
Time bar (total: 10.8s)
| 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)
| 640.0ms | 4 936× | 0 | valid |
| 504.0ms | 2 722× | 1 | valid |
| 143.0ms | 598× | 2 | valid |
| 11.0ms | 170× | 0 | invalid |
ival-sub: 204.0ms (29.9% of total)ival-sqrt: 175.0ms (25.6% of total)ival-mult: 104.0ms (15.2% of total)ival-<=: 99.0ms (14.5% of total)adjust: 61.0ms (8.9% of total)ival-and: 21.0ms (3.1% of total)exact: 17.0ms (2.5% of total)ival-assert: 3.0ms (0.4% of total)| 2× | egg-herbie |
| 176× | accelerator-lowering-fma.f32 |
| 176× | accelerator-lowering-fma.f64 |
| 148× | sub-neg |
| 104× | *-lowering-*.f32 |
| 104× | *-lowering-*.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 54 |
| 1 | 49 | 52 |
| 2 | 125 | 49 |
| 3 | 290 | 49 |
| 4 | 522 | 49 |
| 5 | 609 | 49 |
| 6 | 617 | 49 |
| 0 | 6 | 8 |
| 1 | 10 | 8 |
| 2 | 18 | 8 |
| 3 | 30 | 8 |
| 4 | 48 | 8 |
| 5 | 90 | 8 |
| 6 | 157 | 8 |
| 7 | 203 | 8 |
| 8 | 285 | 8 |
| 9 | 315 | 8 |
| 10 | 331 | 8 |
| 0 | 331 | 8 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(- x (sqrt (- (* x x) eps))) |
| Outputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Inputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps))) |
(- x (sqrt (- (* x x) (neg eps)))) |
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))) |
(neg (- x (sqrt (- (* x x) (neg eps))))) |
(- eps (sqrt (- (* eps eps) x))) |
| Outputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps))) |
(- (neg x) (sqrt (- (* x x) eps))) |
(- x (sqrt (- (* x x) (neg eps)))) |
(- x (sqrt (+ (* x x) eps))) |
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))) |
(+ x (sqrt (- (* x x) eps))) |
(neg (- x (sqrt (- (* x x) (neg eps))))) |
(- (sqrt (+ (* x x) eps)) x) |
(- eps (sqrt (- (* eps eps) x))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 104 | 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 | 104 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 104 | 0 |
| - | 0 | 152 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 104 | 0 | 0 |
| - | 0 | 0 | 152 |
| number | freq |
|---|---|
| 0 | 152 |
| 1 | 104 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 43.0ms | 170× | 1 | valid |
| 16.0ms | 308× | 0 | valid |
| 5.0ms | 34× | 2 | valid |
Compiled 72 to 28 computations (61.1% saved)
adjust: 27.0ms (56% of total)ival-sub: 7.0ms (14.5% of total)ival-sqrt: 7.0ms (14.5% of total)ival-mult: 5.0ms (10.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.5% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% 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))) |
| 176× | accelerator-lowering-fma.f32 |
| 176× | accelerator-lowering-fma.f64 |
| 104× | *-lowering-*.f32 |
| 104× | *-lowering-*.f64 |
| 64× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 24 |
| 1 | 10 | 24 |
| 2 | 18 | 24 |
| 3 | 30 | 24 |
| 4 | 48 | 24 |
| 5 | 90 | 24 |
| 6 | 157 | 24 |
| 7 | 203 | 24 |
| 8 | 285 | 24 |
| 9 | 315 | 24 |
| 10 | 331 | 24 |
| 0 | 331 | 24 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(- x (sqrt (- (* x x) eps))) |
x |
(sqrt (- (* x x) eps)) |
(- (* x x) eps) |
(* x x) |
eps |
| Outputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(sqrt (- (* x x) eps)) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(- (* x x) eps) |
(-.f64 (*.f64 x x) eps) |
(* x x) |
(*.f64 x x) |
eps |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 x x) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (-.f64 (*.f64 x x) eps)) |
| ✓ | accuracy | 62.5% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 10.0ms | 85× | 1 | valid |
| 8.0ms | 154× | 0 | valid |
| 3.0ms | 17× | 2 | valid |
Compiled 26 to 8 computations (69.2% saved)
ival-mult: 4.0ms (33.6% of total)ival-sub: 3.0ms (25.2% of total)ival-sqrt: 3.0ms (25.2% of total)adjust: 2.0ms (16.8% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- x (sqrt (- (* x x) eps)))> |
#<alt (sqrt (- (* x x) eps))> |
#<alt (- (* x x) eps)> |
#<alt (* x x)> |
| Outputs |
|---|
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* 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)))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)> |
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)> |
#<alt (/ (- (* 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)> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))> |
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))> |
#<alt (* -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))))))))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))> |
#<alt (* 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))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -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)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))> |
#<alt (+ (* (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)))))))> |
#<alt (+ (* (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)))))))))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* -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))))))))> |
#<alt x> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))> |
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* 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))))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -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))))))> |
#<alt (* -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)))))))> |
#<alt (* -1 eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (* -1 eps)> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* -1 eps)> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
21 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | eps | @ | 0 | (sqrt (- (* x x) eps)) |
| 1.0ms | eps | @ | inf | (- x (sqrt (- (* x x) eps))) |
| 1.0ms | x | @ | inf | (- x (sqrt (- (* x x) eps))) |
| 1.0ms | eps | @ | 0 | (- x (sqrt (- (* x x) eps))) |
| 1.0ms | x | @ | 0 | (- x (sqrt (- (* x x) eps))) |
| 1× | batch-egg-rewrite |
| 4 146× | accelerator-lowering-fma.f32 |
| 4 146× | accelerator-lowering-fma.f64 |
| 3 310× | *-lowering-*.f32 |
| 3 310× | *-lowering-*.f64 |
| 2 470× | pow-lowering-pow.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 22 |
| 1 | 38 | 22 |
| 2 | 306 | 22 |
| 3 | 3595 | 22 |
| 0 | 8551 | 22 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(sqrt (- (* x x) eps)) |
(- (* x x) eps) |
(* x x) |
| Outputs |
|---|
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) |
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))) |
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) #s(literal -1 binary64))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps)))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)) |
(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))) |
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))))) |
(fma.f64 (*.f64 x x) (/.f64 x (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))) |
(fma.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64) x) |
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) |
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (-.f64 (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (*.f64 x x)) eps))))) |
(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) x) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) |
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) |
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(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 x x eps))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (fma.f64 x x eps))) |
(/.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) #s(literal 1 binary64)) (fma.f64 x x eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (neg.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) |
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (neg.f64 (neg.f64 (fma.f64 x x eps)))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) #s(literal 3 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps)))) (*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) (fma.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (fma.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (*.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))))) |
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (fma.f64 x x eps))) (/.f64 (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps))) (*.f64 (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (fma.f64 x x eps)))) (fma.f64 (*.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps))) (*.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps))) (fma.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) (*.f64 eps (/.f64 eps (fma.f64 x x eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps))) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 (neg.f64 eps) (*.f64 x x))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) (*.f64 (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) (fma.f64 (*.f64 x x) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (/.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) |
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps))) (*.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps)))) (*.f64 (*.f64 eps (/.f64 eps (fma.f64 x x eps))) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))) (fma.f64 (*.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))) |
(/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(/.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (sqrt.f64 (fma.f64 x x eps))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(/.f64 (*.f64 (sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (sqrt.f64 (fma.f64 x x eps))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 eps eps) (*.f64 (*.f64 eps eps) (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) |
(/.f64 (*.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 (*.f64 eps eps) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps eps))) |
(/.f64 (exp.f64 (log.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (exp.f64 (log.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) |
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (log.f64 (fma.f64 x x eps)))) |
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))) |
(/.f64 (exp.f64 (log.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x x eps))))) |
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 4 binary64)) |
(pow.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) #s(literal 1/4 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 (-.f64 (*.f64 x x) eps)))) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps)))) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (-.f64 (*.f64 x x) eps))) |
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(*.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) |
(*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))) |
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(*.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) |
(*.f64 (fma.f64 x x eps) (*.f64 (-.f64 (*.f64 x x) eps) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)))) |
(*.f64 (fma.f64 x x eps) (/.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) |
(*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))))) |
(*.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps)))) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (*.f64 x x) eps))) |
(*.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(*.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (-.f64 eps (*.f64 x x))))) |
(*.f64 (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)) (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps))) (-.f64 (*.f64 x x) eps)) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (fma.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (fma.f64 x x eps))))) (fma.f64 (*.f64 eps (fma.f64 x x eps)) (-.f64 (*.f64 eps (fma.f64 x x eps)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (fma.f64 x x eps))))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (fma.f64 x x eps)))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x x eps))))))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (-.f64 (*.f64 x x) eps) (fma.f64 x x eps)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x eps))))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x)) |
(*.f64 x x) |
| 1× | egg-herbie |
| 11 222× | accelerator-lowering-fma.f32 |
| 11 222× | accelerator-lowering-fma.f64 |
| 4 906× | *-lowering-*.f32 |
| 4 906× | *-lowering-*.f64 |
| 3 416× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 257 | 1257 |
| 1 | 784 | 1238 |
| 2 | 2594 | 1200 |
| 3 | 6944 | 1197 |
| 0 | 8091 | 1129 |
| 1× | iter limit |
| 1× | node limit |
| 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))) |
(* 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) |
(* 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)))))))) |
(* 1/2 (/ eps 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)))) |
(* -1 (* (sqrt eps) (sqrt -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))))) |
(* (sqrt eps) (sqrt -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))))) |
(* (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))))))))) |
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))))))) |
(* -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)))))))) |
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))))) |
(* (sqrt 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)))))) |
(* -1 (* (sqrt 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) |
