
Time bar (total: 9.9s)
| 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 25 to 17 computations (32% saved)
ival-<=: 4.0ms (36.2% of total)ival-sub: 2.0ms (18.1% of total)ival-mult: 2.0ms (18.1% of total)ival-sqrt: 2.0ms (18.1% of total)ival-and: 1.0ms (9% of total)const: 1.0ms (9% of total)backward-pass: 0.0ms (0% of total)| 467.0ms | 4793× | 0 | valid |
| 407.0ms | 2783× | 1 | valid |
| 161.0ms | 680× | 2 | valid |
| 13.0ms | 183× | 0 | invalid |
ival-<=: 168.0ms (24% of total)ival-sub: 159.0ms (22.7% of total)ival-mult: 144.0ms (20.5% of total)ival-sqrt: 124.0ms (17.7% of total)backward-pass: 60.0ms (8.6% of total)ival-and: 27.0ms (3.9% of total)const: 18.0ms (2.6% of total)| 2× | egg-herbie |
| 598× | fnmadd-define |
| 520× | fmsub-define |
| 502× | fnmsub-define |
| 464× | sum3-define |
| 432× | fmm-def |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 21 | 48 |
| 1 | 57 | 46 |
| 2 | 149 | 43 |
| 3 | 426 | 43 |
| 4 | 1130 | 43 |
| 5 | 2064 | 43 |
| 6 | 2308 | 43 |
| 7 | 2332 | 43 |
| 0 | 6 | 7 |
| 1 | 12 | 7 |
| 2 | 20 | 7 |
| 3 | 34 | 7 |
| 4 | 57 | 7 |
| 5 | 133 | 7 |
| 6 | 344 | 7 |
| 7 | 539 | 7 |
| 8 | 721 | 7 |
| 9 | 945 | 7 |
| 10 | 1109 | 7 |
| 11 | 1121 | 7 |
| 0 | 1121 | 7 |
| 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))) |
(- x (sqrt (fmsub x x eps))) |
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps))) |
(- (neg x) (sqrt (fmsub x x eps))) |
(- x (sqrt (- (* x x) (neg eps)))) |
(- x (sqrt (fma x x eps))) |
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))) |
(+ x (sqrt (fmsub x x eps))) |
(neg (- x (sqrt (- (* x x) (neg eps))))) |
(- (sqrt (fma x x eps)) x) |
(- eps (sqrt (- (* eps eps) x))) |
(- eps (sqrt (fmsub eps eps x))) |
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 107 | 0 | - | 1 | (2.8262746450129985e-94 -1.9432281731791863e-189) | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 0 | 0 | - | 0 | - | x |
| 0 | 0 | - | 0 | - | (*.f64 x x) |
| 0 | 0 | - | 0 | - | (-.f64 (*.f64 x x) eps) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (-.f64 (*.f64 x x) eps)) |
| 0 | 0 | - | 0 | - | eps |
| 34.0ms | 34× | 2 | valid |
| 23.0ms | 174× | 1 | valid |
| 22.0ms | 304× | 0 | valid |
Compiled 64 to 20 computations (68.8% saved)
ival-sub: 10.0ms (36.4% of total)ival-mult: 7.0ms (25.5% of total)ival-sqrt: 6.0ms (21.8% of total)backward-pass: 3.0ms (10.9% of total)const: 0.0ms (0% of total)Compiled 10 to 6 computations (40% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 62.4% | (-.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))) |
| 324× | sum3-define |
| 296× | fnmadd-define |
| 214× | fma-define |
| 184× | fma-lowering-fma.f32 |
| 184× | fma-lowering-fma.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 21 |
| 1 | 12 | 21 |
| 2 | 20 | 21 |
| 3 | 34 | 21 |
| 4 | 57 | 21 |
| 5 | 133 | 21 |
| 6 | 344 | 21 |
| 7 | 539 | 21 |
| 8 | 721 | 21 |
| 9 | 945 | 21 |
| 10 | 1109 | 21 |
| 11 | 1121 | 21 |
| 0 | 1121 | 21 |
| 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% | (sqrt.f64 (-.f64 (*.f64 x x) eps)) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 62.4% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 17.0ms | 87× | 1 | valid |
| 11.0ms | 152× | 0 | valid |
| 3.0ms | 17× | 2 | valid |
Compiled 27 to 7 computations (74.1% saved)
ival-sub: 8.0ms (48.4% of total)ival-sqrt: 3.0ms (18.1% of total)ival-mult: 3.0ms (18.1% of total)backward-pass: 2.0ms (12.1% of total)const: 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 | x | @ | inf | (sqrt (- (* x x) eps)) |
| 1.0ms | x | @ | inf | (- x (sqrt (- (* x x) eps))) |
| 1.0ms | eps | @ | 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 |
| 2262× | *-lowering-*.f32 |
| 2262× | *-lowering-*.f64 |
| 1852× | fma-lowering-fma.f32 |
| 1852× | fma-lowering-fma.f64 |
| 1702× | fmsub-define |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 19 |
| 1 | 40 | 19 |
| 2 | 324 | 19 |
| 3 | 4055 | 19 |
| 0 | 8218 | 19 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- x (sqrt (- (* x x) eps))) |
(sqrt (- (* x x) eps)) |
(- (* x x) eps) |
(* x x) |
| Outputs |
|---|
(+.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x) |
(+.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
(+.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)) |
(-.f64 (+.f64 x #s(literal 0 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
(fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(fma.f64 (*.f64 x x) (/.f64 x (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
(fma.f64 (*.f64 x (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x) |
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
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(*.f64 (+.f64 (*.f64 x x) eps) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps))) |
(*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) |
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 x x) eps)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps))) |
(*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(*.f64 (pow.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64))) |
(*.f64 (*.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) (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 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps))) (-.f64 (*.f64 x x) eps)) |
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps)))))) (+.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (-.f64 (*.f64 eps (+.f64 (*.f64 x x) eps)) (*.f64 (*.f64 x x) (*.f64 x x)))))) |
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (-.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (+.f64 (*.f64 x x) eps)))) |
(*.f64 (/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps eps)) (+.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 eps (-.f64 eps (*.f64 x x))))) |
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x))) |
(pow.f64 x #s(literal 2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64)) |
(*.f64 x x) |
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x))) |
| 1× | egg-herbie |
| 4906× | *-lowering-*.f32 |
| 4906× | *-lowering-*.f64 |
| 2924× | +-lowering-+.f64 |
| 2924× | +-lowering-+.f32 |
| 2068× | /-lowering-/.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 257 | 1162 |
| 1 | 856 | 1135 |
| 2 | 3030 | 1098 |
| 0 | 8034 | 1098 |
| 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) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.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 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 (*.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)))) |
(* 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 (*.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 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.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 (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x 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 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -2 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) 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 (*.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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))))))) |
(* 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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #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))))))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (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 (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.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)))))) |
(* 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 (/.f64 x eps) (-.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.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)))))))) |
(* (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 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (*.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))))) 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 (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)) (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)) (*.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))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.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)))))) |
(+ (* (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))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (*.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)))))))) |
(+ (* (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))))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (*.f64 x (+.f64 (*.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)))))))))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(*.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 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))))))) |
(*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)))) |
(* (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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.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)))))) |
(* 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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.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 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))))))) |
(* 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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (*.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 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))))))) |
(* -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 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.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))))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(*.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x))) (*.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)))))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.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)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) 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 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.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) |
(-.f64 #s(literal 0 binary64) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(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 9912 to 1041 computations (89.5% saved)
16 alts after pruning (15 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 278 | 15 | 293 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 278 | 16 | 294 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) | |
| 62.0% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) | |
| 35.3% | (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) | |
| 41.6% | (/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) | |
| 44.0% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) | |
| ▶ | 62.2% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
| 62.0% | (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) | |
| ▶ | 62.2% | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))) |
| ▶ | 4.1% | (-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
| ▶ | 7.2% | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| 6.4% | (-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) | |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 57.9% | (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) | |
| 4.3% | (-.f64 x x) | |
| ▶ | 3.5% | (*.f64 x #s(literal 2 binary64)) |
| 22.8% | (*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #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))))))))) |
Compiled 592 to 310 computations (47.6% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))) |
| ✓ | cost-diff | 0 | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))) |
| ✓ | cost-diff | 0 | (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))) |
| ✓ | cost-diff | 128 | (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))) |
| ✓ | cost-diff | 128 | (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x)))))) |
| ✓ | cost-diff | 384 | (-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
| ✓ | cost-diff | 0 | (/.f64 eps x) |
| ✓ | cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) |
| ✓ | cost-diff | 0 | (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) |
| ✓ | cost-diff | 256 | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| ✓ | cost-diff | 0 | (*.f64 x #s(literal 2 binary64)) |
| ✓ | cost-diff | 64 | (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) |
| ✓ | cost-diff | 64 | (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
| ✓ | cost-diff | 64 | (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
| ✓ | cost-diff | 320 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
| 1832× | sum3-define |
| 1590× | fmsub-define |
| 1534× | fmm-def |
| 1500× | +-lowering-+.f64 |
| 1500× | +-lowering-+.f32 |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 184 |
| 1 | 79 | 174 |
| 2 | 209 | 171 |
| 3 | 473 | 170 |
| 4 | 2184 | 170 |
| 5 | 7784 | 170 |
| 0 | 8142 | 170 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2)))) |
1 |
(/ 1 (- x (pow (- (* x x) eps) 1/2))) |
(- x (pow (- (* x x) eps) 1/2)) |
x |
(pow (- (* x x) eps) 1/2) |
(- (* x x) eps) |
(* x x) |
eps |
1/2 |
(* x 2) |
x |
2 |
(- x (+ x (* -1/2 (/ eps x)))) |
x |
(+ x (* -1/2 (/ eps x))) |
(* -1/2 (/ eps x)) |
-1/2 |
(/ eps x) |
eps |
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
x |
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))) |
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))) |
eps |
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))) |
(/ -1/2 x) |
-1/2 |
(/ (* eps -1/8) (* x (* x x))) |
(* eps -1/8) |
-1/8 |
(* x (* x x)) |
(* x x) |
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps))))) |
x |
(/ 1 (sqrt (/ 1 (- (* x x) eps)))) |
1 |
(sqrt (/ 1 (- (* x x) eps))) |
(/ 1 (- (* x x) eps)) |
(- (* x x) eps) |
(* x x) |
eps |
| Outputs |
|---|
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2)))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
1 |
#s(literal 1 binary64) |
(/ 1 (- x (pow (- (* x x) eps) 1/2))) |
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(- x (pow (- (* x x) eps) 1/2)) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
x |
(pow (- (* x x) eps) 1/2) |
(sqrt.f64 (-.f64 (*.f64 x x) eps)) |
(- (* x x) eps) |
(-.f64 (*.f64 x x) eps) |
(* x x) |
(*.f64 x x) |
eps |
1/2 |
#s(literal 1/2 binary64) |
(* x 2) |
(*.f64 x #s(literal 2 binary64)) |
x |
2 |
#s(literal 2 binary64) |
(- x (+ x (* -1/2 (/ eps x)))) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
x |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(* -1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) |
-1/2 |
#s(literal -1/2 binary64) |
(/ eps x) |
(/.f64 eps x) |
eps |
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
(/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))) x) |
x |
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))) |
(-.f64 x (/.f64 (*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))) x)) |
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))) |
(*.f64 (/.f64 eps x) (-.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/8 binary64) x)) x))) |
eps |
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))) |
(+.f64 (/.f64 #s(literal -1/2 binary64) x) (*.f64 eps (/.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) x))) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
-1/2 |
#s(literal -1/2 binary64) |
(/ (* eps -1/8) (* x (* x x))) |
(*.f64 eps (/.f64 (/.f64 (/.f64 #s(literal -1/8 binary64) x) x) x)) |
(* eps -1/8) |
(*.f64 eps #s(literal -1/8 binary64)) |
-1/8 |
#s(literal -1/8 binary64) |
(* x (* x x)) |
(*.f64 x (*.f64 x x)) |
(* x x) |
(*.f64 x x) |
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps))))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))) |
x |
