1 (* eps (- (* -1 (/ (- (* 2 (/ (pow x 3) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) eps) #s(literal 2 binary64) (*.f64 #s(literal 1/2 binary64) x)) eps)) (/.f64 #s(literal 1/8 binary64) x))) |
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (* -8 (/ (pow x 5) eps)) (* 2 (pow x 3))) eps)) (* -1/2 x)) eps)) (* 1/8 (/ 1 x))))) |
(*.f64 (neg.f64 eps) (-.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) eps) (*.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) x)) eps)) (/.f64 #s(literal 1/8 binary64) x))) |
(* -1 (/ (+ (* -8 (/ (pow x 5) eps)) (* -2 (pow x 3))) eps)) |
(neg.f64 (/.f64 (fma.f64 #s(literal -8 binary64) (/.f64 (pow.f64 x #s(literal 5 binary64)) eps) (*.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* 8 (pow x 5)) (* 32 (/ (pow x 7) eps))) eps))) eps)) |
(neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 7 binary64)) eps) #s(literal 32 binary64) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 8 binary64))) eps))) eps)) |
(* -1 (/ (+ (* -2 (pow x 3)) (* -1 (/ (+ (* -1 (/ (+ (* -128 (/ (pow x 9) eps)) (* -32 (pow x 7))) eps)) (* 8 (pow x 5))) eps))) eps)) |
(neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 8 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal -32 binary64) (pow.f64 x #s(literal 7 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) eps) #s(literal -128 binary64))) eps))) eps))) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 428 |
| 0 | 94 | 377 |
| 1 | 392 | 259 |
| 2 | 3731 | 256 |
| 0 | 8463 | 252 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
(fma.f64 x x (neg.f64 eps)) |
(*.f64 x #s(literal 0 binary64)) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
(neg.f64 (fma.f64 x x (neg.f64 eps))) |
(/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps))))) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
(*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps) |
(/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) |
(/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(/.f64 eps (*.f64 x x)) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) |
(/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) |
| Outputs |
|---|
(*.f64 (pow.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (pow.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) #s(literal -1 binary64))) |
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(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x (neg.f64 eps))) (fma.f64 (neg.f64 x) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
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(fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
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(-.f64 (/.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (*.f64 (neg.f64 x) x) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) #s(literal -1 binary64)))) |
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(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 (neg.f64 (pow.f64 (+.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(-.f64 x (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(fabs.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) #s(literal -1 binary64))) |
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(+.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) x) |
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(*.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (fma.f64 (neg.f64 x) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
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(*.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)))) |
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(fma.f64 (neg.f64 x) x eps) |
(fma.f64 #s(literal -1 binary64) (*.f64 x x) eps) |
(fma.f64 #s(literal -1 binary64) (neg.f64 eps) (*.f64 (neg.f64 x) x)) |
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x)) |
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (neg.f64 eps)) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 (neg.f64 x) x)) |
(fma.f64 (*.f64 x x) #s(literal -1 binary64) (*.f64 (neg.f64 eps) #s(literal -1 binary64))) |
(fma.f64 (neg.f64 eps) #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -1 binary64))) |
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x)) |
(fma.f64 x (neg.f64 x) eps) |
(fma.f64 x x (neg.f64 eps)) |
(sqrt.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) |
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps) |
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (/.f64 (*.f64 eps eps) (fma.f64 x x eps))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))) |
(-.f64 (*.f64 (neg.f64 x) x) (neg.f64 eps)) |
(-.f64 #s(literal 0 binary64) (fma.f64 x x (neg.f64 eps))) |
(-.f64 (*.f64 x x) eps) |
(-.f64 (neg.f64 eps) (*.f64 (neg.f64 x) x)) |
(-.f64 eps (*.f64 x x)) |
(fabs.f64 (-.f64 eps (fma.f64 x x #s(literal 0 binary64)))) |
(fabs.f64 (-.f64 (/.f64 (*.f64 eps eps) (fma.f64 x x eps)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)))) |
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(fabs.f64 (-.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 0 binary64))) |
(fabs.f64 (fma.f64 x x (neg.f64 eps))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (neg.f64 eps))) #s(literal 1 binary64))) |
(exp.f64 (log.f64 (fma.f64 x x (neg.f64 eps)))) |
(+.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)) (*.f64 (neg.f64 eps) #s(literal -1 binary64))) |
(+.f64 (*.f64 (neg.f64 eps) #s(literal -1 binary64)) (*.f64 (*.f64 x x) #s(literal -1 binary64))) |
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(+.f64 (*.f64 (neg.f64 x) x) eps) |
(+.f64 #s(literal 0 binary64) (fma.f64 x x (neg.f64 eps))) |
(+.f64 (*.f64 x x) (neg.f64 eps)) |
(+.f64 (neg.f64 eps) (*.f64 x x)) |
(+.f64 eps (*.f64 (neg.f64 x) x)) |
#s(literal 0 binary64) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(literal 0 binary64)) |
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(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x)) |
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(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x) (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 3/2 binary64))))) |
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 x))) (sqrt.f64 (neg.f64 (neg.f64 x))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x) |
(fma.f64 #s(literal 1 binary64) x (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x)) (/.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x))) |
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) (/.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) x #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(+.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) x) |