(- (pow x 2) eps) |
(- (pow x 2) eps) |
(- (pow x 2) eps) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(pow x 2) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(* -1 eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* -1 eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x) x) (*.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))) |
(-.f64 (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) x) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) 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 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #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) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) #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 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) (fma.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -2 binary64)))) (neg.f64 x)) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 eps (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x))) x) eps))) |
(* -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 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 eps) (*.f64 x x))))) eps)) eps))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (*.f64 x x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* (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 (*.f64 x x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* (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 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(fma.f64 (*.f64 eps #s(literal -1/2 binary64)) (/.f64 x (*.f64 x x)) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(fma.f64 x (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) 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))))))) |
(fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 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)))))))) |
(neg.f64 (fma.f64 x (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps #s(literal -1/8 binary64)) (/.f64 eps (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) x)) |
x |
(+ x (* -1/2 (/ eps x))) |
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)) x) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(fma.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)) x) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64))))) |
(* 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 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.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 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (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))))) |
(neg.f64 (*.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) |
(* -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 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (neg.f64 eps)) |
(* -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))))))) |
(neg.f64 (*.f64 eps (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) |
(* -1 eps) |
(neg.f64 eps) |
(- (pow x 2) eps) |
(-.f64 (*.f64 x x) eps) |
(- (pow x 2) eps) |
(-.f64 (*.f64 x x) eps) |
(- (pow x 2) eps) |
(-.f64 (*.f64 x x) eps) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x (neg.f64 x))) x)) |
(pow x 2) |
(*.f64 x x) |
(+ (* -1 eps) (pow x 2)) |
(-.f64 (*.f64 x x) eps) |
(+ (* -1 eps) (pow x 2)) |
(-.f64 (*.f64 x x) eps) |
(+ (* -1 eps) (pow x 2)) |
(-.f64 (*.f64 x x) eps) |
(* -1 eps) |
(neg.f64 eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(* -1 eps) |
(neg.f64 eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
(pow x 2) |
(*.f64 x x) |
Compiled 9 601 to 1 050 computations (89.1% saved)
10 alts after pruning (10 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 298 | 10 | 308 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 299 | 10 | 309 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 41.2% | (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
| 32.9% | (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) x) | |
| 43.7% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) | |
| 62.0% | (-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) | |
| ▶ | 62.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ▶ | 62.4% | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ▶ | 58.8% | (-.f64 x (sqrt.f64 (neg.f64 eps))) |
| 3.5% | (-.f64 x (neg.f64 x)) | |
| ▶ | 4.4% | (-.f64 x x) |
| 26.8% | (*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))) |
Compiled 268 to 156 computations (41.8% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
| ✓ | cost-diff | 320 | (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) |
| ✓ | cost-diff | 0 | (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) |
| ✓ | cost-diff | 0 | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ✓ | cost-diff | 896 | (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
| ✓ | cost-diff | 0 | (neg.f64 eps) |
| ✓ | cost-diff | 0 | (sqrt.f64 (neg.f64 eps)) |
| ✓ | cost-diff | 0 | (-.f64 x (sqrt.f64 (neg.f64 eps))) |
| ✓ | cost-diff | 192 | (-.f64 x 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)))) |
| 2 770× | *-lowering-*.f32 |
| 2 770× | *-lowering-*.f64 |
| 2 486× | accelerator-lowering-fma.f32 |
| 2 486× | accelerator-lowering-fma.f64 |
| 2 158× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 121 |
| 1 | 59 | 121 |
| 2 | 114 | 121 |
| 3 | 193 | 117 |
| 4 | 289 | 117 |
| 5 | 483 | 117 |
| 6 | 1364 | 117 |
| 7 | 3335 | 117 |
| 8 | 5722 | 117 |
| 9 | 7419 | 117 |
| 0 | 8061 | 114 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- x (sqrt (+ (* x x) (neg eps)))) |
x |
(sqrt (+ (* x x) (neg eps))) |
(+ (* x x) (neg eps)) |
(neg eps) |
eps |
(- x x) |
x |
(- x (sqrt (neg eps))) |
x |
(sqrt (neg eps)) |
(neg eps) |
eps |
(- x (sqrt (* eps (+ (* x (/ x eps)) -1)))) |
x |
(sqrt (* eps (+ (* x (/ x eps)) -1))) |
(* eps (+ (* x (/ x eps)) -1)) |
eps |
(+ (* x (/ x eps)) -1) |
(/ x eps) |
-1 |
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x) |
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) |
eps |
1/2 |
(/ (* 1/8 (* eps eps)) (* x x)) |
(* 1/8 (* eps eps)) |
1/8 |
(* eps eps) |
(* x x) |
x |
| Outputs |
|---|
(- x (sqrt (+ (* x x) (neg eps)))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(sqrt (+ (* x x) (neg eps))) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(+ (* x x) (neg eps)) |
(-.f64 (*.f64 x x) eps) |
(neg eps) |
(neg.f64 eps) |
eps |
(- x x) |
#s(literal 0 binary64) |
x |
(- x (sqrt (neg eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
x |
(sqrt (neg eps)) |
(sqrt.f64 (neg.f64 eps)) |
(neg eps) |
(neg.f64 eps) |
eps |
(- x (sqrt (* eps (+ (* x (/ x eps)) -1)))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(sqrt (* eps (+ (* x (/ x eps)) -1))) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(* eps (+ (* x (/ x eps)) -1)) |
(-.f64 (*.f64 x x) eps) |
eps |
(+ (* x (/ x eps)) -1) |
(fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) |
(/ x eps) |
(/.f64 x eps) |
-1 |
#s(literal -1 binary64) |
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x) |
(*.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) |
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
eps |
1/2 |
#s(literal 1/2 binary64) |
(/ (* 1/8 (* eps eps)) (* x x)) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) |
(* 1/8 (* eps eps)) |
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) |
1/8 |
#s(literal 1/8 binary64) |
(* eps eps) |
(*.f64 eps eps) |
(* x x) |
(*.f64 x x) |
x |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 eps eps) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) |
| ✓ | accuracy | 99.9% | (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
| ✓ | accuracy | 62.0% | (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) |
| ✓ | accuracy | 99.9% | (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) |
| ✓ | accuracy | 99.5% | (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
| ✓ | accuracy | 82.5% | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (neg.f64 eps)) |
| ✓ | accuracy | 100.0% | (neg.f64 eps) |
| ✓ | accuracy | 100.0% | (-.f64 x (sqrt.f64 (neg.f64 eps))) |
| ✓ | accuracy | 100.0% | (-.f64 x x) |
| ✓ | accuracy | 100.0% | (fma.f64 x x (neg.f64 eps)) |
| ✓ | accuracy | 100.0% | (neg.f64 eps) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fma.f64 x x (neg.f64 eps))) |
| ✓ | accuracy | 82.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| 46.0ms | 38× | 1 | valid |
| 26.0ms | 153× | 0 | valid |
| 9.0ms | 55× | 0 | invalid |
| 5.0ms | 9× | 2 | valid |
| 1.0ms | 1× | 3 | valid |
Compiled 131 to 27 computations (79.4% saved)
ival-sqrt: 40.0ms (57.9% of total)ival-mult: 10.0ms (14.5% of total)ival-div: 6.0ms (8.7% of total)ival-sub: 5.0ms (7.2% of total)ival-add: 4.0ms (5.8% of total)adjust: 2.0ms (2.9% of total)ival-neg: 1.0ms (1.4% of total)ival-assert: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- x (sqrt (+ (* x x) (neg eps))))> |
#<alt (sqrt (+ (* x x) (neg eps)))> |
#<alt (+ (* x x) (neg eps))> |
#<alt (neg eps)> |
#<alt (- x x)> |
#<alt (- x (sqrt (neg eps)))> |
#<alt (sqrt (neg eps))> |
#<alt (* eps (+ (* x (/ x eps)) -1))> |
#<alt (- x (sqrt (* eps (+ (* x (/ x eps)) -1))))> |
#<alt (sqrt (* eps (+ (* x (/ x eps)) -1)))> |
#<alt (+ (* x (/ x eps)) -1)> |
#<alt (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x)))> |
#<alt (/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x)> |
#<alt (/ (* 1/8 (* eps eps)) (* x x))> |
#<alt (* 1/8 (* eps eps))> |
#<alt (* eps eps)> |
| Outputs |
|---|
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* 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)))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)> |
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)> |
#<alt (/ (- (* 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)> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))> |
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))> |
#<alt (* -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))))))))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))> |
#<alt (* 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))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -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)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))> |
#<alt (+ (* (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)))))))> |
#<alt (+ (* (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)))))))))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* -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))))))))> |
#<alt x> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))> |
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* 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))))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -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))))))> |
#<alt (* -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)))))))> |
#<alt (* -1 eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (- (pow x 2) eps)> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (* -1 eps)> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* -1 eps)> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt x> |
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt x> |
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))> |
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))> |
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (pow x 2)> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (* -1 eps)> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* eps (- (/ (pow x 2) eps) 1))> |
#<alt (* -1 eps)> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 eps)> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (+ (* -1 eps) (pow x 2))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (- x (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))> |
#<alt (- (* 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)))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)> |
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)> |
#<alt (/ (- (* 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)> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))> |
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))> |
#<alt (* -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))))))))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))> |
#<alt (* 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))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* (sqrt eps) (pow (sqrt -1) 3))> |
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))> |
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))> |
#<alt (* -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)) (pow (sqrt -1) 3)))))> |
#<alt x> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))> |
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (* 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)))))> |
#<alt (* 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))))))> |
#<alt (* -1 (* (sqrt eps) (pow (sqrt -1) 3)))> |
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))> |
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))> |
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))> |
#<alt (+ (* (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)))))))> |
#<alt (+ (* (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)))))))))> |
#<alt x> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))> |