(/ 1 (sqrt (/ 1 (- (* x x) eps)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ 1 (- (* x x) eps))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))) |
(/ 1 (- (* x x) eps)) |
(/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) |
(- (* x x) eps) |
(-.f64 (*.f64 x x) eps) |
(* x x) |
(*.f64 x x) |
eps |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.9% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))) |
| ✓ | accuracy | 62.4% | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))) |
| ✓ | accuracy | 99.8% | (*.f64 x (*.f64 x x)) |
| ✓ | accuracy | 91.5% | (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))) |
| ✓ | accuracy | 89.2% | (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))) |
| ✓ | accuracy | 62.5% | (-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
| ✓ | accuracy | 100.0% | (/.f64 eps x) |
| ✓ | accuracy | 100.0% | (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))) |
| ✓ | accuracy | 100.0% | (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) |
| ✓ | accuracy | 62.5% | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| ✓ | accuracy | 100.0% | (*.f64 x #s(literal 2 binary64)) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 99.6% | (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 99.3% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
| ✓ | accuracy | 62.4% | (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
| 76.0ms | 87× | 1 | valid |
| 70.0ms | 152× | 0 | valid |
| 21.0ms | 17× | 2 | valid |
Compiled 226 to 31 computations (86.3% saved)
ival-div: 31.0ms (33.3% of total)ival-pow: 18.0ms (19.3% of total)ival-mult: 17.0ms (18.2% of total)ival-sub: 10.0ms (10.7% of total)backward-pass: 8.0ms (8.6% of total)ival-add: 5.0ms (5.4% of total)ival-sqrt: 3.0ms (3.2% of total)const: 1.0ms (1.1% of total)| Inputs |
|---|
#<alt (/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2))))> |
#<alt (/ 1 (- x (pow (- (* x x) eps) 1/2)))> |
#<alt (- x (pow (- (* x x) eps) 1/2))> |
#<alt (pow (- (* x x) eps) 1/2)> |
#<alt (* x 2)> |
#<alt (- x (+ x (* -1/2 (/ eps x))))> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (* -1/2 (/ eps x))> |
#<alt (/ eps x)> |
#<alt (- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))))> |
#<alt (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))> |
#<alt (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))> |
#<alt (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))> |
#<alt (- x (/ 1 (sqrt (/ 1 (- (* x x) eps)))))> |
#<alt (/ 1 (sqrt (/ 1 (- (* x x) eps))))> |
#<alt (sqrt (/ 1 (- (* x x) eps)))> |
#<alt (/ 1 (- (* x x) eps))> |
#<alt (- (* x x) eps)> |
#<alt (/ (* eps -1/8) (* x (* x x)))> |
#<alt (* x (* 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))) (* 1/2 (/ eps (pow x 2)))) 2)))> |
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))> |
#<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 (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))> |
#<alt (* 2 (/ x eps))> |
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))> |
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))> |
#<alt (* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))> |
#<alt (/ 1/2 x)> |
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))> |
#<alt (* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))> |
#<alt (* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))> |
#<alt (* 2 (/ x eps))> |
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)> |
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)> |
#<alt (/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)> |
#<alt (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))> |
#<alt (/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)> |
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)> |
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)> |
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))> |
#<alt (* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))> |
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))> |
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))> |
#<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 (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 2 x)> |
#<alt (* 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 (* -1/2 (/ eps x))> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt x> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt x> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))> |
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#<alt (/ eps x)> |
#<alt (/ eps x)> |
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#<alt (/ eps x)> |
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#<alt (/ eps x)> |
#<alt (/ eps x)> |
#<alt (/ eps x)> |
#<alt (/ eps x)> |
#<alt (/ eps x)> |
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#<alt x> |
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#<alt (* 2 x)> |
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#<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> |
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#<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))))))> |
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#<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 (* (sqrt (/ 1 eps)) (sqrt -1))> |
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#<alt (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))))))> |
#<alt (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1)))))))))> |
#<alt (/ 1 x)> |
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#<alt (/ -1 x)> |
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#<alt (* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x))> |
#<alt (/ 1 x)> |
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#<alt (+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))> |
#<alt (+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x))> |
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))> |
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))> |
#<alt (/ -1 eps)> |
#<alt (- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps))> |
#<alt (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps))> |
#<alt (/ 1 (pow x 2))> |
#<alt (/ (+ 1 (/ eps (pow x 2))) (pow x 2))> |
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))> |
#<alt (/ 1 (pow x 2))> |
#<alt (/ (+ 1 (/ eps (pow x 2))) (pow x 2))> |
#<alt (/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2))> |
#<alt (/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2))> |
#<alt (/ 1 (pow x 2))> |
#<alt (+ (/ 1 (pow x 2)) (/ eps (pow x 4)))> |
#<alt (+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2)))> |
#<alt (+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2)))> |
#<alt (/ -1 eps)> |
#<alt (/ (- (* -1 (/ (pow x 2) eps)) 1) eps)> |
#<alt (/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps)> |
#<alt (/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps)> |
#<alt (/ -1 eps)> |
#<alt (* -1 (/ (+ 1 (/ (pow x 2) eps)) eps))> |
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps))> |
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps))> |
#<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 (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (* -1/8 (/ eps (pow x 3)))> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
#<alt (pow x 3)> |
114 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | eps | @ | 0 | (- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
| 6.0ms | x | @ | -inf | (- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
| 2.0ms | x | @ | -inf | (* x (* x x)) |
| 2.0ms | eps | @ | inf | (/ 1 (- x (pow (- (* x x) eps) 1/2))) |
| 1.0ms | eps | @ | inf | (- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
| 1× | batch-egg-rewrite |
| 2522× | *-lowering-*.f32 |
| 2522× | *-lowering-*.f64 |
| 2416× | fma-lowering-fma.f32 |
| 2416× | fma-lowering-fma.f64 |
| 1884× | pow-lowering-pow.f64 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 30 | 147 |
| 1 | 223 | 136 |
| 2 | 2373 | 136 |
| 0 | 8214 | 136 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (/ 1 (- x (pow (- (* x x) eps) 1/2)))) |
(/ 1 (- x (pow (- (* x x) eps) 1/2))) |
(- x (pow (- (* x x) eps) 1/2)) |
(pow (- (* x x) eps) 1/2) |
(* x 2) |
(- x (+ x (* -1/2 (/ eps x)))) |
(+ x (* -1/2 (/ eps x))) |
(* -1/2 (/ eps x)) |
(/ eps x) |
(- x (+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))))) |
(+ x (* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))))) |
(* eps (+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x))))) |
(+ (/ -1/2 x) (/ (* eps -1/8) (* x (* x x)))) |
(- x (/ 1 (sqrt (/ 1 (- (* x x) eps))))) |
(/ 1 (sqrt (/ 1 (- (* x x) eps)))) |
(sqrt (/ 1 (- (* x x) eps))) |
(/ 1 (- (* x x) eps)) |
(- (* x x) eps) |
(/ (* eps -1/8) (* x (* x x))) |
(* x (* x x)) |
| Outputs |
|---|
(+.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x) |
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(exp.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(exp.f64 (*.f64 (log.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
(-.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(fma.f64 #s(literal 1 binary64) x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x) |
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x) |
(fma.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))) x) |
(fma.f64 (neg.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)) x) |
(neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (neg.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (-.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) |
(pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(*.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(*.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(*.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))) |
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(pow.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) #s(literal -1 binary64))) |
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(*.f64 (*.f64 eps #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) (/.f64 eps x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (*.f64 x x) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps #s(literal -1/8 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/8 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x (*.f64 x x))) eps) |
(*.f64 (/.f64 eps (*.f64 x x)) (/.f64 #s(literal -1/8 binary64) x)) |
(*.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 eps (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) x)) |
(*.f64 (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64))) |
(pow.f64 x #s(literal 3 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64)) |
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64)) |
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64)) |
(*.f64 x (*.f64 x x)) |
(*.f64 (*.f64 x x) x) |
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) |
| 1× | egg-herbie |
| 5764× | *-lowering-*.f32 |
| 5764× | *-lowering-*.f64 |
| 2800× | +-lowering-+.f64 |
| 2800× | +-lowering-+.f32 |
| 1460× | fma-lowering-fma.f32 |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 656 | 6016 |
| 1 | 2231 | 5790 |
| 0 | 8158 | 5790 |
| 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))) (* 1/2 (/ eps (pow x 2)))) 2))) |
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2))) |
(* 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))))) |
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2))))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2)))))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2)))))) |
(* 2 (/ x eps)) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))) |
(/ 1/2 x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x)) |
(* 2 (/ x eps)) |
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps) |
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps) |
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps) |
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps) |
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps)) |
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps)) |
(* -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))))))) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 2 x) |
(* 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)) |
(* -1/2 (/ eps x)) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
x |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* -1/2 (/ eps x))) |
(* -1/2 (/ eps x)) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* -1/2 (/ eps x)) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 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)) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(/ eps x) |
(* 1/8 (/ (pow eps 2) (pow x 3))) |
(/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(/ (- (* 1/2 (* eps (pow x 2))) (* -1/8 (pow eps 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 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* -1 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* -1 (/ (- (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* 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))) |
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3)) |
(/ (+ (* -1/8 (pow eps 2)) (* (pow x 2) (+ (* -1/2 eps) (pow x 2)))) (pow x 3)) |
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)))))) |
x |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1))) |
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 1))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(* -1/8 (/ (pow eps 2) (pow x 3))) |
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x))))) |
(* (pow eps 2) (- (/ x (pow eps 2)) (+ (* 1/8 (/ 1 (pow x 3))) (/ 1/2 (* eps x))))) |
(* -1/8 (/ (pow eps 2) (pow x 3))) |
(* -1 (* (pow eps 2) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))) |
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))) |
(* -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))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1/8 (/ (pow eps 2) (pow x 3))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1/8 (/ (pow eps 2) (pow x 3))) |
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(/ (+ (* -1/2 (* eps (pow x 2))) (* -1/8 (pow eps 2))) (pow x 3)) |
(* -1/2 (/ eps x)) |
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x) |
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x) |
(/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x) |
(* -1/2 (/ eps x)) |
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* -1 (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)) |
(* -1/8 (/ eps (pow x 3))) |
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3)) |
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3)) |
(/ (+ (* -1/2 (pow x 2)) (* -1/8 eps)) (pow x 3)) |
(/ -1/2 x) |
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x) |
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x) |
(/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x) |
(/ -1/2 x) |
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)) |
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)) |
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (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))) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -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))))))) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3)))) (sqrt -1)))) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1))))))) |
(+ (* (sqrt (/ 1 eps)) (sqrt -1)) (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/2 (* (sqrt eps) (/ (* (pow x 2) (+ (* 1/2 (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (* eps (pow (sqrt -1) 2)))) (/ 1 (pow eps 4)))) (sqrt -1)))) (* -1/2 (* (sqrt eps) (/ (+ (* 1/4 (/ 1 (* (pow eps 3) (pow (sqrt -1) 2)))) (/ 1 (pow eps 3))) (sqrt -1))))))))) |
(/ 1 x) |
(/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x) |