(+.f64 x (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(*.f64 (fabs.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/4 binary64)))) |
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) (sqrt.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/4 binary64))) |
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) #s(literal 1 binary64)) |
(pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) |
(fabs.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(exp.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) (sinh.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))))) |
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))))) |
(*.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(pow.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) #s(literal 2 binary64)) |
(pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 1 binary64)) |
#s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) |
(sqrt.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 2 binary64))) |
(fabs.f64 (neg.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
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(exp.f64 (*.f64 (log.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)) #s(literal 2 binary64))) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (log.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x))) #s(literal 1 binary64))) |
(exp.f64 (log.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (neg.f64 x)) (neg.f64 x)) |
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x) |
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x)) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(*.f64 x (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x)) |
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(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 3 binary64))) (*.f64 x x)) (fma.f64 (/.f64 eps (*.f64 x x)) (fma.f64 (pow.f64 x #s(literal -2 binary64)) eps #s(literal 1 binary64)) #s(literal 1 binary64))) |
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(*.f64 (pow.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) |
(*.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 x x)) (pow.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))) #s(literal -1 binary64))) |
(*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64))) |
(*.f64 #s(literal 1/4 binary64) (*.f64 x (/.f64 x (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))))) |
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 x (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))))) |
(*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)))) |
(*.f64 (*.f64 x x) (*.f64 #s(literal 1/4 binary64) (pow.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64)))) |
(pow.f64 (/.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64))) #s(literal -1 binary64)) |
(/.f64 (neg.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 x x))) (neg.f64 (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))))) |
(/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))) |
(/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 x x)) (neg.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64))))) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64)))) |
(neg.f64 (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 x x)) (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal -1/2 binary64) x)) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal -2 binary64)))) #s(literal -1 binary64))) |
Compiled 76 299 to 6 705 computations (91.2% saved)
18 alts after pruning (13 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 839 | 8 | 1 847 |
| Fresh | 13 | 5 | 18 |
| Picked | 4 | 1 | 5 |
| Done | 0 | 4 | 4 |
| Total | 1 856 | 18 | 1 874 |
| Status | Accuracy | Program |
|---|---|---|
| 64.2% | (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) | |
| 64.1% | (/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) | |
| 59.0% | (/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) | |
| 63.9% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))) | |
| 99.3% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps))) | |
| 64.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) | |
| 42.6% | (/.f64 #s(literal 1 binary64) #s(approx (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x)) eps))) | |
| ✓ | 64.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ✓ | 25.8% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
| 64.5% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 #s(approx (* (- 1 (/ eps (* x x))) x) (/.f64 (fma.f64 x x (neg.f64 eps)) x)) x)))) | |
| ✓ | 59.4% | (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
| 7.1% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) | |
| ✓ | 3.4% | (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
| 39.8% | #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) | |
| 39.7% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 eps (*.f64 x x)))) | |
| ✓ | 41.9% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
| 41.8% | #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) | |
| 4.2% | #s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
Compiled 1 810 to 540 computations (70.2% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 #s(approx (* (- 1 (/ eps (* x x))) x) (/.f64 (fma.f64 x x (neg.f64 eps)) x)) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) (/.f64 eps (*.f64 x x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 eps (*.f64 x x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x)) eps))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) (*.f64 x x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 x x (*.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x))) (*.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 x x))) eps)) |
(*.f64 (/.f64 (fma.f64 x x (neg.f64 (fma.f64 x x (neg.f64 eps)))) (-.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x))) (-.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
(fma.f64 (/.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) x (/.f64 (neg.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(fma.f64 (/.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (/.f64 (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
(/.f64 (fma.f64 (fma.f64 x x (neg.f64 eps)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (*.f64 x x))) (*.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (*.f64 (*.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64)) eps))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x)) eps))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x) #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps x) (*.f64 #s(literal -1/2 binary64) x)))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))) eps)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (fma.f64 x x (neg.f64 eps)))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))))) |
