
Time bar (total: 4.9s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 1 |
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 2 |
| 25% | 25% | 74.9% | 0.1% | 0% | 0% | 0% | 3 |
| 28.6% | 25% | 62.4% | 0.1% | 0% | 12.5% | 0% | 4 |
| 46.2% | 37.5% | 43.7% | 0.1% | 0% | 18.7% | 0% | 5 |
| 52.2% | 37.5% | 34.3% | 0.1% | 0% | 28.1% | 0% | 6 |
| 65.1% | 43.7% | 23.4% | 0.1% | 0% | 32.8% | 0% | 7 |
| 70.9% | 43.7% | 18% | 0.1% | 0% | 38.2% | 0% | 8 |
| 79.5% | 46.8% | 12.1% | 0.1% | 0% | 41% | 0% | 9 |
| 83.6% | 46.8% | 9.2% | 0.1% | 0% | 43.9% | 0% | 10 |
| 88.7% | 48.4% | 6.1% | 0.1% | 0% | 45.4% | 0% | 11 |
| 91.3% | 48.4% | 4.6% | 0.1% | 0% | 46.9% | 0% | 12 |
Compiled 6 to 6 computations (0% saved)
| 316.0ms | 8 256× | 0 | valid |
| 18.0ms | 515× | 0 | invalid |
ival-add: 65.0ms (46.2% of total)ival-sqrt: 65.0ms (46.2% of total)ival-true: 6.0ms (4.3% of total)ival-assert: 4.0ms (2.8% of total)| 2× | egg-herbie |
| 44× | sub-neg |
| 32× | associate--r+ |
| 24× | neg-mul-1 |
| 22× | cancel-sign-sub-inv |
| 22× | +-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 28 |
| 1 | 27 | 26 |
| 2 | 42 | 26 |
| 3 | 64 | 26 |
| 4 | 123 | 26 |
| 5 | 162 | 26 |
| 6 | 201 | 26 |
| 7 | 212 | 26 |
| 8 | 214 | 26 |
| 0 | 4 | 4 |
| 1 | 5 | 4 |
| 0 | 5 | 4 |
| 1× | iter limit |
| 1× | saturated |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ x y)) |
| Outputs |
|---|
(sqrt (+ x y)) |
(sqrt.f64 (+.f64 x y)) |
| Inputs |
|---|
(sqrt (+ x y)) |
(sqrt (+ (neg x) y)) |
(sqrt (+ x (neg y))) |
(neg (sqrt (+ (neg x) y))) |
(neg (sqrt (+ x (neg y)))) |
(sqrt (+ y x)) |
| Outputs |
|---|
(sqrt (+ x y)) |
(sqrt (+ (neg x) y)) |
(sqrt (- y x)) |
(sqrt (+ x (neg y))) |
(sqrt (- x y)) |
(neg (sqrt (+ (neg x) y))) |
(neg (sqrt (- y x))) |
(neg (sqrt (+ x (neg y)))) |
(neg (sqrt (- x y))) |
(sqrt (+ y x)) |
(sqrt (+ x y)) |
(sort x y)
| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x y)) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | (+.f64 x y) |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 18.0ms | 512× | 0 | valid |
Compiled 34 to 20 computations (41.2% saved)
ival-sqrt: 4.0ms (54.4% of total)ival-add: 3.0ms (40.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Compiled 2 to 2 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (sqrt.f64 (+.f64 x y)) |
Compiled 6 to 4 computations (33.3% saved)
| 1× | egg-herbie |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (+.f64 x y) |
| ✓ | cost-diff | 0 | (sqrt.f64 (+.f64 x y)) |
| 4× | +-lowering-+.f64 |
| 4× | +-lowering-+.f32 |
| 2× | sqrt-lowering-sqrt.f64 |
| 2× | sqrt-lowering-sqrt.f32 |
| 2× | +-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 9 |
| 1 | 5 | 9 |
| 0 | 5 | 9 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt (+ x y)) |
(+ x y) |
x |
y |
| Outputs |
|---|
(sqrt (+ x y)) |
(sqrt.f64 (+.f64 x y)) |
(+ x y) |
(+.f64 x y) |
x |
y |
Found 2 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (+.f64 x y) |
| ✓ | accuracy | 100.0% | (sqrt.f64 (+.f64 x y)) |
| 9.0ms | 256× | 0 | valid |
Compiled 11 to 6 computations (45.5% saved)
ival-add: 2.0ms (55.3% of total)ival-sqrt: 2.0ms (55.3% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt (+ x y))> |
#<alt (+ x y)> |
| Outputs |
|---|
#<alt (sqrt y)> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))> |
#<alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (sqrt x)> |
#<alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))> |
#<alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))> |
#<alt (sqrt y)> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))> |
#<alt y> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt x> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt x> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt y> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt y> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | x | @ | -inf | (sqrt (+ x y)) |
| 1.0ms | y | @ | -inf | (sqrt (+ x y)) |
| 1.0ms | x | @ | inf | (sqrt (+ x y)) |
| 1.0ms | y | @ | inf | (sqrt (+ x y)) |
| 0.0ms | y | @ | 0 | (sqrt (+ x y)) |
| 1× | batch-egg-rewrite |
| 5 128× | accelerator-lowering-fma.f32 |
| 5 128× | accelerator-lowering-fma.f64 |
| 4 292× | /-lowering-/.f32 |
| 4 292× | /-lowering-/.f64 |
| 3 378× | *-lowering-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 4 | 7 |
| 1 | 20 | 7 |
| 2 | 143 | 7 |
| 3 | 1362 | 7 |
| 0 | 8302 | 7 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt (+ x y)) |
(+ x y) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 x y)))) |
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64))) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x y) (+.f64 x y))) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(exp.f64 (fma.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64) (*.f64 (log.f64 (+.f64 x y)) #s(literal 1/4 binary64)))) |
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64))) |
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64))) |
(sqrt.f64 (+.f64 x y)) |