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x) |
(/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x) |
(/ -1 x) |
(* -1 (/ (+ 1 (* 1/2 (/ eps (pow x 2)))) x)) |
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)) |
(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1 (pow eps 3)) (* -1/2 (* eps (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2)))))) (pow x 6))) (* 1/2 (/ eps (pow x 2)))))) x)) |
(/ 1 x) |
(+ (* 1/2 (/ eps (pow x 3))) (/ 1 x)) |
(+ (* eps (+ (* 3/8 (/ eps (pow x 5))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) |
(+ (* eps (+ (* eps (+ (* 5/16 (/ eps (pow x 7))) (* 3/8 (/ 1 (pow x 5))))) (* 1/2 (/ 1 (pow x 3))))) (/ 1 x)) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 7))) (/ (+ (* 1/4 (/ (* eps (pow x 4)) (pow (sqrt -1) 2))) (pow x 6)) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 eps)) (* (sqrt -1) (+ (* -1/4 (* eps (pow x 4))) (pow x 6)))))) (pow eps 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))) |
(/ -1 eps) |
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps)) |
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(/ 1 (pow x 2)) |
(/ (+ 1 (/ eps (pow x 2))) (pow x 2)) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2)) |
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2)) |
(/ 1 (pow x 2)) |
(/ (+ 1 (/ eps (pow x 2))) (pow x 2)) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2)) |
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2)) |
(/ 1 (pow x 2)) |
(+ (/ 1 (pow x 2)) (/ eps (pow x 4))) |
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2))) |
(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) |
(/ -1 eps) |
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps) |
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps) |
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps) |
(/ -1 eps) |
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps)) |
(* -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))))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(* -1/8 (/ eps (pow x 3))) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
(pow x 3) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.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 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1/2 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)))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.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 (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)))) |
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2))) |
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2))) |
(*.f64 (+.f64 (+.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) x) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
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(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
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(* (sqrt eps) (sqrt -1)) |
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(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
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(* 2 (/ x eps)) |
(/.f64 (*.f64 x #s(literal 2 binary64)) eps) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
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(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
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(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x)) |
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(/.f64 (-.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 5/128 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1/2 binary64)) (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))))) (-.f64 #s(literal 0 binary64) x)) |
(* 2 (/ x eps)) |
(/.f64 (*.f64 x #s(literal 2 binary64)) eps) |
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(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps) |
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(/.f64 (-.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) eps) |
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(* (sqrt (/ 1 eps)) (sqrt -1)) |
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(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
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(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
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(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x) |
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.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) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
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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 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))) |
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(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) x) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
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(* 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)))) |
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(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (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 (/.f64 x eps) (-.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps 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 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64))) (-.f64 (-.f64 (/.f64 x eps) (*.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)))))) |
(* (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 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (/.f64 (+.f64 x (*.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)))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 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 (-.f64 (/.f64 (-.f64 x (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 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))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.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))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 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))))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 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))))))) |
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)))) |
(* (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 (+.f64 (*.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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (/.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))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) |
(* 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 (+.f64 (+.f64 (*.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)))) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 (*.f64 (sqrt.f64 #s(literal -1 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)))))) |
(* -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 #s(literal 0 binary64) (*.f64 eps (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 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)))) (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))))) |
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))) |
(*.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 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)))) (+.f64 (*.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64))))) (-.f64 #s(literal 0 binary64) eps)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
x |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(*.f64 x (*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
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(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)) |
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x)) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x) |
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x) |
(- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))) |
(/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.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 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1/2 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)))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.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 (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (*.f64 x (*.f64 x (*.f64 x x))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)))) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 2 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x 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 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 #s(literal 2 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))))))) |
(* 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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #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))))))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (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 (/.f64 x eps) (-.f64 (*.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps 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 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/8 binary64))) (-.f64 (-.f64 (/.f64 x eps) (*.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)))))) |
(* (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 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
(*.f64 (-.f64 (/.f64 (+.f64 x (*.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)))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 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 (-.f64 (/.f64 (-.f64 x (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 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))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.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))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 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))))))))) |
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) (/.f64 (*.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 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))))))) |
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
(* -1 x) |
(-.f64 #s(literal 0 binary64) x) |
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) |
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(+.f64 x (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)))) |
(* (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 (+.f64 (*.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 (+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (/.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))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))) |
(* 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 (+.f64 (+.f64 (*.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)))) (+.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (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))))) |
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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 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x) |
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(/.f64 #s(literal -1 binary64) x) |
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(* -1 (/ (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow eps 2)) (* 1/4 (pow eps 2))) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) x)) |
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(/.f64 #s(literal 1 binary64) x) |
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(* (sqrt (/ 1 eps)) (sqrt -1)) |
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(* (sqrt (/ 1 eps)) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) |
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(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(- (* -1 (/ (pow x 2) (pow eps 2))) (/ 1 eps)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 3))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
(+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))) (/.f64 #s(literal -1 binary64) eps)) |
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow eps 4))) (/ 1 (pow eps 3)))) (/ 1 (pow eps 2)))) (/ 1 eps)) |
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(/ 1 (pow x 2)) |
(/.f64 #s(literal 1 binary64) (*.f64 x x)) |
(/ (+ 1 (/ eps (pow x 2))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2)) |
(/.f64 (+.f64 (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) (*.f64 x x)) |
(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 x x)) |
(/ 1 (pow x 2)) |
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(/ (+ 1 (/ eps (pow x 2))) (pow x 2)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))) (*.f64 x x)) |
(/ (- (+ 1 (/ (pow eps 2) (pow x 4))) (* -1 (/ eps (pow x 2)))) (pow x 2)) |
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(/ (- (+ 1 (/ (pow eps 3) (pow x 6))) (+ (* -1 (/ eps (pow x 2))) (* -1 (/ (pow eps 2) (pow x 4))))) (pow x 2)) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (*.f64 eps eps)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 eps (*.f64 x x))) (/.f64 (*.f64 eps eps) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 x x)) |
(/ 1 (pow x 2)) |
(/.f64 #s(literal 1 binary64) (*.f64 x x)) |
(+ (/ 1 (pow x 2)) (/ eps (pow x 4))) |
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 eps (*.f64 x (*.f64 x (*.f64 x x))))) |
(+ (* eps (+ (/ 1 (pow x 4)) (/ eps (pow x 6)))) (/ 1 (pow x 2))) |
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(+ (* eps (+ (* eps (+ (/ 1 (pow x 6)) (/ eps (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))) |
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(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(/ (- (* -1 (/ (pow x 2) eps)) 1) eps) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(/ (- (* -1 (/ (pow x 4) (pow eps 2))) (+ 1 (/ (pow x 2) eps))) eps) |
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps) #s(literal 1 binary64)) eps) |
(/ (- (* -1 (/ (pow x 6) (pow eps 3))) (+ 1 (+ (/ (pow x 2) eps) (/ (pow x 4) (pow eps 2))))) eps) |
(/.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 eps (*.f64 eps eps)))) (-.f64 (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps) #s(literal 1 binary64))) eps) |
(/ -1 eps) |
(/.f64 #s(literal -1 binary64) eps) |
(* -1 (/ (+ 1 (/ (pow x 2) eps)) eps)) |
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) eps)) (pow x 2)) eps))) eps)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 x x)) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) eps) (* -1 (pow x 4))) eps)) (pow x 2)) eps))) eps)) |
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (/.f64 (pow.f64 x #s(literal 6 binary64)) eps)) eps)) (*.f64 x x)) eps)) (-.f64 #s(literal 0 binary64) eps)) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) 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 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.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) |
(-.f64 #s(literal 0 binary64) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(* -1/8 (/ eps (pow x 3))) |
(/.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) x) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
(pow x 3) |
(*.f64 x (*.f64 x x)) |
Compiled 27954 to 3320 computations (88.1% saved)
28 alts after pruning (25 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1182 | 17 | 1199 |
| Fresh | 2 | 8 | 10 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1187 | 28 | 1215 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) | |
| 62.0% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) | |
| ▶ | 15.5% | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| 41.6% | (/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) | |
| 35.9% | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 43.5% | (/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) | |