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))> |
#<alt (* -1 x)> |
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* -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))))))))> |
#<alt -1> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (/ (pow x 2) eps)> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (/ (pow x 2) eps)> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))> |
#<alt (/ (pow x 2) eps)> |
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)> |
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)> |
#<alt (/ (+ (* -1 eps) (pow x 2)) eps)> |
#<alt -1> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt -1> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (- (/ (pow x 2) eps) 1)> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (* 1/2 eps)> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (* 1/8 (pow eps 2))> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
#<alt (pow eps 2)> |
81 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 14.0ms | eps | @ | 0 | (/ (* 1/8 (* eps eps)) (* x x)) |
| 1.0ms | eps | @ | -inf | (* eps (+ (* x (/ x eps)) -1)) |
| 1.0ms | eps | @ | 0 | (* eps (+ (* x (/ x eps)) -1)) |
| 1.0ms | eps | @ | -inf | (- x (sqrt (* eps (+ (* x (/ x eps)) -1)))) |
| 1.0ms | x | @ | 0 | (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) |
| 1× | batch-egg-rewrite |
| 898× | accelerator-lowering-fma.f32 |
| 898× | accelerator-lowering-fma.f64 |
| 808× | *-lowering-*.f32 |
| 808× | *-lowering-*.f64 |
| 630× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 25 | 113 |
| 1 | 162 | 113 |
| 0 | 1393 | 105 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- x (sqrt (+ (* x x) (neg eps)))) |
(sqrt (+ (* x x) (neg eps))) |
(+ (* x x) (neg eps)) |
(neg eps) |
(- x x) |
(- x (sqrt (neg eps))) |
(sqrt (neg eps)) |
(* eps (+ (* x (/ x eps)) -1)) |
(- x (sqrt (* eps (+ (* x (/ x eps)) -1)))) |
(sqrt (* eps (+ (* x (/ x eps)) -1))) |
(+ (* x (/ x eps)) -1) |
(+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) |
(/ (+ (* eps 1/2) (/ (* 1/8 (* eps eps)) (* x x))) x) |
(/ (* 1/8 (* eps eps)) (* x x)) |
(* 1/8 (* eps eps)) |
(* eps eps) |
| Outputs |
|---|
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(+.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) (/.f64 (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (neg.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(/.f64 (fma.f64 x (*.f64 x x) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (*.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)) (-.f64 (*.f64 x x) eps))))) |
(*.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(exp.f64 (*.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))) |
(hypot.f64 x (sqrt.f64 (neg.f64 eps))) |
(hypot.f64 (sqrt.f64 (neg.f64 eps)) x) |
(hypot.f64 (sqrt.f64 (neg.f64 eps)) (pow.f64 x #s(literal 1 binary64))) |
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (sqrt.f64 (neg.f64 eps))) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) (sqrt.f64 (-.f64 (*.f64 x x) (neg.f64 eps)))) |
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) |
(+.f64 (*.f64 x x) (neg.f64 eps)) |
(+.f64 (neg.f64 eps) (*.f64 x x)) |
(-.f64 (*.f64 x x) eps) |
(-.f64 #s(literal 0 binary64) (-.f64 eps (*.f64 x x))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) (neg.f64 eps))) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) (neg.f64 eps)))) |
(-.f64 (fma.f64 x x #s(literal 0 binary64)) eps) |
(sqrt.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps))) |
(fma.f64 x x (neg.f64 eps)) |
(fma.f64 eps #s(literal -1 binary64) (*.f64 x x)) |
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) (*.f64 x x)) |
(fma.f64 #s(literal -1 binary64) eps (*.f64 x x)) |
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (neg.f64 eps)) |
(/.f64 (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) |
(/.f64 (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 eps eps (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (neg.f64 (*.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (-.f64 (*.f64 x x) (neg.f64 eps))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (fma.f64 x x eps)) |
(/.f64 (neg.f64 (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (neg.f64 (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) (neg.f64 (-.f64 (*.f64 x x) (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 eps eps (*.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 (neg.f64 eps) (*.f64 x x))) |
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64)) |
(*.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(*.f64 (fma.f64 (neg.f64 eps) (*.f64 eps eps) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 eps) (-.f64 (neg.f64 eps) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (neg.f64 eps)))) |
(+.f64 #s(literal 0 binary64) (neg.f64 eps)) |
(-.f64 #s(literal 0 binary64) eps) |
(sqrt.f64 (*.f64 eps eps)) |
(neg.f64 eps) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 eps eps (*.f64 #s(literal 0 binary64) eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (+.f64 #s(literal 0 binary64) eps)) |
(pow.f64 (neg.f64 eps) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (neg.f64 eps)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 eps eps) #s(literal 1/2 binary64)) |
(*.f64 eps #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps))) |
(*.f64 #s(literal -1 binary64) eps) |
#s(literal 0 binary64) |
(+.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps)))) |
(+.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) x) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps)))) (/.f64 (*.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps))) (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (neg.f64 eps)))) (/.f64 (neg.f64 eps) (+.f64 x (sqrt.f64 (neg.f64 eps))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (neg.f64 eps)) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))) (-.f64 (*.f64 x x) (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps)))) (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps)))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps))))) (neg.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (neg.f64 eps))) (neg.f64 (+.f64 x (sqrt.f64 (neg.f64 eps))))) |
(/.f64 (fma.f64 x (*.f64 x x) (pow.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (*.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps)))) (*.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))))) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 (neg.f64 (sqrt.f64 (neg.f64 eps))) (neg.f64 (sqrt.f64 (neg.f64 eps))))) (-.f64 x (neg.f64 (sqrt.f64 (neg.f64 eps))))) |
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (neg.f64 eps) (sqrt.f64 (neg.f64 eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 x (sqrt.f64 (neg.f64 eps)) (neg.f64 eps))))) |
(*.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (neg.f64 eps))))) |
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 1/2 binary64))) |
(sqrt.f64 (neg.f64 eps)) |
(pow.f64 (neg.f64 eps) #s(literal 1/2 binary64)) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 eps)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)) |
(*.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))) |
(+.f64 (neg.f64 eps) (/.f64 (*.f64 (*.f64 x x) eps) eps)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) (neg.f64 eps)) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) eps) |
(-.f64 (fma.f64 x (*.f64 (/.f64 x eps) eps) #s(literal 0 binary64)) eps) |
(sqrt.f64 (*.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(fma.f64 x (*.f64 (/.f64 x eps) eps) (neg.f64 eps)) |
(fma.f64 eps (/.f64 (*.f64 x x) eps) (neg.f64 eps)) |
(fma.f64 eps #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 x x) eps) eps)) |
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) (/.f64 (*.f64 (*.f64 x x) eps) eps)) |
(fma.f64 (/.f64 x eps) (*.f64 x eps) (neg.f64 eps)) |
(fma.f64 (/.f64 (*.f64 x x) eps) eps (neg.f64 eps)) |
(fma.f64 #s(literal -1 binary64) eps (/.f64 (*.f64 (*.f64 x x) eps) eps)) |
(fma.f64 (*.f64 eps x) (/.f64 x eps) (neg.f64 eps)) |
(fma.f64 (*.f64 eps (/.f64 x eps)) x (neg.f64 eps)) |
(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) #s(literal 3 binary64)) (*.f64 (neg.f64 eps) (*.f64 eps eps))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) (/.f64 (*.f64 (*.f64 x x) eps) eps) (-.f64 (*.f64 eps eps) (*.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) (neg.f64 eps))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) (/.f64 (*.f64 (*.f64 x x) eps) eps)) (*.f64 eps eps)) (-.f64 (/.f64 (*.f64 (*.f64 x x) eps) eps) (neg.f64 eps))) |
(/.f64 (*.f64 eps (fma.f64 (/.f64 (*.f64 x x) eps) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal -1 binary64))) (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)) eps)))) |
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal -1 binary64))) (fma.f64 x (/.f64 x eps) #s(literal 1 binary64))) |
(/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 x x) eps) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal -1 binary64)) eps) (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1 binary64)) eps)))) |
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal -1 binary64)) eps) (fma.f64 x (/.f64 x eps) #s(literal 1 binary64))) |
(pow.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) #s(literal 1/2 binary64)) |
(*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) |
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps) |
(*.f64 (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))) |
(*.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 eps)) (*.f64 (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(*.f64 (*.f64 (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) (sqrt.f64 eps)) (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) |
(+.f64 x (neg.f64 (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))) |
(+.f64 (neg.f64 (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) x) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (fma.f64 x x (fma.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))) (/.f64 (*.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (fma.f64 x x (fma.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))) (/.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (+.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) x) |
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) x) |
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) x) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (-.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))) (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (-.f64 (*.f64 x x) (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)))))) |
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(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (*.f64 (fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)))) x)) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 x))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) x) |
(/.f64 (*.f64 (fma.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 eps #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x))))) |
(pow.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 x))) |
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64))) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 eps #s(literal 1/2 binary64)))) |
(neg.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (neg.f64 (*.f64 x x)))) |
(neg.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))))) |
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (neg.f64 (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x))) |
(/.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x) x) |
(/.f64 (*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) #s(literal 1 binary64)) (*.f64 x x)) |
(/.f64 (neg.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (neg.f64 (neg.f64 (*.f64 x x)))) |
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x)) (neg.f64 x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 eps eps)) x) |
(pow.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x))) |
(*.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (*.f64 eps eps) x)) |
(*.f64 (/.f64 (*.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x)) |
(*.f64 (*.f64 eps eps) (*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (*.f64 eps eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps))) |
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 x x))) |
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 eps (/.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) x) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (*.f64 eps eps) (*.f64 x x)) #s(literal 1/8 binary64)) |
(*.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) x) (/.f64 eps x)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) |
(*.f64 (*.f64 eps eps) #s(literal 1/8 binary64)) |
(*.f64 (*.f64 eps #s(literal 1/8 binary64)) eps) |
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64))) |
(neg.f64 (*.f64 eps (neg.f64 eps))) |
(neg.f64 (*.f64 (neg.f64 eps) eps)) |
(pow.f64 eps #s(literal 2 binary64)) |
(pow.f64 (neg.f64 eps) #s(literal 2 binary64)) |
(*.f64 eps eps) |
(*.f64 (neg.f64 eps) (neg.f64 eps)) |
(*.f64 #s(literal -1 binary64) (*.f64 eps (neg.f64 eps))) |
(*.f64 #s(literal 1 binary64) (*.f64 eps eps)) |
(*.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64))) |