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (-.f64 x y))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (*.f64 (-.f64 x y) (fma.f64 x x (*.f64 y y))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 x y)))) (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 x y)))) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (*.f64 (-.f64 x y) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 y x)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 y x)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))))) (*.f64 (*.f64 y (/.f64 y (-.f64 x y))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))))))) (sqrt.f64 (fma.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))) (fma.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y)))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y)))))) (sqrt.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x (-.f64 x y) (*.f64 y y)))) (sqrt.f64 (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (-.f64 x y))) (sqrt.f64 (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y))) (sqrt.f64 (fma.f64 x x (*.f64 y y)))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y)))))) |
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 x y))))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) y)))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 y x)))) (neg.f64 (sqrt.f64 (-.f64 y x)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))) |
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 x y))))) |
(pow.f64 (+.f64 x y) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) #s(literal -1/2 binary64)) |
(pow.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x y) (+.f64 x y)) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (+.f64 x y))) |
(*.f64 (sqrt.f64 (+.f64 x y)) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 x y)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(*.f64 (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (pow.f64 (/.f64 (+.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (sqrt.f64 (/.f64 (+.f64 x y) (fma.f64 x (-.f64 x y) (*.f64 y y))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)))) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x y))) |
(*.f64 (pow.f64 (+.f64 x y) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x y) #s(literal 1/4 binary64))) |
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(*.f64 (-.f64 (*.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (-.f64 x y) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 x y) (-.f64 x y)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 x y) (-.f64 y x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 y x)))) |
(*.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))))) (*.f64 (*.f64 y (/.f64 y (-.f64 x y))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y))) (fma.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))) (*.f64 (/.f64 (*.f64 x x) (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))))) |
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 x (-.f64 x y)) (/.f64 x (-.f64 x y)))) (*.f64 (*.f64 y y) (*.f64 (/.f64 y (-.f64 x y)) (/.f64 y (-.f64 x y))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))) |
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x (-.f64 x y) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) |
(*.f64 (/.f64 (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(*.f64 (/.f64 (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y))) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))) |
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (fma.f64 (*.f64 y (*.f64 y y)) (*.f64 (-.f64 y x) (*.f64 (-.f64 y x) (-.f64 y x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 y (-.f64 y x)) (fma.f64 y (-.f64 y x) (-.f64 #s(literal 0 binary64) (*.f64 x x))) (*.f64 x (*.f64 x (*.f64 x x))))) |
(*.f64 (/.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x))))) (-.f64 (*.f64 x x) (*.f64 y (-.f64 y x)))) |
(*.f64 (/.f64 (*.f64 (+.f64 x y) (-.f64 x y)) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y))) (fma.f64 x x (*.f64 y (+.f64 x y)))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y (*.f64 y y)) (-.f64 (*.f64 y (*.f64 y y)) (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x y) (*.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))) (*.f64 (fma.f64 x x (*.f64 y (+.f64 x y))) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y y) (fma.f64 x x (*.f64 y y)) (*.f64 x (*.f64 x (*.f64 x x)))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 x y) (*.f64 (fma.f64 x x (*.f64 y y)) (*.f64 (+.f64 x y) (-.f64 x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 y y)))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))) |
(*.f64 (exp.f64 (log.f64 (*.f64 (+.f64 x y) (-.f64 x y)))) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 x y))))) |
| 1× | egg-herbie |
| 28 536× | accelerator-lowering-fma.f32 |
| 28 536× | accelerator-lowering-fma.f64 |
| 5 638× | *-lowering-*.f32 |
| 5 638× | *-lowering-*.f64 |
| 2 832× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 156 | 630 |
| 1 | 454 | 600 |
| 2 | 1425 | 582 |
| 3 | 4619 | 570 |
| 0 | 8274 | 534 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
y |
(+ x y) |
(+ x y) |
(+ x y) |
x |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
x |
(+ x y) |
(+ x y) |
(+ x y) |
y |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x #s(literal 1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 x (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal -1/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 x (fma.f64 (*.f64 y y) (fma.f64 y (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 y (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal -1/8 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y (*.f64 y #s(literal -1/8 binary64))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (*.f64 y (*.f64 y y)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(sqrt x) |