| 44.0% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) | |
| 44.4% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) | |
| 43.1% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) | |
| 30.3% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)) | |
| 43.6% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) | |
| ▶ | 62.2% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
| 43.5% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) | |
| 43.9% | (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) | |
| 62.0% | (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) | |
| ▶ | 7.2% | (-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
| 5.3% | (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) | |
| 57.6% | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) | |
| ✓ | 7.2% | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| 6.4% | (-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) | |
| 6.4% | (-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) | |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| ▶ | 57.9% | (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
| ▶ | 4.3% | (-.f64 x x) |
| 35.9% | (*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) | |
| 43.4% | (*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) | |
| ✓ | 3.5% | (*.f64 x #s(literal 2 binary64)) |
| 43.8% | (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
Compiled 1070 to 535 computations (50% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (-.f64 #s(literal 0 binary64) eps) |
| ✓ | cost-diff | 0 | (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) |
| ✓ | cost-diff | 0 | (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
| ✓ | cost-diff | 0 | (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) |
| ✓ | cost-diff | 128 | (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) |
| ✓ | cost-diff | 768 | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 0 | (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) |
| ✓ | cost-diff | 0 | (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
| ✓ | cost-diff | 0 | (-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
| ✓ | cost-diff | 128 | (-.f64 x x) |
| ✓ | cost-diff | 0 | (sqrt.f64 (-.f64 (*.f64 x x) eps)) |
| ✓ | cost-diff | 0 | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
| ✓ | cost-diff | 256 | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
| 4012× | *-lowering-*.f32 |
| 4012× | *-lowering-*.f64 |
| 2374× | fma-lowering-fma.f32 |
| 2374× | fma-lowering-fma.f64 |
| 2074× | /-lowering-/.f32 |
Useful iterations: 4 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 149 |
| 1 | 70 | 147 |
| 2 | 187 | 145 |
| 3 | 650 | 142 |
| 4 | 3162 | 139 |
| 5 | 7215 | 139 |
| 0 | 8143 | 139 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) |
1 |
(/ 1 (- x (sqrt (- (* x x) eps)))) |
(- x (sqrt (- (* x x) eps))) |
x |
(sqrt (- (* x x) eps)) |
(- (* x x) eps) |
(* x x) |
eps |
(- x x) |
x |
(- x (/ (+ (* x x) (* eps -1/2)) x)) |
x |
(/ (+ (* x x) (* eps -1/2)) x) |
(+ (* x x) (* eps -1/2)) |
(* x x) |
(* eps -1/2) |
eps |
-1/2 |
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps)))) |
(- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
0 |
(* (/ 1/4 (* x x)) (* eps eps)) |
(/ 1/4 (* x x)) |
1/4 |
(* x x) |
x |
(* eps eps) |
eps |
(+ 0 (/ -1/2 (/ x eps))) |
(/ -1/2 (/ x eps)) |
-1/2 |
(/ x eps) |
(- x (sqrt (- 0 eps))) |
x |
(sqrt (- 0 eps)) |
(- 0 eps) |
0 |
eps |
| Outputs |
|---|
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
1 |
#s(literal 1 binary64) |
(/ 1 (- x (sqrt (- (* x x) eps)))) |
(/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(- 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 |
(- x x) |
#s(literal 0 binary64) |
x |
(- x (/ (+ (* x x) (* eps -1/2)) x)) |
(+.f64 x (/.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)) x)) |
x |
(/ (+ (* x x) (* eps -1/2)) x) |
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
(+ (* x x) (* eps -1/2)) |
(+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) |
(* x x) |
(*.f64 x x) |
(* eps -1/2) |
(*.f64 eps #s(literal -1/2 binary64)) |
eps |
-1/2 |
#s(literal -1/2 binary64) |
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps)))) |
(*.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 eps #s(literal 1/2 binary64)) x)) |
(- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
(/.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x) x) |
0 |
#s(literal 0 binary64) |
(* (/ 1/4 (* x x)) (* eps eps)) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) |
(/ 1/4 (* x x)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
1/4 |
#s(literal 1/4 binary64) |
(* x x) |
(*.f64 x x) |
x |
(* eps eps) |
(*.f64 eps eps) |
eps |
(+ 0 (/ -1/2 (/ x eps))) |
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
(/ -1/2 (/ x eps)) |
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
-1/2 |
#s(literal -1/2 binary64) |
(/ x eps) |
(/.f64 x eps) |
(- x (sqrt (- 0 eps))) |
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
x |
(sqrt (- 0 eps)) |
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) |
(- 0 eps) |
(-.f64 #s(literal 0 binary64) eps) |
0 |
#s(literal 0 binary64) |
eps |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (-.f64 #s(literal 0 binary64) eps) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) |
| ✓ | accuracy | 100.0% | (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
| ✓ | accuracy | 99.8% | (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
| ✓ | accuracy | 99.3% | (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
| ✓ | accuracy | 82.6% | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | accuracy | 62.1% | (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps)) |
| ✓ | accuracy | 100.0% | (*.f64 eps #s(literal -1/2 binary64)) |
| ✓ | accuracy | 100.0% | (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) |
| ✓ | accuracy | 99.9% | (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
| ✓ | accuracy | 80.6% | (-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
| ✓ | accuracy | 100.0% | (-.f64 x x) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
| ✓ | accuracy | 99.4% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
| ✓ | accuracy | 80.6% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 60.0ms | 150× | 0 | valid |
| 24.0ms | 44× | 1 | valid |
| 13.0ms | 52× | 0 | invalid |
| 8.0ms | 10× | 2 | valid |
Compiled 176 to 29 computations (83.5% saved)
ival-sub: 29.0ms (44.3% of total)ival-div: 14.0ms (21.4% of total)ival-mult: 10.0ms (15.3% of total)ival-sqrt: 5.0ms (7.6% of total)backward-pass: 4.0ms (6.1% of total)ival-add: 3.0ms (4.6% of total)const: 1.0ms (1.5% of total)| Inputs |
|---|
#<alt (/ 1 (/ 1 (- x (sqrt (- (* x x) eps)))))> |
#<alt (/ 1 (- x (sqrt (- (* x x) eps))))> |
#<alt (- x (sqrt (- (* x x) eps)))> |
#<alt (sqrt (- (* x x) eps))> |
#<alt (- x x)> |
#<alt (- x (/ (+ (* x x) (* eps -1/2)) x))> |
#<alt (/ (+ (* x x) (* eps -1/2)) x)> |
#<alt (+ (* x x) (* eps -1/2))> |
#<alt (* x x)> |
#<alt (/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps))))> |
#<alt (- 0 (* (/ 1/4 (* x x)) (* eps eps)))> |
#<alt (+ 0 (/ -1/2 (/ x eps)))> |
#<alt (* (/ 1/4 (* x x)) (* eps eps))> |
#<alt (- x (sqrt (- 0 eps)))> |
#<alt (sqrt (- 0 eps))> |
#<alt (- 0 eps)> |
#<alt (- (* x x) eps)> |
#<alt (* eps -1/2)> |
#<alt (/ -1/2 (/ x eps))> |
#<alt (/ 1/4 (* 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))) (* 1/2 (/ eps (pow x 2)))) 2)))> |
#<alt (* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))> |
#<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 (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2)))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))> |
#<alt (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2))))))> |
#<alt (* 2 (/ x eps))> |
#<alt (* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2)))))> |
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2)))))> |
#<alt (* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))> |
#<alt (/ 1/2 x)> |
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))> |
#<alt (* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x))> |
#<alt (* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x))> |
#<alt (* 2 (/ x eps))> |
#<alt (/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps)> |
#<alt (/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps)> |
#<alt (/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps)> |
#<alt (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))))> |
#<alt (/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps)> |
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps)> |
#<alt (/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps)> |
#<alt (* (sqrt (/ 1 eps)) (sqrt -1))> |
#<alt (* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps))> |
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps))> |
#<alt (* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps))> |
#<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 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt 0> |
#<alt (* 1/2 (/ 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 x))> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)> |
#<alt x> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt x> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))> |
#<alt x> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (+ x (* -1/2 (/ eps x)))> |
#<alt (* -1/2 (/ eps x))> |
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))> |
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))> |
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))> |
#<alt (* -1/2 (/ eps x))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))> |
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))> |
#<alt (* -1/2 eps)> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (pow x 2)> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (+ (* -1/2 eps) (pow x 2))> |
#<alt (* -1/2 eps)> |
#<alt (* eps (- (/ (pow x 2) eps) 1/2))> |
#<alt (* eps (- (/ (pow x 2) eps) 1/2))> |
#<alt (* eps (- (/ (pow x 2) eps) 1/2))> |
#<alt (* -1/2 eps)> |
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps)))))> |
#<alt (* -1 (* eps (+ 1/2 (* -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)> |
#<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 (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<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 (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<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 (* -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 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 (* -1/2 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 (* -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 (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
102 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | inf | (- x (/ (+ (* x x) (* eps -1/2)) x)) |
| 1.0ms | eps | @ | 0 | (- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
| 1.0ms | x | @ | 0 | (- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
| 1.0ms | eps | @ | inf | (- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
| 0.0ms | eps | @ | 0 | (- x (sqrt (- 0 eps))) |
| 1× | batch-egg-rewrite |
| 3046× | /-lowering-/.f32 |
| 3046× | /-lowering-/.f64 |
| 2802× | *-lowering-*.f32 |
| 2802× | *-lowering-*.f64 |
| 1600× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 28 | 123 |
| 1 | 218 | 120 |
| 2 | 2097 | 109 |
| 0 | 9748 | 109 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (/ 1 (- x (sqrt (- (* x x) eps))))) |
(/ 1 (- x (sqrt (- (* x x) eps)))) |
(- x (sqrt (- (* x x) eps))) |
(sqrt (- (* x x) eps)) |
(- x x) |
(- x (/ (+ (* x x) (* eps -1/2)) x)) |
(/ (+ (* x x) (* eps -1/2)) x) |
(+ (* x x) (* eps -1/2)) |
(* x x) |
(/ (- 0 (* (/ 1/4 (* x x)) (* eps eps))) (+ 0 (/ -1/2 (/ x eps)))) |
(- 0 (* (/ 1/4 (* x x)) (* eps eps))) |
(+ 0 (/ -1/2 (/ x eps))) |
(* (/ 1/4 (* x x)) (* eps eps)) |
(- x (sqrt (- 0 eps))) |
(sqrt (- 0 eps)) |
(- 0 eps) |
(- (* x x) eps) |
(* eps -1/2) |
(/ -1/2 (/ x eps)) |
(/ 1/4 (* x x)) |
| Outputs |
|---|
(+.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))) |
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) x) |
(+.f64 (*.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal 1 binary64))) |
(exp.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(exp.f64 (*.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64))) |
(-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) |
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal -1 binary64))) |
(-.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) (/.f64 (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.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))))) |
(-.f64 (/.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) #s(literal 1 binary64)) (/.f64 (/.f64 (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (/.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)) (/.f64 (/.f64 (+.f64 (*.f64 x x) eps) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64))) |
(-.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))))) (/.f64 (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))))) |
(-.f64 (/.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (/.f64 (+.f64 (*.f64 x x) eps) (*.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (/.f64 (+.f64 (*.f64 x x) eps) (-.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(fma.f64 #s(literal 1 binary64) x (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal 1 binary64))) |
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)) x) |
(neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) |
(/.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 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal -1 binary64)) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (*.f64 x x) (-.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))))))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.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 (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps)) (-.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.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))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.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 (neg.f64 (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps))) (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps))) (neg.f64 (-.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) |
(/.f64 (-.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x x)) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) (*.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) (*.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) (+.f64 (*.f64 x x) eps))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))))) |
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps)))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (+.f64 (*.f64 x x) (+.f64 (+.f64 (*.f64 x x) eps) (*.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))))) |
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (+.f64 (*.f64 x x) eps)))) (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) eps))))) |
(/.f64 (+.f64 (neg.f64 (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 3/2 binary64))) (*.f64 x (*.f64 x x))) (+.f64 (+.f64 (*.f64 x x) eps) (-.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) x)))) |
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(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) eps)))) |
(/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (pow.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) #s(literal 3 binary64))) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps))) (*.f64 (*.f64 x x) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)))))) |