(*.f64 (*.f64 (neg.f64 eps) #s(literal -1 binary64)) eps) |
| 1× | egg-herbie |
| 17 934× | accelerator-lowering-fma.f32 |
| 17 934× | accelerator-lowering-fma.f64 |
| 6 134× | *-lowering-*.f32 |
| 6 134× | *-lowering-*.f64 |
| 3 902× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 339 | 3850 |
| 1 | 1027 | 3783 |
| 2 | 3443 | 3687 |
| 0 | 8585 | 3515 |
| 1× | iter limit |
| 1× | node limit |
| 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))) |
(* 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) |
(* 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)))))))) |
(* 1/2 (/ eps 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)))) |
(* -1 (* (sqrt eps) (sqrt -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))))) |
(* (sqrt eps) (sqrt -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))))) |
(* (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))))))))) |
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))))))) |
(* -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)))))))) |
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))))) |
(* (sqrt 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)))))) |
(* -1 (* (sqrt 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) |
(- (pow x 2) eps) |
(- (pow x 2) eps) |
(- (pow x 2) eps) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(pow x 2) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(* -1 eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* -1 eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
(* -1 (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
x |
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
x |
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1))) |
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1))) |
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(- x (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(* (sqrt eps) (sqrt -1)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(pow x 2) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(* -1 eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* eps (- (/ (pow x 2) eps) 1)) |
(* -1 eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(* -1 eps) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(+ (* -1 eps) (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (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))) |
(* 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) |
(* 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)))))))) |
(* 1/2 (/ eps 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)))) |
(* -1 (* (sqrt eps) (sqrt -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))))) |
(* (sqrt eps) (pow (sqrt -1) 3)) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))) |
(* -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)) (pow (sqrt -1) 3))))) |
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))))) |
(* (sqrt 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)))))) |
(* -1 (* (sqrt eps) (pow (sqrt -1) 3))) |
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))) |
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))) |
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))) |
(* (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))))))))) |
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))))))) |
(* -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 |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
(/ (pow x 2) eps) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(/ (pow x 2) eps) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
(/ (pow x 2) eps) |
(/ (+ (* -1 eps) (pow x 2)) eps) |
(/ (+ (* -1 eps) (pow x 2)) eps) |
(/ (+ (* -1 eps) (pow x 2)) eps) |
-1 |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
-1 |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
(- (/ (pow x 2) eps) 1) |
(* 1/2 eps) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 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)) (* 1/2 (* eps (pow x 2)))) (pow x 2)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (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)) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(* 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)) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(* 1/2 (/ eps x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (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)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(* 1/2 (/ eps x)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(* 1/2 (/ eps x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(* 1/8 (pow eps 2)) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
(pow eps 2) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x) x) (*.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 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) 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 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.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))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 2 binary64))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -2 binary64))) (neg.f64 x)) |
(* -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 (fma.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -2 binary64)))) (neg.f64 x)) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) 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)))) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 #s(literal 5/128 binary64) (/.f64 eps (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps))) |
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (/.f64 x 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 eps (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/8 binary64)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x eps)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 eps (+.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 eps (+.f64 (/.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) |
(* -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 eps (+.f64 (/.f64 (-.f64 x (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 eps) (*.f64 x x))))) eps)) eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* (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 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* (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 (*.f64 x x) (fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(fma.f64 (/.f64 eps (*.f64 x x)) (*.f64 #s(literal -1/2 binary64) x) x) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) 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))))))) |
(fma.f64 x (fma.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps #s(literal -1/16 binary64)) (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64))))) x) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 x (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 x (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 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)))))))) |
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(* -1 (* (sqrt eps) (sqrt -1))) |
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(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
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(* -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)))))) |
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(* -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))))))) |
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(*.f64 x x) |
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(-.f64 (*.f64 x x) eps) |
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0 |
#s(literal 0 binary64) |
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#s(literal 0 binary64) |
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#s(literal 0 binary64) |
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#s(literal 0 binary64) |
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x |
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(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
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(-.f64 (*.f64 x x) eps) |
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(*.f64 x (fma.f64 x (/.f64 (neg.f64 eps) (*.f64 x x)) x)) |
(* -1 (* (sqrt eps) (sqrt -1))) |
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(- x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 #s(literal -1/2 binary64) x) x) (*.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 (*.f64 x x) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x)) |
(* 1/2 (/ eps x)) |
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(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) 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) |
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(* 2 x) |
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(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
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(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
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(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
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(* (sqrt eps) (pow (sqrt -1) 3)) |
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x |
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(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) x) |
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(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
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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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(* -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)))))))) |
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#s(literal -1 binary64) |
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(- (/ (pow x 2) eps) 1) |
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(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2)))) |
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(fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) |
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#s(literal -1 binary64) |
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#s(literal -1 binary64) |
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(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
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(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
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(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
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(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
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(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
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(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))) |
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(*.f64 eps #s(literal 1/2 binary64)) |
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(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(* 1/2 eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x (*.f64 x x))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x (*.f64 x x))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 eps x)))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(* 1/8 (pow eps 2)) |
(*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
(pow eps 2) |
(*.f64 eps eps) |
Compiled 10 100 to 1 145 computations (88.7% saved)
11 alts after pruning (7 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 592 | 6 | 598 |
| Fresh | 4 | 1 | 5 |
| Picked | 1 | 4 | 5 |
| Done | 0 | 0 | 0 |
| Total | 597 | 11 | 608 |
| Status | Accuracy | Program |
|---|---|---|
| 34.0% | (/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x) | |
| ✓ | 41.2% | (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
| ▶ | 58.4% | (/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| ▶ | 41.2% | (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
| 24.5% | (/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) | |
| ▶ | 43.7% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| ✓ | 62.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ✓ | 58.8% | (-.f64 x (sqrt.f64 (neg.f64 eps))) |
| ▶ | 3.5% | x |
| ▶ | 4.4% | #s(literal 0 binary64) |
Compiled 222 to 133 computations (40.1% saved)
| 1× | egg-herbie |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
| ✓ | cost-diff | 0 | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| ✓ | cost-diff | 0 | (neg.f64 eps) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| ✓ | cost-diff | 256 | (-.f64 (*.f64 x x) (neg.f64 eps)) |
| 2 808× | accelerator-lowering-fma.f32 |
| 2 808× | accelerator-lowering-fma.f64 |
| 1 968× | *-lowering-*.f32 |
| 1 968× | *-lowering-*.f64 |
| 1 188× | div-sub |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 91 |
| 1 | 44 | 89 |
| 2 | 88 | 89 |
| 3 | 266 | 89 |
| 4 | 1032 | 89 |
| 5 | 2032 | 89 |
| 6 | 3527 | 89 |
| 7 | 4822 | 89 |
| 8 | 5324 | 89 |
| 9 | 5383 | 89 |
| 10 | 5393 | 89 |
| 11 | 5401 | 89 |
| 12 | 5933 | 89 |
| 13 | 6221 | 89 |
| 14 | 6315 | 89 |
| 15 | 6391 | 89 |
| 16 | 6481 | 89 |
| 17 | 6481 | 89 |
| 18 | 6481 | 89 |
| 19 | 6481 | 89 |
| 20 | 6649 | 89 |
| 21 | 6779 | 89 |
| 22 | 6787 | 89 |