#s(approx (- x (sqrt (- (* x x) eps))) (exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal -1 binary64)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x x (/.f64 (-.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (neg.f64 (fma.f64 x x (neg.f64 eps))))))) |
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 (-.f64 (*.f64 (fma.f64 x x (neg.f64 eps)) (*.f64 x x)) (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x (neg.f64 (fma.f64 x x (neg.f64 eps)))) #s(literal -1 binary64)) (*.f64 x x))) |
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (neg.f64 eps)) #s(literal 2 binary64)))) (-.f64 (*.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) (fma.f64 x x (neg.f64 eps))) (/.f64 (neg.f64 (pow.f64 (fma.f64 x x (neg.f64 eps)) #s(literal 3/2 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 x x (neg.f64 eps))))) |
(-.f64 x (sqrt.f64 (/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))))))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps))) |
3 calls:
| 18.0ms | eps |
| 14.0ms | x |
| 14.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.3% | 1 | x |
| 99.3% | 1 | eps |
| 99.3% | 1 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 10 computations (0% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 #s(approx (* (- 1 (/ eps (* x x))) x) (/.f64 (fma.f64 x x (neg.f64 eps)) x)) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) x) x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) (/.f64 eps (*.f64 x x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) x)) (/.f64 eps (*.f64 x x)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))))) |
(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (sqrt (+ (* x x) (neg eps))) x) (+ (* x x) (neg (+ (* x x) (neg eps))))) (/.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (*.f64 #s(literal 2 binary64) x)) eps))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x))))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))))) |
(/.f64 (-.f64 (*.f64 x x) (fma.f64 x x (neg.f64 eps))) (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) (*.f64 x x)) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) eps) (*.f64 x x)) x (*.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (fma.f64 (neg.f64 x) x (fma.f64 x x eps)))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)) |
3 calls:
| 8.0ms | eps |
| 8.0ms | x |
| 8.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 90.2% | 2 | x |
| 81.5% | 2 | eps |
| 98.7% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 10 computations (0% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x x) #s(approx (- (* x x) eps) (neg.f64 eps))) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) x)) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 #s(approx (* (- 1 (/ eps (* x x))) x) (/.f64 (fma.f64 x x (neg.f64 eps)) x)) x)))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
1 calls:
| 4.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
1 calls:
| 3.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))) |
1 calls:
| 3.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 96.0% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (/ (- (/ (pow (/ (* 1/8 eps) x) 2) (+ (* 1/8 (/ eps x)) (* -1/2 x))) (/ (* 1/4 (* x x)) (+ (* 1/8 (/ eps x)) (* -1/2 x)))) (* x x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)) |
1 calls:
| 3.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 95.8% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 8 to 6 computations (25% saved)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
3 calls:
| 21.0ms | x |
| 2.0ms | eps |
| 2.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 59.4% | 1 | eps |
| 59.4% | 1 | x |
| 59.4% | 1 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 10 computations (0% saved)
Total -0.8b remaining (-1.3%)
Threshold costs -0.8b (-1.3%)
| Inputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) (*.f64 x #s(literal 0 binary64))) |
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))) |
| Outputs |
|---|
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
3 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.2% | 1 | eps |
| 4.2% | 1 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 4.2% | 1 | x |
Compiled 10 to 10 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -6.9519756074022525e-155 | 0.0 |
Compiled 11 to 11 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -6.9519756074022525e-155 | 0.0 |
Compiled 11 to 11 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -6.9519756074022525e-155 | 0.0 |
Compiled 11 to 11 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -6.9519756074022525e-155 | 0.0 |
Compiled 11 to 11 computations (0% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -6.9519756074022525e-155 | 0.0 |
Compiled 11 to 11 computations (0% saved)
| 1× | egg-herbie |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 69 | 266 |
| 1 | 139 | 251 |
| 2 | 362 | 247 |
| 3 | 1580 | 239 |
| 4 | 6246 | 239 |
| 1× | node limit |
| Inputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) (+.f64 (-.f64 (*.f64 x x) (*.f64 x x)) eps))) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 x x (neg.f64 eps))) x) eps) #s(literal -1 binary64)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (*.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -3019169939857233/60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390325231616 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 #s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps))) |
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) |
#s(approx (+ (/ (* x x) (+ (sqrt (+ (* x x) (neg eps))) x)) (/ (* (neg (sqrt (+ (* x x) (neg eps)))) (sqrt (+ (* x x) (neg eps)))) (+ (sqrt (+ (* x x) (neg eps))) x))) #s(approx (* x 0) #s(literal 0 binary64))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 56 | 428 |
| 0 | 94 | 377 |
| 1 | 392 | 259 |
| 2 | 3731 | 256 |
| 0 | 8463 | 252 |
| 0 | 32 | 169 |
| 0 | 53 | 169 |
| 1 | 218 | 161 |
| 2 | 1685 | 161 |
| 0 | 8852 | 161 |
| 0 | 6 | 22 |
| 0 | 10 | 22 |
| 1 | 47 | 22 |
| 2 | 378 | 22 |
| 3 | 4841 | 22 |
| 0 | 9913 | 19 |
| 0 | 296 | 1303 |
| 0 | 965 | 1243 |
| 0 | 1522 | 10312 |
| 0 | 5489 | 9809 |
| 0 | 257 | 1067 |
| 0 | 842 | 1017 |
| 0 | 44 | 356 |
| 0 | 76 | 346 |
| 1 | 347 | 281 |
| 2 | 3391 | 273 |
| 0 | 8360 | 269 |
| 0 | 1215 | 6099 |
| 0 | 4389 | 5811 |
| 1× | fuel |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
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| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 530 to 222 computations (58.1% saved)
Compiled 582 to 166 computations (71.5% saved)
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