(sqrt.f64 x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal -1/8 binary64)))) (sqrt.f64 x)) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(fma.f64 y (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal 1/16 binary64)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)) |
(sqrt y) |
(sqrt.f64 y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 y (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (*.f64 x (*.f64 #s(literal 1/16 binary64) (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(*.f64 y (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x x)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (/.f64 (*.f64 x (*.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))))) |
y |
(+ x y) |
(+.f64 y x) |
(+ x y) |
(+.f64 y x) |
(+ x y) |
(+.f64 y x) |
x |
(* x (+ 1 (/ y x))) |
(+.f64 y x) |
(* x (+ 1 (/ y x))) |
(+.f64 y x) |
(* x (+ 1 (/ y x))) |
(+.f64 y x) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 y x) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 y x) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(+.f64 y x) |
x |
(+ x y) |
(+.f64 y x) |
(+ x y) |
(+.f64 y x) |
(+ x y) |
(+.f64 y x) |
y |
(* y (+ 1 (/ x y))) |
(+.f64 y x) |
(* y (+ 1 (/ x y))) |
(+.f64 y x) |
(* y (+ 1 (/ x y))) |
(+.f64 y x) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 y x) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 y x) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(+.f64 y x) |
Compiled 7 918 to 856 computations (89.2% saved)
4 alts after pruning (3 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 271 | 3 | 274 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 271 | 4 | 275 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 98.5% | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
| ▶ | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ▶ | 97.1% | (sqrt.f64 y) |
Compiled 32 to 23 computations (28.1% saved)
| 1× | egg-herbie |
Found 9 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) y) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
| ✓ | cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
| ✓ | cost-diff | 0 | (+.f64 x y) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (+.f64 x y)) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
| ✓ | cost-diff | 0 | (sqrt.f64 y) |
| 24× | *-lowering-*.f32 |
| 24× | *-lowering-*.f64 |
| 12× | accelerator-lowering-fma.f32 |
| 12× | accelerator-lowering-fma.f64 |
| 10× | *-commutative |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 55 |
| 1 | 22 | 55 |
| 2 | 29 | 55 |
| 3 | 31 | 55 |
| 0 | 31 | 54 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(sqrt y) |
y |
(/ 1 (sqrt (/ 1 (+ x y)))) |
1 |
(sqrt (/ 1 (+ x y))) |
(/ 1 (+ x y)) |
(+ x y) |
x |
y |
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y)) |
(sqrt (/ 1 y)) |
(/ 1 y) |
1 |
y |
(* 1/2 x) |
1/2 |
x |
(sqrt y) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
y |
(/ 1 (sqrt (/ 1 (+ x y)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ 1 (+ x y))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))) |
(/ 1 (+ x y)) |
(/.f64 #s(literal 1 binary64) (+.f64 y x)) |
(+ x y) |
(+.f64 y x) |
x |
y |
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
1 |
#s(literal 1 binary64) |
y |
(* 1/2 x) |
(*.f64 x #s(literal 1/2 binary64)) |
1/2 |
#s(literal 1/2 binary64) |
x |
(sqrt y) |
(sqrt.f64 y) |
Found 9 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (*.f64 #s(literal 1/2 binary64) x) |
| ✓ | accuracy | 100.0% | (sqrt.f64 y) |
| ✓ | accuracy | 100.0% | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
| ✓ | accuracy | 100.0% | (+.f64 x y) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) (+.f64 x y)) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y))) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
| ✓ | accuracy | 100.0% | (sqrt.f64 y) |
| 27.0ms | 256× | 0 | valid |
Compiled 56 to 16 computations (71.4% saved)
ival-div: 5.0ms (30.4% of total)ival-sqrt: 5.0ms (30.4% of total)ival-mult: 3.0ms (18.2% of total)ival-add: 2.0ms (12.2% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (sqrt y)> |
#<alt (/ 1 (sqrt (/ 1 (+ x y))))> |
#<alt (sqrt (/ 1 (+ x y)))> |
#<alt (/ 1 (+ x y))> |
#<alt (+ x y)> |
#<alt (+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (/ 1 y)> |
#<alt (* 1/2 x)> |
| Outputs |
|---|
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (sqrt y)> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))> |
#<alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))> |
#<alt (sqrt x)> |
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))> |
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))> |
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))> |
#<alt (sqrt x)> |
#<alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))> |
#<alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))> |
#<alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))> |
#<alt (sqrt y)> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))> |
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))> |