| 23 | 6787 | 89 |
| 24 | 6787 | 89 |
| 0 | 6787 | 84 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
(- (* x x) (neg eps)) |
(* x x) |
x |
(neg eps) |
eps |
(+ x (sqrt (neg eps))) |
(sqrt (neg eps)) |
0 |
x |
(/ (* eps 1/2) x) |
(* eps 1/2) |
eps |
1/2 |
x |
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x) |
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) |
eps |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
(/ 1/8 (* x x)) |
1/8 |
(* x x) |
x |
1/2 |
| Outputs |
|---|
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
(/.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(- (* x x) (neg eps)) |
(fma.f64 x x eps) |
(* x x) |
(*.f64 x x) |
x |
(neg eps) |
(neg.f64 eps) |
eps |
(+ x (sqrt (neg eps))) |
(+.f64 x (sqrt.f64 (neg.f64 eps))) |
(sqrt (neg eps)) |
(sqrt.f64 (neg.f64 eps)) |
0 |
#s(literal 0 binary64) |
x |
(/ (* eps 1/2) x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps 1/2) |
(*.f64 eps #s(literal 1/2 binary64)) |
eps |
1/2 |
#s(literal 1/2 binary64) |
x |
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) |
(*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
eps |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(/ 1/8 (* x x)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
1/8 |
#s(literal 1/8 binary64) |
(* x x) |
(*.f64 x x) |
x |
1/2 |
#s(literal 1/2 binary64) |
Found 10 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
| ✓ | accuracy | 91.8% | (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 78.6% | (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| ✓ | accuracy | 100.0% | (*.f64 eps #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (neg.f64 eps) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) (neg.f64 eps)) |
| ✓ | accuracy | 100.0% | (+.f64 x (sqrt.f64 (neg.f64 eps))) |
| ✓ | accuracy | 99.5% | (/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| 31.0ms | 201× | 0 | valid |
| 7.0ms | 55× | 0 | invalid |
Compiled 90 to 20 computations (77.8% saved)
ival-div: 10.0ms (39.2% of total)ival-mult: 8.0ms (31.4% of total)ival-add: 2.0ms (7.8% of total)ival-sqrt: 2.0ms (7.8% of total)ival-sub: 1.0ms (3.9% of total)ival-neg: 1.0ms (3.9% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (- (* x x) (neg eps))> |
#<alt (/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps))))> |
#<alt (* x x)> |
#<alt (neg eps)> |
#<alt (/ (* eps 1/2) x)> |
#<alt (* eps 1/2)> |
#<alt (/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x)> |
#<alt (* eps (+ (* eps (/ 1/8 (* x x))) 1/2))> |
#<alt (+ (* eps (/ 1/8 (* x x))) 1/2)> |
#<alt (/ 1/8 (* x x))> |
#<alt (+ x (sqrt (neg eps)))> |
| Outputs |
|---|
#<alt eps> |
#<alt (+ eps (pow x 2))> |
#<alt (+ eps (pow x 2))> |
#<alt (+ eps (pow x 2))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (* (pow x 2) (+ 1 (/ eps (pow x 2))))> |
#<alt (pow x 2)> |
#<alt (+ eps (pow x 2))> |
#<alt (+ eps (pow x 2))> |
#<alt (+ eps (pow x 2))> |
#<alt eps> |
#<alt (* eps (+ 1 (/ (pow x 2) eps)))> |
#<alt (* eps (+ 1 (/ (pow x 2) eps)))> |
#<alt (* eps (+ 1 (/ (pow x 2) eps)))> |
#<alt eps> |
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))> |
#<alt (* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1)))> |
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt x> |
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt (* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt (* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x)))))> |
#<alt x> |
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1)))> |
#<alt (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))> |
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))> |
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))> |
#<alt (+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))))> |
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2)))> |
#<alt (- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2)))> |
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps)))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (pow x 2)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 eps)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* 1/2 eps)> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))> |
#<alt (* 1/2 eps)> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (* 1/2 eps)> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt x> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
54 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | 0 | (/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
| 2.0ms | eps | @ | -inf | (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) |
| 1.0ms | eps | @ | -inf | (/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x) |
| 1.0ms | eps | @ | inf | (/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
| 1.0ms | eps | @ | -inf | (/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
| 1× | batch-egg-rewrite |
| 7 072× | accelerator-lowering-fma.f32 |
| 7 072× | accelerator-lowering-fma.f64 |
| 5 886× | *-lowering-*.f32 |
| 5 886× | *-lowering-*.f64 |
| 4 460× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 74 |
| 1 | 112 | 66 |
| 2 | 843 | 66 |
| 0 | 8405 | 62 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- (* x x) (neg eps)) |
(/ (- (* x x) (neg eps)) (+ x (sqrt (neg eps)))) |
(* x x) |
(neg eps) |
(/ (* eps 1/2) x) |
(* eps 1/2) |
(/ (* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) x) |
(* eps (+ (* eps (/ 1/8 (* x x))) 1/2)) |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
(/ 1/8 (* x x)) |
(+ x (sqrt (neg eps))) |
| Outputs |
|---|
(+.f64 (*.f64 x x) eps) |
(+.f64 eps (*.f64 x x)) |
(+.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))))) |
(+.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps)))) |
(+.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) x) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps))))) |
(+.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(+.f64 (*.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(+.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(-.f64 (*.f64 x x) (fabs.f64 eps)) |
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x eps))) |
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps))) |
(fma.f64 x x eps) |
(fma.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(fma.f64 (*.f64 x x) #s(literal 1 binary64) eps) |
(fma.f64 eps #s(literal 1 binary64) (*.f64 x x)) |
(fma.f64 (fabs.f64 eps) #s(literal -1 binary64) (*.f64 x x)) |
(fma.f64 (sqrt.f64 (fabs.f64 eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x x)) |
(fma.f64 (sqrt.f64 (fabs.f64 eps)) (*.f64 (sqrt.f64 (fabs.f64 eps)) #s(literal -1 binary64)) (*.f64 x x)) |
(fma.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) x (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (neg.f64 (sqrt.f64 (fabs.f64 eps))))) |
(fma.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(fma.f64 (neg.f64 x) (neg.f64 x) eps) |
(fma.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(fma.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (neg.f64 (/.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))))) |
(fma.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (neg.f64 (/.f64 (*.f64 eps eps) (-.f64 (*.f64 x x) eps)))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x x) eps) |
(fma.f64 #s(literal 1 binary64) eps (*.f64 x x)) |
(fma.f64 #s(literal -1 binary64) (fabs.f64 eps) (*.f64 x x)) |
(fma.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)) eps) |
(fma.f64 #s(literal -1 binary64) (*.f64 (fabs.f64 eps) #s(literal 1 binary64)) (*.f64 x x)) |
(fma.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (sqrt.f64 (fabs.f64 eps)) (*.f64 x x)) |
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) eps) |
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (*.f64 x x)) |
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (pow.f64 (fabs.f64 eps) #s(literal 1/4 binary64))) (pow.f64 (fabs.f64 eps) #s(literal 1/4 binary64)) (*.f64 x x)) |
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(/.f64 (neg.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (fabs.f64 eps))) (*.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (neg.f64 (neg.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))))) |
(/.f64 (/.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x x eps)) |
(/.f64 (*.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (*.f64 (fma.f64 x x eps) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (fma.f64 (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)) (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)) (*.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))))) |
(/.f64 (/.f64 (fma.f64 x x eps) #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)) (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))) (fma.f64 x (/.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))) |
(/.f64 (*.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (fma.f64 x x eps)) |
(/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (neg.f64 (fma.f64 x x eps))) |
(/.f64 (*.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (fma.f64 x x eps) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(/.f64 (*.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (neg.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))) |
(/.f64 (*.f64 (*.f64 (fma.f64 x (neg.f64 x) eps) (fma.f64 x x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x (neg.f64 x) eps)) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) (fma.f64 x (*.f64 x x) (*.f64 eps (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (fabs.f64 eps)) eps)) (neg.f64 (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) (-.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (neg.f64 (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 x (sqrt.f64 (fabs.f64 eps))) (neg.f64 (*.f64 (*.f64 x x) eps))))) |
(/.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (fma.f64 x x eps))) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (/.f64 (fma.f64 x x eps) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) #s(literal -1 binary64)) |
(*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) #s(literal 1 binary64)) |
(*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (neg.f64 (fma.f64 x x eps)) (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(*.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 #s(literal 1 binary64) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (fma.f64 x x eps)) |
(*.f64 #s(literal -1 binary64) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) |
(*.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (-.f64 (*.f64 x x) eps) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (fma.f64 x (neg.f64 x) eps) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (neg.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (fma.f64 x x eps)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (-.f64 (*.f64 x x) eps))) |
(*.f64 (/.f64 (fma.f64 x x eps) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (/.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (neg.f64 (fma.f64 x x eps))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (fma.f64 x x eps))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (fma.f64 x x eps))) |
(*.f64 (/.f64 (*.f64 (fma.f64 x x eps) (-.f64 (*.f64 x x) eps)) (/.f64 (fma.f64 x x eps) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(*.f64 (/.f64 (fma.f64 x x eps) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (*.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x eps))) |
(*.f64 (*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) |
(*.f64 (*.f64 (fma.f64 x x eps) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (fabs.f64 eps)))))) (-.f64 (*.f64 x x) eps)) |
(*.f64 (/.f64 (fma.f64 x x eps) (neg.f64 (fma.f64 x x eps))) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) |
(*.f64 (/.f64 (fma.f64 x x eps) (-.f64 (*.f64 x (*.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (neg.f64 (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)))) (*.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (fma.f64 x (*.f64 (/.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (+.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x (*.f64 (/.f64 x (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (+.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (fma.f64 x (*.f64 x x) (*.f64 eps (sqrt.f64 (fabs.f64 eps))))) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (*.f64 x x) eps)) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (*.f64 x x) eps))) |
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps))) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 eps (fma.f64 x (neg.f64 x) eps)))) |
(*.f64 (/.f64 (fma.f64 x x eps) (*.f64 (-.f64 (*.f64 x x) eps) (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (-.f64 (*.f64 x x) eps)) |
(*.f64 (/.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (fabs.f64 eps) (*.f64 (-.f64 (sqrt.f64 (fabs.f64 eps)) x) (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (fabs.f64 eps) (*.f64 x (-.f64 x (sqrt.f64 (fabs.f64 eps))))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) |
| 1× | egg-herbie |
| 8 308× | accelerator-lowering-fma.f32 |
| 8 308× | accelerator-lowering-fma.f64 |
| 3 220× | *-lowering-*.f32 |
| 3 220× | *-lowering-*.f64 |
| 2 588× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 217 | 2074 |
| 1 | 656 | 1962 |
| 2 | 2041 | 1828 |
| 3 | 6613 | 1827 |