(/.f64 (+.f64 (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) (pow.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) eps) #s(literal 3 binary64))) (+.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (-.f64 (*.f64 (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) eps) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) eps)) (*.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 eps)) (sqrt.f64 eps)) eps))))) |
(/.f64 (+.f64 (*.f64 eps (*.f64 eps eps)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 eps eps) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) eps)))) |
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) #s(literal 3 binary64)) (*.f64 eps (*.f64 eps eps))) (+.f64 (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) (+.f64 (*.f64 x x) #s(literal 0 binary64))) (-.f64 (*.f64 eps eps) (*.f64 (+.f64 (*.f64 x x) #s(literal 0 binary64)) eps)))) |
(pow.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) #s(literal 2 binary64)) |
(pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 1 binary64)) |
(pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) |
(pow.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (*.f64 x x) eps) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps))) #s(literal -1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 (*.f64 x x) eps)) (sqrt.f64 (+.f64 (*.f64 x x) eps))) |
(*.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps))))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 x x) eps)))) |
(*.f64 (+.f64 x (sqrt.f64 eps)) (-.f64 x (sqrt.f64 eps))) |
(*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps))) |
(*.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 eps (*.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64))) |
(*.f64 eps #s(literal -1/2 binary64)) |
(*.f64 #s(literal -1/2 binary64) eps) |
(+.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(+.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) |
(exp.f64 (*.f64 (log.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(-.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) |
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(fma.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) |
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) x) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 eps x)) #s(literal 0 binary64)) |
(fma.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 0 binary64)) |
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 0 binary64)) |
(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 0 binary64)) |
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) eps #s(literal 0 binary64)) |
(fma.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) eps #s(literal 0 binary64)) |
(fma.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) eps #s(literal 0 binary64)) |
(neg.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(/.f64 #s(literal -1 binary64) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps)) |
(/.f64 (neg.f64 (*.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (/.f64 #s(literal 1 binary64) eps))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(pow.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) #s(literal 1 binary64)) |
(pow.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) |
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x)) |
(*.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 eps x))) |
(*.f64 #s(literal -1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) x))) |
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x)) |
(*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps))) (*.f64 x (*.f64 x x))) (*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 x (*.f64 eps #s(literal -1/2 binary64)))) |
(*.f64 (/.f64 x (*.f64 eps #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1/2 binary64)) #s(literal -1 binary64))) |
(*.f64 (/.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 (/.f64 #s(literal -1/2 binary64) x) eps) |
(*.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) eps) |
(*.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x)) eps) |
(exp.f64 (*.f64 (log.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) #s(literal -1 binary64))) |
(neg.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64))))) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/.f64 #s(literal 1/4 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) x)))) |
(/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x))) |
(/.f64 #s(literal -1/4 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))) |
(/.f64 (/.f64 #s(literal 1/4 binary64) x) x) |
(/.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x)) (-.f64 #s(literal 0 binary64) x)) |
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/4 binary64) x))) (neg.f64 (-.f64 #s(literal 0 binary64) x))) |
(pow.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal 1/4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (/.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) |
(*.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/4 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) |
(*.f64 (/.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1 binary64) x)) |
| 1× | egg-herbie |
| 4134× | *-lowering-*.f32 |
| 4134× | *-lowering-*.f64 |
| 2200× | +-lowering-+.f64 |
| 2200× | +-lowering-+.f32 |
| 1694× | fma-lowering-fma.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 445 | 3907 |
| 1 | 1515 | 3762 |
| 2 | 5623 | 3712 |
| 0 | 8028 | 3712 |
| 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))) (* 1/2 (/ eps (pow x 2)))) 2))) |
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2))) |
(* 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))))) |
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2))))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2)))))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (sqrt -1))))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (* eps (pow (sqrt -1) 2)))))) |
(* 2 (/ x eps)) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
(* x (- (+ (* -1 (/ (+ (* -1/4 (* eps (+ (* -1/8 eps) (* 1/4 eps)))) (+ (* -1/16 (pow eps 2)) (* 2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))))) (pow x 6))) (* 2 (/ 1 eps))) (+ (* -1/8 (/ eps (pow x 4))) (+ (* 1/4 (/ eps (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))) |
(/ 1/2 x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x)) |
(* 2 (/ x eps)) |
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps) |
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps) |
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps) |
(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(/ (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2)))) eps) |
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (pow eps 2)))) (/ x (pow (sqrt -1) 2))) eps) |
(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(* -1 (/ (+ (* -1 x) (* -1 (* (sqrt eps) (sqrt -1)))) eps)) |
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps)) |
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps)) |
(* -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))))))) |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
(* 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 x)) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
x |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 1 (* -1/2 (/ eps (pow x 2))))) |
x |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1))) |
x |
(+ x (* -1/2 (/ eps x))) |
(+ x (* -1/2 (/ eps x))) |
(+ x (* -1/2 (/ eps x))) |
(* -1/2 (/ eps x)) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
(* -1/2 (/ eps x)) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (pow x 2)) |
(+ (* -1/2 eps) (pow x 2)) |
(+ (* -1/2 eps) (pow x 2)) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(pow x 2) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(* (pow x 2) (+ 1 (* -1/2 (/ eps (pow x 2))))) |
(pow x 2) |
(+ (* -1/2 eps) (pow x 2)) |
(+ (* -1/2 eps) (pow x 2)) |
(+ (* -1/2 eps) (pow x 2)) |
(* -1/2 eps) |
(* eps (- (/ (pow x 2) eps) 1/2)) |
(* eps (- (/ (pow x 2) eps) 1/2)) |
(* eps (- (/ (pow x 2) eps) 1/2)) |
(* -1/2 eps) |
(* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1/2 (* -1 (/ (pow x 2) eps))))) |
(* -1 (* eps (+ 1/2 (* -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) |
(* 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)) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -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)) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* -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))) |
(* -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 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))))) |
(* -1/2 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)) |
(* -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)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
| Outputs |
|---|
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.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 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1/2 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)))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.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 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2))) |
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(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) x) |
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(* 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)))) |
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(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (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))))) |
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(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))) |
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(* (sqrt eps) (sqrt -1)) |
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) |
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(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* -1 (/ x (* eps (pow (sqrt -1) 2))))) |
(-.f64 (/.f64 x eps) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
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(* 2 (/ x eps)) |
(/.f64 (*.f64 x #s(literal 2 binary64)) eps) |
(* x (- (* 2 (/ 1 eps)) (* 1/2 (/ 1 (pow x 2))))) |
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) |
(* x (- (+ (* -1 (/ (+ (* -1/8 eps) (* 1/4 eps)) (pow x 4))) (* 2 (/ 1 eps))) (* 1/2 (/ 1 (pow x 2))))) |
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(/ 1/2 x) |
(/.f64 #s(literal 1/2 binary64) x) |
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x)) |
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)) |
(* -1 (/ (- (* -1/16 (/ (pow eps 2) (pow x 4))) (+ 1/2 (* 1/8 (/ eps (pow x 2))))) x)) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (/ (- (* -1 (/ (+ (* 1/128 (pow eps 3)) (* 1/32 (pow eps 3))) (pow x 6))) (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2)))))) x)) |
(/.f64 (-.f64 (-.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal 1/8 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) x)) |
(* 2 (/ x eps)) |
(/.f64 (*.f64 x #s(literal 2 binary64)) eps) |
(/ (+ (* -1/2 (/ eps x)) (* 2 x)) eps) |
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps) |
(/ (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) eps) |
(/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps) |
(/ (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) eps) |
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(* -1 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) |
(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) |
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(/.f64 (-.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) eps) |
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(/ (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* -1 (/ (+ (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4))) (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (sqrt -1)))) (pow eps 3)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3))) (/ x (pow (sqrt -1) 2))))) eps) |
(/.f64 (-.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) x) (+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps eps)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (*.f64 (sqrt.f64 eps) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 (/.f64 (sqrt.f64 (*.f64 eps (*.f64 eps eps))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 x x) #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps))))) eps) |
(* (sqrt (/ 1 eps)) (sqrt -1)) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) |
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(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)) eps) |
(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps))) eps)) |
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(* -1 (/ (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (* eps (pow x 3))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* -1 (* eps x))) eps))) eps)) |
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (*.f64 eps x) (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64))) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (+.f64 (*.f64 eps (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/2 binary64))) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64))))) eps)) eps))) eps) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(- x (* (sqrt eps) (sqrt -1))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))) |
(-.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (*.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 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 #s(literal -1/2 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)))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #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 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 eps #s(literal 1/2 binary64))) (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.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 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (*.f64 x x))) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 (+.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x 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 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 #s(literal -2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))) (/.f64 (*.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64)))))) |
(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) |
(/.f64 (+.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps (/.f64 eps (*.f64 x x)))) (*.f64 eps #s(literal 1/2 binary64))) x) |
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) |
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(* (sqrt eps) (sqrt -1)) |
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(* -1 x) |
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(* (sqrt eps) (sqrt -1)) |
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(* 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)))) (+ (* 1/16 (* (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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#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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(* 1/2 (/ eps x)) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
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(/ (+ (* -1/2 eps) (pow x 2)) x) |
(/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x) |
(/ (+ (* -1/2 eps) (pow x 2)) x) |
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(/ (+ (* -1/2 eps) (pow x 2)) x) |
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(* eps (- (/ x eps) (* 1/2 (/ 1 x)))) |