| 0 | 8201 | 1713 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
eps |
(+ eps (pow x 2)) |
(+ eps (pow x 2)) |
(+ eps (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(pow x 2) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(pow x 2) |
(+ eps (pow x 2)) |
(+ eps (pow x 2)) |
(+ eps (pow x 2)) |
eps |
(* eps (+ 1 (/ (pow x 2) eps))) |
(* eps (+ 1 (/ (pow x 2) eps))) |
(* eps (+ 1 (/ (pow x 2) eps))) |
eps |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
x |
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
(* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x))))) |
(* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x))))) |
x |
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1))) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1))) |
(/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(pow x 2) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 eps) |
(* 1/2 (/ eps x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (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)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(* 1/2 (/ eps x)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(* 1/2 (/ eps x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* 1/2 eps) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2))))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 1/8 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 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)) (* 1/2 (* eps (pow x 2)))) (pow x 2)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (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)) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
(* 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)) |
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(* 1/8 (/ eps (pow x 2))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 1/8 (/ eps (pow x 2))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* 1/8 (/ eps (pow x 2))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(* (sqrt eps) (sqrt -1)) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
x |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
x |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
| Outputs |
|---|
eps |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(* (pow x 2) (+ 1 (/ eps (pow x 2)))) |
(*.f64 x (fma.f64 x (/.f64 eps (*.f64 x x)) x)) |
(pow x 2) |
(*.f64 x x) |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
(+ eps (pow x 2)) |
(fma.f64 x x eps) |
eps |
(* eps (+ 1 (/ (pow x 2) eps))) |
(fma.f64 x x eps) |
(* eps (+ 1 (/ (pow x 2) eps))) |
(fma.f64 x x eps) |
(* eps (+ 1 (/ (pow x 2) eps))) |
(fma.f64 x x eps) |
eps |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(fma.f64 x x eps) |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(fma.f64 x x eps) |
(* -1 (* eps (- (* -1 (/ (pow x 2) eps)) 1))) |
(fma.f64 x x eps) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* x (- (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 x (fma.f64 x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* x (- (* x (- (+ (* -1 (* (sqrt (/ 1 eps)) (/ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (fma.f64 x (neg.f64 (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
x |
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x))))) |
(fma.f64 x (/.f64 (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) x) x) |
(* x (- (+ 1 (/ eps (pow x 2))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x))))) |
(fma.f64 x (/.f64 (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) x) x) |
(* x (- (+ 1 (+ (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- eps (* -1 (* eps (pow (sqrt -1) 2))))) (pow x 3)))) (/ eps (pow x 2)))) (+ (* -1 (/ (* eps (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt eps) (/ (sqrt -1) x))))) |
(-.f64 x (/.f64 (*.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))) x)) |
x |
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1))) |
(fma.f64 x (/.f64 (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) x) x) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1 eps) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1))) |
(fma.f64 x (/.f64 (*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) x) x) |
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 eps) (* -1 (* (sqrt eps) (/ (* (sqrt -1) (- (* -1 eps) (* eps (pow (sqrt -1) 2)))) x)))) (* eps (pow (sqrt -1) 2))) x)) (* (sqrt eps) (sqrt -1))) x)) 1))) |
(-.f64 x (/.f64 (*.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64))))) x)) |
(/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1)))) |
(*.f64 x (/.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(fma.f64 x (/.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(fma.f64 x (/.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))) |
(+ (/ eps (+ x (* (sqrt eps) (sqrt -1)))) (/ (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))) |
(fma.f64 x (/.f64 x (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) x)) |
(- (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (/ x (pow (sqrt -1) 2))) |
(fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 eps)) #s(literal -1 binary64)) (/.f64 (*.f64 eps x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))))) (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) x))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))) (/ (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (* (pow eps 2) (pow (sqrt -1) 2))))) (+ (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (/ (* eps x) (pow (sqrt -1) 2)))) (sqrt -1))) (/ x (pow (sqrt -1) 2)))) |
(+.f64 x (fma.f64 x (-.f64 (/.f64 (*.f64 x (fma.f64 (*.f64 x x) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 eps x))) (*.f64 eps (neg.f64 eps))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (-.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 eps)) #s(literal -1 binary64)) (/.f64 (*.f64 eps x) (neg.f64 (sqrt.f64 #s(literal -1 binary64))))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps))) |
(neg.f64 (fma.f64 (sqrt.f64 eps) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) eps))) (neg.f64 x))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) (* eps x)) eps))) |
(neg.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 eps) (*.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (neg.f64 eps)))) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
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(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(fma.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)) x) x) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(fma.f64 x (/.f64 (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) #s(literal 0 binary64)) x) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps (sqrt.f64 #s(literal -1 binary64))) x) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(fma.f64 (neg.f64 eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
Compiled 28 937 to 2 756 computations (90.5% saved)
13 alts after pruning (7 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 187 | 6 | 1 193 |
| Fresh | 1 | 1 | 2 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 3 | 4 |
| Total | 1 191 | 13 | 1 204 |
| Status | Accuracy | Program |
|---|---|---|
| 34.0% | (/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x) | |
| ✓ | 41.2% | (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
| ▶ | 43.2% | (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
| ✓ | 43.7% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| ▶ | 61.6% | (/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| ✓ | 62.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ▶ | 60.1% | (-.f64 x (sqrt.f64 (fabs.f64 eps))) |
| 41.2% | (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) | |
| ▶ | 41.0% | (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
| ▶ | 43.5% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
| ✓ | 3.5% | x |
| ✓ | 4.4% | #s(literal 0 binary64) |
Compiled 230 to 146 computations (36.5% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 0 | (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 0 | (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 2 binary64) eps) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) |
| ✓ | cost-diff | 1088 | (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
| ✓ | cost-diff | 0 | (fabs.f64 eps) |
| ✓ | cost-diff | 0 | (sqrt.f64 (fabs.f64 eps)) |
| ✓ | cost-diff | 0 | (-.f64 x (sqrt.f64 (fabs.f64 eps))) |
| ✓ | cost-diff | 0 | (neg.f64 eps) |
| ✓ | cost-diff | 0 | (sqrt.f64 (neg.f64 eps)) |
| ✓ | cost-diff | 0 | (+.f64 x (sqrt.f64 (neg.f64 eps))) |
| ✓ | cost-diff | 0 | (/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| 19 210× | accelerator-lowering-fma.f32 |
| 19 210× | accelerator-lowering-fma.f64 |
| 2 272× | *-lowering-*.f32 |
| 2 272× | *-lowering-*.f64 |
| 1 844× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 102 |
| 1 | 48 | 102 |
| 2 | 78 | 102 |
| 3 | 114 | 102 |
| 4 | 165 | 102 |
| 5 | 379 | 102 |
| 6 | 744 | 102 |
| 7 | 1510 | 102 |
| 8 | 3963 | 102 |
| 9 | 6102 | 102 |
| 10 | 7617 | 102 |
| 11 | 7771 | 102 |
| 12 | 7824 | 102 |
| 13 | 7844 | 102 |
| 0 | 8574 | 99 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ eps (+ x (sqrt (neg eps)))) |
eps |
(+ x (sqrt (neg eps))) |
x |
(sqrt (neg eps)) |
(neg eps) |
(- x (sqrt (fabs eps))) |
x |
(sqrt (fabs eps)) |
(fabs eps) |
eps |
(* (/ 1/2 x) eps) |
(/ 1/2 x) |
1/2 |
x |
eps |
(/ (/ 1 x) (/ 2 eps)) |
(/ 1 x) |
1 |
x |
(/ 2 eps) |
2 |
eps |
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) |
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
eps |
(/ 1/8 (* x x)) |
1/8 |
(* x x) |
x |
1/2 |
| Outputs |
|---|
(/ eps (+ x (sqrt (neg eps)))) |
(/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
eps |
(+ x (sqrt (neg eps))) |
(+.f64 x (sqrt.f64 (neg.f64 eps))) |
x |
(sqrt (neg eps)) |
(sqrt.f64 (neg.f64 eps)) |
(neg eps) |
(neg.f64 eps) |
(- x (sqrt (fabs eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
x |
(sqrt (fabs eps)) |
(sqrt.f64 (fabs.f64 eps)) |
(fabs eps) |
(fabs.f64 eps) |
eps |
(* (/ 1/2 x) eps) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
1/2 |
#s(literal 1/2 binary64) |
x |
eps |
(/ (/ 1 x) (/ 2 eps)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
x |
(/ 2 eps) |
(/.f64 #s(literal 2 binary64) eps) |
2 |
#s(literal 2 binary64) |
eps |
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) |
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
(fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) |
eps |
(/ 1/8 (* x x)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
1/8 |
#s(literal 1/8 binary64) |
(* x x) |
(*.f64 x x) |
x |
1/2 |
#s(literal 1/2 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
| ✓ | accuracy | 86.7% | (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
| ✓ | accuracy | 78.6% | (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 2 binary64) eps) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) x) |
| ✓ | accuracy | 99.3% | (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 99.7% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (fabs.f64 eps)) |
| ✓ | accuracy | 100.0% | (fabs.f64 eps) |
| ✓ | accuracy | 100.0% | (-.f64 x (sqrt.f64 (fabs.f64 eps))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (neg.f64 eps)) |
| ✓ | accuracy | 100.0% | (neg.f64 eps) |
| ✓ | accuracy | 100.0% | (+.f64 x (sqrt.f64 (neg.f64 eps))) |
| ✓ | accuracy | 99.5% | (/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| 36.0ms | 201× | 0 | valid |
| 9.0ms | 55× | 0 | invalid |
Compiled 103 to 26 computations (74.8% saved)
ival-div: 13.0ms (44.9% of total)ival-mult: 6.0ms (20.7% of total)ival-sqrt: 3.0ms (10.4% of total)ival-add: 2.0ms (6.9% of total)ival-fabs: 1.0ms (3.5% of total)ival-sub: 1.0ms (3.5% of total)ival-neg: 1.0ms (3.5% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ eps (+ x (sqrt (neg eps))))> |
#<alt (+ x (sqrt (neg eps)))> |
#<alt (sqrt (neg eps))> |
#<alt (neg eps)> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (sqrt (fabs eps))> |
#<alt (fabs eps)> |
#<alt (* (/ 1/2 x) eps)> |
#<alt (/ 1/2 x)> |
#<alt (/ (/ 1 x) (/ 2 eps))> |
#<alt (/ 1 x)> |
#<alt (/ 2 eps)> |
#<alt (* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps)> |
#<alt (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x)> |
#<alt (+ (* eps (/ 1/8 (* x x))) 1/2)> |
#<alt (/ 1/8 (* x x))> |
| Outputs |
|---|
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))> |
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))> |
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))> |
#<alt (/ eps (+ x (* (sqrt eps) (sqrt -1))))> |
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))> |
#<alt (- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps)))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps)))> |
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (/ eps x)> |
#<alt (/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)> |
#<alt (/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)> |
#<alt (/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x)> |
#<alt (/ eps x)> |
#<alt (* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x))> |
#<alt (* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))> |
#<alt (* -1 (/ (+ (* -1 eps) (* -1 (/ (- (* -1 (/ (- (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) x)) (* (pow eps 2) (pow (sqrt -1) 2))) x)) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt x> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt (* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x))))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* (sqrt eps) (sqrt -1)))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* (sqrt eps) (sqrt -1))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 eps)> |
#<alt (* -1 (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt x> |
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))> |
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))> |
#<alt (* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps))))))> |
#<alt x> |
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))> |
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))> |
#<alt (* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (- x (sqrt (fabs eps)))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (sqrt (fabs eps))> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (fabs eps)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (/ 1/2 x)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 1 x)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (/ 2 eps)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))> |
#<alt (* 1/2 (/ eps x))> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)> |
#<alt (* 1/2 (/ eps x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))> |
#<alt (/ 1/2 x)> |
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))> |
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))> |
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))> |
#<alt (* 1/8 (/ eps (pow x 3)))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ eps (pow x 3)))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))> |
#<alt (* 1/8 (/ eps (pow x 3)))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))> |
#<alt (/ 1/2 x)> |
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)> |
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)> |
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)> |
#<alt (/ 1/2 x)> |
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))> |
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))> |
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))> |
#<alt (* 1/8 (/ eps (pow x 2)))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt 1/2> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (+ 1/2 (* 1/8 (/ eps (pow x 2))))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
#<alt (/ 1/8 (pow x 2))> |
72 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | eps | @ | inf | (/ eps (+ x (sqrt (neg eps)))) |
| 0.0ms | eps | @ | 0 | (/ eps (+ x (sqrt (neg eps)))) |
| 0.0ms | x | @ | inf | (/ eps (+ x (sqrt (neg eps)))) |
| 0.0ms | eps | @ | -inf | (/ eps (+ x (sqrt (neg eps)))) |
| 0.0ms | x | @ | -inf | (/ eps (+ x (sqrt (neg eps)))) |
| 1× | batch-egg-rewrite |
| 4 604× | *-lowering-*.f32 |
| 4 604× | *-lowering-*.f64 |
| 4 240× | accelerator-lowering-fma.f32 |
| 4 240× | accelerator-lowering-fma.f64 |
| 3 782× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 24 | 84 |
| 1 | 133 | 84 |
| 2 | 905 | 84 |
| 0 | 9122 | 81 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ eps (+ x (sqrt (neg eps)))) |
(+ x (sqrt (neg eps))) |
(sqrt (neg eps)) |
(neg eps) |
(- x (sqrt (fabs eps))) |
(sqrt (fabs eps)) |
(fabs eps) |
(* (/ 1/2 x) eps) |
(/ 1/2 x) |
(/ (/ 1 x) (/ 2 eps)) |
(/ 1 x) |
(/ 2 eps) |
(* (/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) eps) |
(/ (+ (* eps (/ 1/8 (* x x))) 1/2) x) |
(+ (* eps (/ 1/8 (* x x))) 1/2) |
(/ 1/8 (* x x)) |
| Outputs |
|---|
(+.f64 #s(literal 0 binary64) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(+.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x)) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(+.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x))) |
(+.f64 (*.f64 (/.f64 eps (fma.f64 x x eps)) x) (*.f64 (/.f64 eps (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps))))) |
(+.f64 (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))))) |
(+.f64 (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))))) (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))))) |
(+.f64 (*.f64 x (/.f64 eps (fma.f64 x x eps))) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (fma.f64 x x eps)))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(fma.f64 x (/.f64 eps (fma.f64 x x eps)) (*.f64 (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps (fma.f64 x x eps)))) |
(fma.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))))) |
(fma.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))))) |
(fma.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(fma.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 x x))) |
(fma.f64 (/.f64 eps (fma.f64 x x eps)) x (*.f64 (/.f64 eps (fma.f64 x x eps)) (neg.f64 (sqrt.f64 (fabs.f64 eps))))) |
(neg.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps))) |
(/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps)))) |
(/.f64 (fabs.f64 eps) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps))) |
(/.f64 (*.f64 eps (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) |
(/.f64 (*.f64 eps (-.f64 x (sqrt.f64 (fabs.f64 eps)))) (fma.f64 x x eps)) |
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (*.f64 (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))) eps)) (*.f64 (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (*.f64 (*.f64 eps eps) (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) #s(literal 1 binary64)) (*.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 eps (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (fabs.f64 eps) (*.f64 (-.f64 (sqrt.f64 (fabs.f64 eps)) x) (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))))) (*.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 x x)))))) |
(/.f64 (*.f64 eps (*.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) (*.f64 (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(/.f64 (*.f64 eps (fma.f64 x x eps)) (*.f64 (fma.f64 x x eps) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 eps (fma.f64 x (*.f64 x x) (*.f64 eps (sqrt.f64 (fabs.f64 eps))))) (*.f64 (fma.f64 x x eps) (fma.f64 x x (fma.f64 x (sqrt.f64 (fabs.f64 eps)) (fabs.f64 eps))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (*.f64 #s(literal 0 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))) (+.f64 #s(literal 0 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps)))))) |
(/.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (fma.f64 x (*.f64 (*.f64 x x) (*.f64 x (*.f64 x x))) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 (fabs.f64 eps) (*.f64 (-.f64 (sqrt.f64 (fabs.f64 eps)) x) (-.f64 (sqrt.f64 (fabs.f64 eps)) x)))))) (fma.f64 x (*.f64 x (*.f64 x x)) (*.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (-.f64 (-.f64 (fabs.f64 eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (*.f64 x x))))) |
(/.f64 (*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))))) (+.f64 (fma.f64 x x eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(/.f64 (*.f64 (/.f64 eps (fma.f64 x x eps)) (fma.f64 x x eps)) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) |
(/.f64 (*.f64 (/.f64 eps (fma.f64 x x eps)) (fma.f64 x (*.f64 x x) (*.f64 eps (sqrt.f64 (fabs.f64 eps))))) (fma.f64 x x (fma.f64 x (sqrt.f64 (fabs.f64 eps)) (fabs.f64 eps)))) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) (*.f64 eps eps)) |
(/.f64 (*.f64 (neg.f64 (*.f64 eps eps)) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) eps) |
(pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps) #s(literal -1 binary64)) |
(*.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (fabs.f64 eps) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (sqrt.f64 (fabs.f64 eps)) (*.f64 (sqrt.f64 (fabs.f64 eps)) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))))) |
(*.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 (neg.f64 x) (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) eps) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (*.f64 (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps)))) eps)) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x eps)) (*.f64 (-.f64 x (sqrt.f64 (fabs.f64 eps))) eps)) |
(*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 eps (fma.f64 eps (neg.f64 (sqrt.f64 (fabs.f64 eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (fabs.f64 eps))))))) |
(*.f64 (/.f64 eps (fma.f64 x x eps)) (-.f64 x (sqrt.f64 (fabs.f64 eps)))) |
(*.f64 (/.f64 eps #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (/.f64 (sqrt.f64 (fabs.f64 eps)) #s(literal -1 binary64)) (/.f64 (sqrt.f64 (fabs.f64 eps)) (+.f64 x (sqrt.f64 (fabs.f64 eps))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 x (sqrt.f64 (fabs.f64 eps))) eps) #s(literal -1/2 binary64))) |
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(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) #s(literal 1/4 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64))) #s(literal 1 binary64)) (neg.f64 (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x))))) |
(/.f64 (*.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))) |
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 (*.f64 x x) #s(literal -8 binary64))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)))) (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)))))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 (*.f64 x x) #s(literal -8 binary64)))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) (*.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 eps (*.f64 x (*.f64 x #s(literal 8 binary64)))) #s(literal 9 binary64)) #s(literal 1/512 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x))))) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (-.f64 #s(literal 1/64 binary64) (/.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))))) |
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x))))) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/8 binary64))) |
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64)) (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/512 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) (+.f64 #s(literal 1/16 binary64) (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) #s(literal 1/4 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(/.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64))) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) |
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x))))) |
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 eps (*.f64 x (*.f64 x #s(literal 8 binary64)))) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))) |
(*.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)))) #s(literal 1 binary64))) |
(*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))) |
(*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)))))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)))) |
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/64 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 (*.f64 x x) #s(literal -8 binary64)))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x #s(literal 8 binary64)))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(neg.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal -1 binary64) x))) |
(neg.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) (neg.f64 x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x #s(literal 8 binary64))))) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x)) |
(/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal 8 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x #s(literal 8 binary64))) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) #s(literal -8 binary64))) |
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x #s(literal 8 binary64)) (neg.f64 x))) |
(/.f64 #s(literal -1/8 binary64) (*.f64 x (neg.f64 x))) |
(/.f64 (/.f64 #s(literal 1/8 binary64) x) x) |
(/.f64 (/.f64 #s(literal -1/8 binary64) x) (neg.f64 x)) |
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) x)) (neg.f64 x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1 binary64)) (neg.f64 x)) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64)) x) |
(pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/8 binary64) x)) |
(*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) |
(*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) |
(*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x)) |
(*.f64 (pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x (*.f64 x #s(literal 8 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))) |
| 1× | egg-herbie |
| 6 716× | accelerator-lowering-fma.f32 |
| 6 716× | accelerator-lowering-fma.f64 |
| 4 318× | *-lowering-*.f32 |
| 4 318× | *-lowering-*.f64 |
| 1 752× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 202 | 2052 |
| 1 | 577 | 1978 |
| 2 | 1676 | 1916 |
| 3 | 5467 | 1907 |
| 0 | 8382 | 1824 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(/ eps x) |
(/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x) |
(/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x) |
(/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x) |
(/ eps x) |
(* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)) |
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x)) |
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (* -1 (/ (- (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) x)) (* (pow eps 2) (pow (sqrt -1) 2))) x)) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x)) |