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(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) 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 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.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) |
(-.f64 #s(literal 0 binary64) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(-.f64 #s(literal 0 binary64) (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 eps) |
(*.f64 eps #s(literal -1/2 binary64)) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
Compiled 27639 to 3043 computations (89% saved)
33 alts after pruning (29 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1254 | 10 | 1264 |
| Fresh | 1 | 19 | 20 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 2 | 3 |
| Total | 1259 | 33 | 1292 |
| Status | Accuracy | Program |
|---|---|---|
| 50.6% | (fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) | |
| ▶ | 62.0% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
| ▶ | 16.5% | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| 15.5% | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) | |
| 41.6% | (/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) | |
| ▶ | 35.9% | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
| 43.5% | (/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) | |
| 26.2% | (/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) | |
| 44.0% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) | |
| 44.4% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) | |
| 43.1% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) | |
| 30.3% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (-.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)) | |
| 43.6% | (/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) | |
| ✓ | 62.2% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
| 43.5% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) | |
| 43.9% | (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) | |
| 62.0% | (-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) | |
| 4.1% | (-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x)) | |
| 3.5% | (-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) | |
| ✓ | 7.2% | (-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
| 5.3% | (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) | |
| 57.6% | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) | |
| ✓ | 7.2% | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| 6.4% | (-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) | |
| 6.4% | (-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) | |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 57.9% | (-.f64 x (sqrt.f64 (neg.f64 eps))) | |
| 35.9% | (*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) | |
| 43.4% | (*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) | |
| 43.8% | (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) | |
| ▶ | 42.9% | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
| 3.5% | x | |
| ▶ | 4.3% | #s(literal 0 binary64) |
Compiled 1334 to 674 computations (49.5% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
| ✓ | cost-diff | 128 | (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | cost-diff | 2944 | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
| ✓ | cost-diff | 0 | (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x) |
| ✓ | cost-diff | 128 | (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
| ✓ | cost-diff | 128 | (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) |
| ✓ | cost-diff | 512 | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
| ✓ | cost-diff | 128 | (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) |
| ✓ | cost-diff | 128 | (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps) |
| ✓ | cost-diff | 192 | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
| ✓ | cost-diff | 0 | (-.f64 (*.f64 x x) eps) |
| ✓ | cost-diff | 0 | (*.f64 x x) |
| ✓ | cost-diff | 512 | (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) |
| ✓ | cost-diff | 512 | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
| 5144× | *-lowering-*.f32 |
| 5144× | *-lowering-*.f64 |
| 3700× | +-lowering-+.f64 |
| 3700× | +-lowering-+.f32 |
| 1782× | times-frac |
Useful iterations: 3 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 373 |
| 1 | 98 | 329 |
| 2 | 335 | 233 |
| 3 | 1636 | 229 |
| 0 | 8436 | 229 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2))) |
(- (* x x) (- (* x x) eps)) |
(* x x) |
x |
(- (* x x) eps) |
eps |
(+ x (pow (- (* x x) eps) 1/2)) |
(pow (- (* x x) eps) 1/2) |
1/2 |
0 |
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)) |
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps) |
(/ (/ 1/4 (* x x)) (/ -1/2 x)) |
(/ 1/4 (* x x)) |
1/4 |
(* x x) |
x |
(/ -1/2 x) |
-1/2 |
eps |
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps)))) |
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) |
0 |
(/ (* (/ 1/4 x) (* eps eps)) x) |
(* (/ 1/4 x) (* eps eps)) |
(/ 1/4 x) |
1/4 |
x |
(* eps eps) |
eps |
(+ 0 (/ -1/2 (/ x eps))) |
(/ -1/2 (/ x eps)) |
-1/2 |
(/ x eps) |
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))) |
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) |
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) |
(* x x) |
x |
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))) |
(+ x (/ -1/2 (/ x eps))) |
(/ -1/2 (/ x eps)) |
-1/2 |
(/ x eps) |
eps |
(+ x (+ x (/ -1/2 (/ x eps)))) |
(- 0 (/ -1/2 (/ x eps))) |
0 |
| Outputs |
|---|
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2))) |
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(- (* x x) (- (* x x) eps)) |
eps |
(* x x) |
(*.f64 x x) |
x |
(- (* x x) eps) |
(-.f64 (*.f64 x x) eps) |
eps |
(+ x (pow (- (* x x) eps) 1/2)) |
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
(pow (- (* x x) eps) 1/2) |
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
0 |
#s(literal 0 binary64) |
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)) |
(*.f64 x (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps) |
(*.f64 #s(literal -1/2 binary64) (/.f64 eps (/.f64 (*.f64 x x) x))) |
(/ (/ 1/4 (* x x)) (/ -1/2 x)) |
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 x x)) |
(/ 1/4 (* x x)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
1/4 |
#s(literal 1/4 binary64) |
(* x x) |
(*.f64 x x) |
x |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
-1/2 |
#s(literal -1/2 binary64) |
eps |
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps)))) |
(*.f64 (*.f64 x (*.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) #s(literal 1 binary64)) |
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) |
(*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 eps (/.f64 eps x)) x)) |
0 |
#s(literal 0 binary64) |
(/ (* (/ 1/4 x) (* eps eps)) x) |
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps (/.f64 eps x))) x) |
(* (/ 1/4 x) (* eps eps)) |
(*.f64 #s(literal 1/4 binary64) (*.f64 eps (/.f64 eps x))) |
(/ 1/4 x) |
(/.f64 #s(literal 1/4 binary64) x) |
1/4 |
#s(literal 1/4 binary64) |
x |
(* eps eps) |
(*.f64 eps eps) |
eps |
(+ 0 (/ -1/2 (/ x eps))) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(/ -1/2 (/ x eps)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
-1/2 |
#s(literal -1/2 binary64) |
(/ x eps) |
(/.f64 x eps) |
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) |
(*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) |
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) |
(+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))))) |
(* x x) |
(*.f64 x x) |
x |
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))) |
(*.f64 (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64)))) |
(+ x (/ -1/2 (/ x eps))) |
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/ -1/2 (/ x eps)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
-1/2 |
#s(literal -1/2 binary64) |
(/ x eps) |
(/.f64 x eps) |
eps |
(+ x (+ x (/ -1/2 (/ x eps)))) |
(+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (*.f64 x #s(literal 2 binary64))) |
(- 0 (/ -1/2 (/ x eps))) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
0 |
#s(literal 0 binary64) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 99.6% | (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | accuracy | 99.6% | (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) |
| ✓ | accuracy | 99.3% | (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
| ✓ | accuracy | 74.0% | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
| ✓ | accuracy | 99.3% | (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)) |
| ✓ | accuracy | 87.2% | (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x) |
| ✓ | accuracy | 83.8% | (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) |
| ✓ | accuracy | 74.7% | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
| ✓ | accuracy | 100.0% | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
| ✓ | accuracy | 99.7% | (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
| ✓ | accuracy | 99.6% | (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps) |
| ✓ | accuracy | 63.4% | (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) |
| ✓ | accuracy | 100.0% | (-.f64 (*.f64 x x) eps) |
| ✓ | accuracy | 100.0% | (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) |
| ✓ | accuracy | 99.5% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
| ✓ | accuracy | 62.9% | (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) |
| 77.0ms | 86× | 1 | valid |
| 61.0ms | 153× | 0 | valid |
| 26.0ms | 17× | 2 | valid |
Compiled 334 to 34 computations (89.8% saved)
ival-div: 26.0ms (24.8% of total)ival-pow: 25.0ms (23.8% of total)ival-mult: 16.0ms (15.3% of total)ival-add: 14.0ms (13.3% of total)ival-sub: 13.0ms (12.4% of total)backward-pass: 8.0ms (7.6% of total)ival-neg: 2.0ms (1.9% of total)const: 1.0ms (1% of total)| Inputs |
|---|
#<alt (/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2)))> |
#<alt (- (* x x) (- (* x x) eps))> |
#<alt (* x x)> |
#<alt (- (* x x) eps)> |
#<alt (neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps))> |
#<alt (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)> |
#<alt (/ (/ 1/4 (* x x)) (/ -1/2 x))> |
#<alt (/ 1/4 (* x x))> |
#<alt (/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps))))> |
#<alt (- 0 (/ (* (/ 1/4 x) (* eps eps)) x))> |
#<alt (+ 0 (/ -1/2 (/ x eps)))> |
#<alt (/ (* (/ 1/4 x) (* eps eps)) x)> |
#<alt (/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))))> |
#<alt (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps))))> |
#<alt (- 0 (/ -1/2 (/ x eps)))> |
#<alt (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))> |
#<alt (+ x (pow (- (* x x) eps) 1/2))> |
#<alt (* (/ 1/4 x) (* eps eps))> |
#<alt (/ -1/2 (/ x eps))> |
#<alt (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))> |
| Outputs |
|---|
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<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 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)> |
#<alt (* 2 x)> |
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))> |
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))> |
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))> |
#<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 (* (sqrt eps) (/ 1 (sqrt -1)))> |
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))> |
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))> |
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* (sqrt eps) (sqrt -1)))> |
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))> |
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt eps> |
#<alt 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 (- (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 (* 1/2 (/ 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 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 (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<alt (/ 1/4 (pow x 2))> |
#<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 (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* -1/4 (/ (pow eps 2) (pow x 2)))> |
#<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 (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<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 (* 1/8 (/ (pow eps 3) (pow x 3)))> |
#<alt (/ (+ (* 1/8 (pow eps 3)) (* 1/2 (* eps (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))> |
#<alt (/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3))> |
#<alt (* 3/2 (* eps x))> |
#<alt (* x (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps)))> |
#<alt (* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))> |
#<alt (* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))))> |
#<alt (* 3/2 (* eps x))> |
#<alt (* -1 (* x (+ (* -3/2 eps) (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))))))> |
#<alt (* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))> |
#<alt (* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4)))))))> |
#<alt (* 1/2 (/ (* eps (+ (* 2 (pow x 2)) (pow x 2))) x))> |
#<alt (* eps (+ (* -3/4 (/ eps x)) (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x))))> |
#<alt (* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))> |
#<alt (* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x))))))> |
#<alt (* 1/8 (/ (pow eps 3) (pow x 3)))> |
#<alt (* (pow eps 3) (- (* 1/8 (/ 1 (pow x 3))) (* 3/4 (/ 1 (* eps x)))))> |
#<alt (* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))> |
#<alt (* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x))))> |
#<alt (* 1/8 (/ (pow eps 3) (pow x 3)))> |
#<alt (* -1 (* (pow eps 3) (- (* 3/4 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3))))))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))> |
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3))))))> |
#<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 (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* 3 (pow x 2))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (+ (* 2 (pow x 2)) (pow x 2))> |
#<alt (+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps))))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (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 (* 2 x)> |
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))> |
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))> |
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))> |
#<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))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))> |
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))> |
#<alt (* 2 x)> |
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))> |
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))> |
#<alt (+ (* 2 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 (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))> |
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))> |
#<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)) (/ x eps)))))> |
#<alt (* -1 (* (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 (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 2) x))> |
#<alt (* 1/4 (/ (pow eps 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 (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))> |
#<alt (/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2))> |
#<alt (* 2 (pow x 2))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* 2 (pow x 2))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))> |
#<alt (* 2 (pow x 2))> |
#<alt (+ (* -3/2 eps) (* 2 (pow x 2)))> |
#<alt (+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))> |
#<alt (+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps))))> |
#<alt (* 1/4 (/ (pow eps 2) (pow x 2)))> |
#<alt (* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))> |
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2)))))> |
111 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 15.0ms | x | @ | inf | (+ x (pow (- (* x x) eps) 1/2)) |
| 6.0ms | eps | @ | inf | (/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2))) |