(* (sqrt eps) (sqrt -1)) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
x |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
x |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(* (sqrt eps) (sqrt -1)) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* (sqrt eps) (sqrt -1)) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 eps) |
(* -1 (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
x |
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps)))))) |
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps)))))) |
(* x (+ 1 (* -1 (* (/ 1 x) (sqrt (fabs eps)))))) |
x |
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1))) |
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1))) |
(* -1 (* x (- (* (/ 1 x) (sqrt (fabs eps))) 1))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(- x (sqrt (fabs eps))) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(sqrt (fabs eps)) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(fabs eps) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(/ 1/2 x) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(* 1/2 (/ eps x)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(/ 2 eps) |
(* 1/2 (/ eps x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(* (pow eps 2) (+ (* 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))))) |
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (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)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3)) |
(* 1/2 (/ eps x)) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x) |
(* 1/2 (/ eps x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)) |
(/ 1/2 x) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(* 1/8 (/ eps (pow x 3))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* 1/8 (/ eps (pow x 3))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))) |
(* 1/8 (/ eps (pow x 3))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/ 1/2 x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/ 1/2 x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(* 1/8 (/ eps (pow x 2))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(* 1/8 (/ eps (pow x 2))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(* 1/8 (/ eps (pow x 2))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
1/2 |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
(/ 1/8 (pow x 2)) |
| Outputs |
|---|
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) |
(/ eps (+ x (* (sqrt eps) (sqrt -1)))) |
(/.f64 eps (fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x)) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))) |
(fma.f64 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (+ (* -1 (/ (pow x 3) (* eps (pow (sqrt -1) 4)))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))) |
(fma.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* eps x)) eps))) |
(+.f64 (neg.f64 (*.f64 (sqrt.f64 eps) (+.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (*.f64 x x) eps))))) x) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (* -1 (* eps (pow x 3))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) eps)) (* eps x)) eps))) |
(-.f64 (-.f64 x (/.f64 (*.f64 (*.f64 x x) (fma.f64 eps x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))))) (*.f64 eps eps))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* x (- (* (sqrt (/ 1 eps)) (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x) #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* x (- (* x (- (* -1 (/ x (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(fma.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 x (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(/ eps x) |
(/.f64 eps x) |
(/ (+ eps (* -1 (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 x)) eps) x) |
(/ (- (+ eps (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x) |
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (/.f64 eps x))) x)) x) |
(/ (- (+ eps (* -1 (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) (pow x 3))))) (+ (* -1 (/ (* (pow eps 2) (pow (sqrt -1) 2)) (pow x 2))) (* (sqrt (pow eps 3)) (/ (sqrt -1) x)))) x) |
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 eps #s(literal 5 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (*.f64 eps eps)) x)) x)) x) |
(/ eps x) |
(/.f64 eps x) |
(* -1 (/ (+ (* -1 eps) (* (sqrt (pow eps 3)) (/ (sqrt -1) x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (neg.f64 x)) eps) x) |
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (/ (* (pow eps 2) (pow (sqrt -1) 2)) x) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x)) |
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (*.f64 eps (/.f64 eps x))) x)) x) |
(* -1 (/ (+ (* -1 eps) (* -1 (/ (- (* -1 (/ (- (* (sqrt (pow eps 5)) (/ (pow (sqrt -1) 3) x)) (* (pow eps 2) (pow (sqrt -1) 2))) x)) (* (sqrt (pow eps 3)) (sqrt -1))) x))) x)) |
(/.f64 (-.f64 eps (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 eps #s(literal 5 binary64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (*.f64 eps eps)) x)) x)) x) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
x |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* x (+ 1 (* (sqrt eps) (/ (sqrt -1) x)))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
x |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* -1 (* x (- (* -1 (* (sqrt eps) (/ (sqrt -1) x))) 1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(+ x (* (sqrt eps) (sqrt -1))) |
(fma.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)) x) |
(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(fma.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x) |
(* -1 (* (sqrt eps) (sqrt -1))) |
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(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3)) |
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* 1/8 (/ eps (pow x 2))) |
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2))))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* 1/8 (/ eps (pow x 2))) |
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(* 1/8 (/ eps (pow x 2))) |
(*.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x)) |
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2)) |
(/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x x)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(+ 1/2 (* 1/8 (/ eps (pow x 2)))) |
(fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
(/ 1/8 (pow x 2)) |
(/.f64 #s(literal 1/8 binary64) (*.f64 x x)) |
Compiled 19 446 to 2 180 computations (88.8% saved)
16 alts after pruning (6 fresh and 10 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 131 | 4 | 1 135 |
| Fresh | 0 | 2 | 2 |
| Picked | 0 | 5 | 5 |
| Done | 1 | 5 | 6 |
| Total | 1 132 | 16 | 1 148 |
| Status | Accuracy | Program |
|---|---|---|
| 34.0% | (/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x) | |
| ✓ | 43.2% | (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
| ✓ | 43.7% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| ✓ | 61.6% | (/.f64 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| 11.3% | (/.f64 eps x) | |
| ✓ | 62.5% | (-.f64 x (sqrt.f64 (fma.f64 x x (neg.f64 eps)))) |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
| ✓ | 60.1% | (-.f64 x (sqrt.f64 (fabs.f64 eps))) |
| 41.2% | (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) | |
| ✓ | 41.0% | (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
| 39.0% | (*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps) | |
| ✓ | 43.5% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
| 32.8% | (*.f64 (*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)) x))) eps) | |
| 59.6% | (neg.f64 (sqrt.f64 (fabs.f64 eps))) | |
| ✓ | 3.5% | x |
| ✓ | 4.4% | #s(literal 0 binary64) |
Compiled 478 to 211 computations (55.9% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps) |
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/.f64 (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) x) |
(*.f64 (*.f64 (fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)) x))) eps) |
(/.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 eps eps) (*.f64 x x)) (fma.f64 (*.f64 eps (*.f64 eps eps)) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))) x) |
(*.f64 eps (fma.f64 eps (fma.f64 eps (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
3 calls:
| 11.0ms | eps |
| 8.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 8.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 88.2% | 2 | x |
| 83.6% | 2 | eps |
| 99.0% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 16 to 10 computations (37.5% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
(-.f64 x (/.f64 (-.f64 (*.f64 x x) eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(*.f64 (/.f64 (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))) eps) |
(/.f64 (*.f64 eps (fma.f64 eps #s(literal 1/8 binary64) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))) (*.f64 x (*.f64 x x))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x) |
1 calls:
| 7.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)) |
1 calls:
| 6.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps) |
1 calls:
| 5.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.9% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (neg.f64 eps)) (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
1 calls:
| 5.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #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 eps (+.f64 x (sqrt.f64 (neg.f64 eps)))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 2 binary64) eps)) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
1 calls:
| 7.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
1 calls:
| 4.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.2% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
1 calls:
| 3.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.0% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (fabs.f64 eps))) |
(/.f64 eps x) |
3 calls:
| 6.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 63.2% | 2 | eps |
| 62.3% | 2 | x |
| 65.8% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 16 to 10 computations (37.5% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
| Outputs |
|---|
(neg.f64 (sqrt.f64 (fabs.f64 eps))) |
(/.f64 eps x) |
1 calls:
| 3.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 65.2% | 2 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 10 to 6 computations (40% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
(/.f64 eps x) |
| Outputs |
|---|
(/.f64 eps x) |
3 calls:
| 5.0ms | x |
| 2.0ms | eps |
| 2.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 11.3% | 1 | x |
| 11.3% | 1 | eps |
| 11.3% | 1 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
Compiled 16 to 10 computations (37.5% saved)
Total -0.8b remaining (-1.4%)
Threshold costs -0.8b (-1.4%)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(-.f64 x x) |
(-.f64 x (neg.f64 x)) |
| Outputs |
|---|
#s(literal 0 binary64) |
3 calls:
| 2.0ms | x |
| 2.0ms | eps |
| 2.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.4% | 1 | eps |
| 4.4% | 1 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 4.4% | 1 | x |
Compiled 16 to 10 computations (37.5% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -2.0075112324576588e-153 | 0.0 |
Compiled 13 to 11 computations (15.4% saved)
| 1× | egg-herbie |
| 22× | *-commutative_binary64 |
| 16× | +-commutative_binary64 |
| 16× | sub-neg_binary64 |
| 8× | neg-sub0_binary64 |
| 8× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 48 | 272 |
| 1 | 64 | 272 |
| 2 | 76 | 272 |
| 3 | 83 | 272 |
| 4 | 86 | 272 |
| 1× | saturated |
| Inputs |
|---|
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x)) |
(/.f64 eps x) |
#s(literal 0 binary64) |
| Outputs |
|---|
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (fma.f64 eps #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) eps)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (*.f64 eps (/.f64 (fma.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (*.f64 eps (fma.f64 x (/.f64 x eps) #s(literal -1 binary64))))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 x (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x)) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -7547924849643083/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (sqrt.f64 (fabs.f64 eps))) (/.f64 eps x)) |
(/.f64 eps x) |
#s(literal 0 binary64) |
| 17 934× | accelerator-lowering-fma.f32 |
| 17 934× | accelerator-lowering-fma.f64 |
| 11 222× | accelerator-lowering-fma.f32 |
| 11 222× | accelerator-lowering-fma.f64 |
| 8 308× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 22 |
| 1 | 38 | 22 |
| 2 | 306 | 22 |
| 3 | 3595 | 22 |
| 0 | 8551 | 22 |
| 0 | 202 | 2052 |
| 1 | 577 | 1978 |
| 2 | 1676 | 1916 |
| 3 | 5467 | 1907 |
| 0 | 8382 | 1824 |
| 0 | 25 | 113 |
| 1 | 162 | 113 |
| 0 | 1393 | 105 |
| 0 | 339 | 3850 |
| 1 | 1027 | 3783 |
| 2 | 3443 | 3687 |
| 0 | 8585 | 3515 |
| 0 | 257 | 1257 |
| 1 | 784 | 1238 |
| 2 | 2594 | 1200 |
| 3 | 6944 | 1197 |
| 0 | 8091 | 1129 |
| 0 | 217 | 2074 |
| 1 | 656 | 1962 |
| 2 | 2041 | 1828 |
| 3 | 6613 | 1827 |
| 0 | 8201 | 1713 |
| 0 | 17 | 74 |
| 1 | 112 | 66 |
| 2 | 843 | 66 |
| 0 | 8405 | 62 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
Compiled 671 to 306 computations (54.4% saved)
Compiled 592 to 122 computations (79.4% saved)
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