| 1.0ms | x | @ | 0 | (/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2))) |
| 1.0ms | eps | @ | 0 | (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) |
| 1.0ms | x | @ | 0 | (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) |
| 1× | batch-egg-rewrite |
| 4286× | *-lowering-*.f32 |
| 4286× | *-lowering-*.f64 |
| 3058× | /-lowering-/.f32 |
| 3058× | /-lowering-/.f64 |
| 1938× | +-lowering-+.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 261 |
| 1 | 259 | 230 |
| 2 | 2840 | 198 |
| 0 | 9781 | 198 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ (- (* x x) (- (* x x) eps)) (+ x (pow (- (* x x) eps) 1/2))) |
(- (* x x) (- (* x x) eps)) |
(* x x) |
(- (* x x) eps) |
(neg (* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps)) |
(* (/ (/ 1/4 (* x x)) (/ -1/2 x)) eps) |
(/ (/ 1/4 (* x x)) (/ -1/2 x)) |
(/ 1/4 (* x x)) |
(/ (- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) (+ 0 (/ -1/2 (/ x eps)))) |
(- 0 (/ (* (/ 1/4 x) (* eps eps)) x)) |
(+ 0 (/ -1/2 (/ x eps))) |
(/ (* (/ 1/4 x) (* eps eps)) x) |
(/ (* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))))) |
(* (+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) (- 0 (/ -1/2 (/ x eps)))) |
(- 0 (/ -1/2 (/ x eps))) |
(+ (* x x) (* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps)))))) |
(+ x (pow (- (* x x) eps) 1/2)) |
(* (/ 1/4 x) (* eps eps)) |
(/ -1/2 (/ x eps)) |
(* (+ x (/ -1/2 (/ x eps))) (+ x (+ x (/ -1/2 (/ x eps))))) |
| Outputs |
|---|
(+.f64 x (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))) |
(+.f64 x (*.f64 (neg.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 (*.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)))))) |
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 x x) eps)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) (-.f64 (*.f64 x x) eps) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))) (-.f64 (*.f64 x x) eps)))) |
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(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (*.f64 x x))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 (*.f64 x x) (/.f64 (-.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) x) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)))))) |
(/.f64 (+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) x) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) |
(*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) |
| 1× | egg-herbie |
| 5924× | *-lowering-*.f32 |
| 5924× | *-lowering-*.f64 |
| 2130× | +-lowering-+.f64 |
| 2130× | +-lowering-+.f32 |
| 1744× | times-frac |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 461 | 3973 |
| 1 | 1577 | 3840 |
| 2 | 5844 | 3798 |
| 0 | 8771 | 3798 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(* 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 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x) |
(* 2 x) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4))))))))) |
(* 1/2 (/ 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)))) |
(* (sqrt eps) (/ 1 (sqrt -1))) |
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
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) |
(- (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))))) |
(* 1/2 (/ 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)) |
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(* 1/2 (/ eps x)) |
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(* 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)) |
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(* -1/2 (/ eps x)) |
(* -1/2 (/ eps x)) |
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(* -1/2 (/ eps x)) |
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(* -1/2 (/ eps x)) |
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(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
(/ -1/2 x) |
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(/ -1/2 x) |
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(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
(/ 1/4 (pow x 2)) |
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(* 1/2 (/ eps x)) |
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(* -1/4 (/ (pow eps 2) (pow x 2))) |
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(* -1/4 (/ (pow eps 2) (pow x 2))) |
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(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
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(* -1/4 (/ (pow eps 2) (pow x 2))) |
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(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
(* -1/4 (/ (pow eps 2) (pow x 2))) |
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(* -1/2 (/ eps x)) |
(* -1/2 (/ eps x)) |
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(* -1/2 (/ eps x)) |
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(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* 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)) |
(* 1/8 (/ (pow eps 3) (pow x 3))) |
(/ (+ (* 1/8 (pow eps 3)) (* 1/2 (* eps (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))))) (pow x 3)) |
(/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3)) |
(/ (+ (* 1/8 (pow eps 3)) (* (pow x 2) (+ (* 1/2 (* eps (+ (* -1 eps) (* -1/2 eps)))) (* 3/2 (* eps (pow x 2)))))) (pow x 3)) |
(* 3/2 (* eps x)) |
(* x (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps))) |
(* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps)))) |
(* x (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* 3/2 eps)))) |
(* 3/2 (* eps x)) |
(* -1 (* x (+ (* -3/2 eps) (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2)))))) |
(* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4))))))) |
(* -1 (* x (+ (* -3/2 eps) (+ (* -1/2 (/ (* eps (+ (* -1 eps) (* -1/2 eps))) (pow x 2))) (* -1/8 (/ (pow eps 3) (pow x 4))))))) |
(* 1/2 (/ (* eps (+ (* 2 (pow x 2)) (pow x 2))) x)) |
(* eps (+ (* -3/4 (/ eps x)) (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)))) |
(* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x)))))) |
(* eps (+ (* 1/2 (/ (+ (* 2 (pow x 2)) (pow x 2)) x)) (* eps (- (* 1/8 (/ eps (pow x 3))) (* 3/4 (/ 1 x)))))) |
(* 1/8 (/ (pow eps 3) (pow x 3))) |
(* (pow eps 3) (- (* 1/8 (/ 1 (pow x 3))) (* 3/4 (/ 1 (* eps x))))) |
(* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x)))) |
(* (pow eps 3) (- (+ (* 1/2 (/ (+ x (* 2 x)) (pow eps 2))) (* 1/8 (/ 1 (pow x 3)))) (/ 3/4 (* eps x)))) |
(* 1/8 (/ (pow eps 3) (pow x 3))) |
(* -1 (* (pow eps 3) (- (* 3/4 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))) |
(* -1 (* (pow eps 3) (- (* -1 (/ (- (* 1/2 (/ (+ x (* 2 x)) eps)) (* 3/4 (/ 1 x))) eps)) (* 1/8 (/ 1 (pow x 3)))))) |
(* 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)) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 3 (pow x 2)))))) (pow x 2)) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* (pow x 2) (+ 3 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(+ (* 2 (pow x 2)) (pow x 2)) |
(+ (* -3/2 eps) (+ (* 2 (pow x 2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2))) |
(+ (* 2 (pow x 2)) (+ (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2)) (pow x 2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* 1/4 (/ 1 (pow x 2))) (/ (pow x 2) (pow eps 2)))) (* 3/2 (/ 1 eps)))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -1 (/ (+ (* 2 (pow x 2)) (pow x 2)) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
(* (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))) |
(* 2 x) |
(* x (+ 2 (* -1/2 (/ eps (pow x 2))))) |
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))) |
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))) |
(* 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))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)) |
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)) |
(* 2 x) |
(+ (* -1/2 (/ eps x)) (* 2 x)) |
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))) |
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))) |
(* (sqrt eps) (sqrt -1)) |
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))) |
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))) |
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))) |
(* -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))))) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 2) x)) |
(* 1/4 (/ (pow eps 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)) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2)) |
(* 2 (pow x 2)) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* 2 (pow x 2)) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(* 2 (pow x 2)) |
(+ (* -3/2 eps) (* 2 (pow x 2))) |
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2))) |
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps)))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
| Outputs |
|---|
(* (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 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64))) |
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))) |
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1)))) |
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) (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 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.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 (+.f64 (/.f64 (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x)))) x) |
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x) |
(/.f64 (-.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) x) |
(* 2 x) |
(*.f64 x #s(literal 2 binary64)) |
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2))) |
(*.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64)) (neg.f64 x)) |
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2))))))) |
(*.f64 (-.f64 (/.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))) (neg.f64 x)) |
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4))))))))) |
(*.f64 (-.f64 (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (*.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (*.f64 eps (*.f64 (*.f64 eps eps) #s(literal 1/16 binary64)))) (*.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 eps #s(literal -1/4 binary64)))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 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 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x 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 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #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))))))))) |
(* (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 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal 1 binary64))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2))) |
(+.f64 (/.f64 x #s(literal 1 binary64)) (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64)) (*.f64 eps eps)))) |
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2))))) |
(-.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps #s(literal -1/2 binary64))) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (*.f64 (*.f64 (sqrt.f64 eps) x) (*.f64 (/.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 eps (*.f64 eps eps)))) (+.f64 (/.f64 x #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)))) |
(* -1 (* (sqrt eps) (sqrt -1))) |
(*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
(+ x (* -1 (* (sqrt eps) (sqrt -1)))) |
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps))) |
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x x)) (*.f64 (sqrt.f64 eps) #s(literal 1/2 binary64))) (*.f64 eps x)) eps)) |
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps))) |
(-.f64 (*.f64 (sqrt.f64 eps) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (/.f64 (+.f64 (*.f64 (neg.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 x x) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))) (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 eps (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 eps (*.f64 eps eps)))))))) (-.f64 #s(literal 0 binary64) eps)) (*.f64 eps x)) eps)) |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
eps |
(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) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) 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 (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(pow x 2) |
(*.f64 x x) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))) |
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2))))) |
(*.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.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) |
(-.f64 #s(literal 0 binary64) eps) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* eps (- (/ (pow x 2) eps) 1)) |
(*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) |
(* -1 eps) |
(-.f64 #s(literal 0 binary64) eps) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps))))) |
(*.f64 eps (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps)))) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* 1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ -1/2 x) |
(/.f64 #s(literal -1/2 binary64) x) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
(/ 1/4 (pow x 2)) |
(/.f64 #s(literal 1/4 binary64) (*.f64 x x)) |
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
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(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
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(* 1/4 (/ (pow eps 2) x)) |
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(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* 1/4 (/ (pow eps 2) x)) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* -1/2 (/ eps x)) |
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (* -1/2 eps)))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 eps (*.f64 #s(literal -3/2 binary64) (*.f64 x x))) (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64))) (*.f64 x x)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)))))) (*.f64 x x)) |
(/ (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1 eps) (+ (* -1/2 eps) (* 2 (pow x 2)))))) (pow x 2)) |
(/.f64 (+.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x (*.f64 x (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)))))) (*.f64 x x)) |
(* 2 (pow x 2)) |
(*.f64 #s(literal 2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(* 2 (pow x 2)) |
(*.f64 #s(literal 2 binary64) (*.f64 x x)) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2)))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(* (pow x 2) (+ 2 (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 4))))))) |
(*.f64 (*.f64 x x) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)) (/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64)))))) |
(* 2 (pow x 2)) |
(*.f64 #s(literal 2 binary64) (*.f64 x x)) |
(+ (* -3/2 eps) (* 2 (pow x 2))) |
(+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x))) |
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -3/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal 1/4 binary64)) x)))) |
(+ (* 2 (pow x 2)) (* eps (- (* 1/4 (/ eps (pow x 2))) 3/2))) |
(+.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 eps (+.f64 #s(literal -3/2 binary64) (/.f64 (*.f64 (/.f64 eps x) #s(literal 1/4 binary64)) x)))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -3/2 binary64) eps))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 x x) eps) eps)) (/.f64 #s(literal -3/2 binary64) eps)))) |
(* (pow eps 2) (- (+ (* 2 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ 1 (pow x 2)))) (* 3/2 (/ 1 eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 x x) eps) eps)) (/.f64 #s(literal -3/2 binary64) eps)))) |
(* 1/4 (/ (pow eps 2) (pow x 2))) |
(/.f64 (*.f64 (*.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)) |
(* (pow eps 2) (- (* 1/4 (/ 1 (pow x 2))) (* 3/2 (/ 1 eps)))) |
(*.f64 (*.f64 eps eps) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -3/2 binary64) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 eps eps) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 x x) eps))) eps))) |
(* (pow eps 2) (+ (* -1 (/ (+ 3/2 (* -2 (/ (pow x 2) eps))) eps)) (* 1/4 (/ 1 (pow x 2))))) |
(*.f64 (*.f64 eps eps) (-.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal -2 binary64) (/.f64 (*.f64 x x) eps))) eps))) |
Compiled 96830 to 4642 computations (95.2% saved)
49 alts after pruning (44 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 2106 | 33 | 2139 |
| Fresh | 13 | 11 | 24 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 3 | 4 |
| Total | 2123 | 49 | 2172 |
| Status | Accuracy | Program |
|---|---|---|
| 18.9% | (/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps) | |
| 3.5% | (/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 7.5% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) | |
| 7.3% | (/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))) | |
| 18.8% | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) | |
| 16.5% | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) | |
| 16.5% | (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) | |
| 27.1% | (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) | |
| 41.6% | (/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x) | |
| 28.7% | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))))) | |
| 35.9% | (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 36.1% | (/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 36.1% | (/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 26.2% | (/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) | |
| 34.5% | (/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 35.1% | (/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 42.7% | (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) | |
| 36.5% | (/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) | |
| 44.0% | (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) | |
| 99.5% | (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) | |
| 25.8% | (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) | |
| 44.4% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) | |
| 43.1% | (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) | |
| 43.5% | (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) | |
| 43.9% | (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) | |
| 43.6% | (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) | |
| 3.5% | (-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) | |
| ✓ | 7.2% | (-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
| 5.3% | (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) | |
| 57.6% | (-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) | |
| ✓ | 7.2% | (-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
| ✓ | 62.4% | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 57.9% | (-.f64 x (sqrt.f64 (neg.f64 eps))) | |
| 6.3% | (*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) | |
| 6.7% | (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) | |
| 33.4% | (*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))))) | |
| 43.8% | (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) | |
| 25.8% | (neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) | |
| 43.8% | (neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) | |
| 25.8% | (neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) | |
| 43.0% | (neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) | |
| 42.9% | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps)) | |
| 42.9% | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) | |
| ✓ | 42.9% | (neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
| 42.7% | (neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) | |
| 35.0% | (neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) | |
| 25.7% | (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) | |
| 3.5% | x | |
| ✓ | 4.3% | #s(literal 0 binary64) |
Compiled 2790 to 940 computations (66.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(*.f64 x #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) |
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) |
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x) |
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) |
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps) |
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) |
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) |
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x)) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) |
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (+.f64 (*.f64 eps (-.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 eps (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)) |
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (*.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))) |
(*.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 eps (+.f64 (/.f64 (*.f64 eps #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))))))))) |
(fma.f64 x (/.f64 (*.f64 x x) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))) (neg.f64 (/.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (*.f64 x x) (+.f64 (-.f64 (*.f64 x x) eps) (*.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))) |
| Outputs |
|---|
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
3 calls:
| 26.0ms | x |
| 26.0ms | eps |
| 24.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.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 #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) |
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) |
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x) |
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) |
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps) |
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) |
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) |
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x)) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) eps)))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) |
3 calls:
| 21.0ms | (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) |
| 21.0ms | eps |
| 21.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 89.0% | 2 | x |
| 81.5% | 2 | eps |
| 98.8% | 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 #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) |
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) |
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x) |
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) |
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps) |
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) |
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) |
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x)) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))))) |
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) |
| Outputs |
|---|
(-.f64 x (sqrt.f64 (neg.f64 eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
1 calls:
| 21.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 87.4% | 2 | x |
Compiled 3 to 2 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(*.f64 x #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) |
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) |
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x))) x) |
(/.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 eps (*.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))) x) |
(neg.f64 (*.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))))) |
(neg.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) |
(/.f64 (*.f64 (*.f64 (/.f64 #s(literal -1/4 binary64) (*.f64 x x)) eps) eps) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/2 binary64) x)) eps) |
(-.f64 x (+.f64 x (*.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (*.f64 eps #s(literal -1/8 binary64)) (*.f64 x (*.f64 x x))))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) (/.f64 eps x))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 eps eps)) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) eps) x) eps) x)) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) |
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps)) |
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 1/4 binary64) x))) (*.f64 eps eps))) (+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) |
(/.f64 (-.f64 (*.f64 x x) (-.f64 (*.f64 x x) eps)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)))) |
(/.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))) |
(*.f64 (*.f64 (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) |
(/.f64 (+.f64 (/.f64 (*.f64 (*.f64 eps (*.f64 eps eps)) #s(literal 1/16 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 eps eps)) (*.f64 x x)))) x) |
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 eps eps)) (*.f64 x x)) (/.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (/.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 eps (*.f64 eps eps))))) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) |
(/.f64 (/.f64 (*.f64 eps (*.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 eps (+.f64 (/.f64 (*.f64 eps #s(literal -3/4 binary64)) x) (/.f64 (*.f64 #s(literal 3/2 binary64) (*.f64 x x)) x))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 eps (*.f64 #s(literal 1/2 binary64) (*.f64 eps #s(literal -3/2 binary64)))) (*.f64 x x)) (*.f64 eps #s(literal 3/2 binary64)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x (*.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) x))) (neg.f64 x)) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))) (*.f64 x (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))))) |
(/.f64 (*.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 3 binary64) (/.f64 (*.f64 eps #s(literal -3/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(-.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 eps #s(literal -1/2 binary64)) (-.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (+.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 #s(literal -1/8 binary64) (*.f64 eps (*.f64 eps eps)))))) x)) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(*.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps))) (/.f64 eps (/.f64 x #s(literal -1/2 binary64))))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))))))) |
(/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps))) (+.f64 x (+.f64 x (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) (/.f64 x eps)))) (+.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x eps) (/.f64 x eps)))) (*.f64 (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))) (*.f64 (+.f64 x (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (-.f64 x x) (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))))))) |
(*.f64 (/.f64 (*.f64 (+.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps))) (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x)))))) (-.f64 (*.f64 x x) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal -1/2 binary64)))) (+.f64 (/.f64 eps (/.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 2 binary64) x))))) |
| Outputs |
|---|
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
2 calls:
| 18.0ms | eps |
| 17.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 44.4% | 1 | eps |
| 44.4% | 1 | x |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(*.f64 x #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal 2 binary64)) eps)) |
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) eps))) |
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)))) |
(-.f64 x (/.f64 (+.f64 (*.f64 x x) (*.f64 eps #s(literal -1/2 binary64))) x)) |
(/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x)) |
(neg.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/2 binary64) (*.f64 x x))) (*.f64 x eps))) |
(neg.f64 (*.f64 (/.f64 (*.f64 eps (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1/2 binary64)) x)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal -1/2 binary64) x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 x x)) eps)) |
(neg.f64 (*.f64 (/.f64 (/.f64 x #s(literal -1/2 binary64)) (/.f64 (*.f64 x x) #s(literal 1/4 binary64))) eps)) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))) |
(-.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))) |
| Outputs |
|---|
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
2 calls:
| 8.0ms | x |
| 7.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 44.0% | 1 | eps |
| 44.0% | 1 | x |
Compiled 6 to 4 computations (33.3% saved)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(*.f64 x #s(literal 2 binary64)) |
(-.f64 x x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps) |
(/.f64 #s(literal 1/2 binary64) (/.f64 x eps)) |
| Outputs |
|---|
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
2 calls:
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 43.8% | 1 | x |
| 43.8% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
Total -0.8b remaining (-1.3%)
Threshold costs -0.8b (-1.3%)
| Inputs |
|---|
#s(literal 0 binary64) |
x |
(*.f64 x #s(literal 2 binary64)) |
(-.f64 x x) |
| Outputs |
|---|
#s(literal 0 binary64) |
2 calls:
| 4.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.3% | 1 | x |
| 4.3% | 1 | eps |
Compiled 6 to 4 computations (33.3% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | -4.036970285649756e-148 | 0.0 |
Compiled 15 to 10 computations (33.3% saved)
| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 15.0ms | 5.4015481891800596e-92 | 3.959523178213477e-89 |
| 6.0ms | 55× | 1 | valid |
| 4.0ms | 73× | 0 | valid |
| 0.0ms | 9× | 0 | invalid |
Compiled 207 to 154 computations (25.6% saved)
ival-mult: 2.0ms (34.2% of total)ival-sub: 2.0ms (34.2% of total)ival-sqrt: 2.0ms (34.2% of total)backward-pass: 1.0ms (17.1% of total)const: 0.0ms (0% of total)| 1× | egg-herbie |
| 20× | +-commutative_binary64 |
| 18× | *-commutative_binary64 |
| 12× | sub-neg_binary64 |
| 6× | neg-sub0_binary64 |
| 6× | neg-mul-1_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 97 |
| 1 | 62 | 97 |
| 2 | 71 | 97 |
| 3 | 76 | 97 |
| 4 | 78 | 97 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -5758609657015291/14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps))) |
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
#s(literal 0 binary64) |
| Outputs |
|---|
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) |
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal -5758609657015291/14396524142538228424993723224595141948383030778566133225922417832357880258148761185020930195532450742879746914027266864394266451377581759004827248578768524336431104 binary64)) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))) eps))) |
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))) |
(if (<=.f64 x #s(literal 3554922854784611/1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 x #s(literal 2 binary64)) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)) eps)) |
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) |
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) |
#s(literal 0 binary64) |
| 5924× | *-lowering-*.f32 |
| 5924× | *-lowering-*.f64 |
| 5764× | *-lowering-*.f32 |
| 5764× | *-lowering-*.f64 |
| 4906× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 461 | 3973 |
| 1 | 1577 | 3840 |
| 2 | 5844 | 3798 |
| 0 | 8771 | 3798 |
| 0 | 6 | 19 |
| 1 | 40 | 19 |
| 2 | 324 | 19 |
| 3 | 4055 | 19 |
| 0 | 8218 | 19 |
| 0 | 28 | 123 |
| 1 | 218 | 120 |
| 2 | 2097 | 109 |
| 0 | 9748 | 109 |
| 0 | 257 | 1162 |
| 1 | 856 | 1135 |
| 2 | 3030 | 1098 |
| 0 | 8034 | 1098 |
| 0 | 656 | 6016 |
| 1 | 2231 | 5790 |
| 0 | 8158 | 5790 |
| 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× | node limit |
Compiled 211 to 118 computations (44.1% saved)
Compiled 244 to 110 computations (54.9% saved)
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