#<alt (sqrt (/ 1 y))> |
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))> |
#<alt (+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5))))))))> |
#<alt (+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5)))))))))> |
#<alt (sqrt (/ 1 x))> |
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))> |
#<alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))))> |
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))> |
#<alt (sqrt (/ 1 x))> |
#<alt (+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)))> |
#<alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y)))))> |
#<alt (+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5)))))))))> |
#<alt (sqrt (/ 1 y))> |
#<alt (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))> |
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))> |
#<alt (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))> |
#<alt (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))> |
#<alt (+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))> |
#<alt (/ 1 y)> |
#<alt (+ (* -1 (/ x (pow y 2))) (/ 1 y))> |
#<alt (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))> |
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))> |
#<alt (/ 1 x)> |
#<alt (/ (+ 1 (* -1 (/ y x))) x)> |
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)> |
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)> |
#<alt (/ 1 x)> |
#<alt (* -1 (/ (- (/ y x) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))> |
#<alt (/ 1 x)> |
#<alt (+ (* -1 (/ y (pow x 2))) (/ 1 x))> |
#<alt (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))> |
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))> |
#<alt (/ 1 y)> |
#<alt (/ (+ 1 (* -1 (/ x y))) y)> |
#<alt (/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)> |
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)> |
#<alt (/ 1 y)> |
#<alt (* -1 (/ (- (/ x y) 1) y))> |
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))> |
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))> |
#<alt y> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt x> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt (* x (+ 1 (/ y x)))> |
#<alt x> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))> |
#<alt x> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt (+ x y)> |
#<alt y> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt (* y (+ 1 (/ x y)))> |
#<alt y> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (sqrt y)> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (sqrt y)> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<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)> |
42 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (sqrt (/ 1 (+ x y))) |
| 1.0ms | y | @ | -inf | (/ 1 (+ x y)) |
| 1.0ms | x | @ | 0 | (+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y)) |
| 1.0ms | y | @ | -inf | (sqrt (/ 1 (+ x y))) |
| 1.0ms | x | @ | inf | (sqrt (/ 1 (+ x y))) |
| 1× | batch-egg-rewrite |
| 4 850× | accelerator-lowering-fma.f32 |
| 4 850× | accelerator-lowering-fma.f64 |
| 3 186× | *-lowering-*.f32 |
| 3 186× | *-lowering-*.f64 |
| 1 918× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 14 | 45 |
| 1 | 74 | 37 |
| 2 | 482 | 37 |
| 0 | 4627 | 36 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(/ 1 (sqrt (/ 1 (+ x y)))) |
(sqrt (/ 1 (+ x y))) |
(/ 1 (+ x y)) |
(+ x y) |
(+ (* (sqrt (/ 1 y)) (* 1/2 x)) (sqrt y)) |
(sqrt (/ 1 y)) |
(/ 1 y) |
(* 1/2 x) |
| Outputs |
|---|
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 y))) |
(fabs.f64 (sqrt.f64 y)) |
(sqrt.f64 y) |
(/.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(pow.f64 y #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y))) |
(exp.f64 (*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 y x)) #s(literal 0 binary64)))) |
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 (+.f64 y x))) #s(literal -1/2 binary64))) |
(exp.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 y x)) #s(literal 0 binary64)))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x)))) |
(sqrt.f64 (+.f64 y x)) |
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))))) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 y x)))) |
(/.f64 (sqrt.f64 (+.f64 y x)) #s(literal 1 binary64)) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 y x))) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))) |
(/.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (-.f64 x y))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x y)))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 y x))) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 y x) (-.f64 x y)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 x y)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (sqrt.f64 (-.f64 y x))) |
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y)))))) |
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) (neg.f64 (sqrt.f64 (-.f64 x y)))) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 y (*.f64 y y) (*.f64 x (*.f64 x x))))) (sqrt.f64 (fma.f64 y y (*.f64 x (-.f64 x y))))) |
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(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y)) |
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 y) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))) |
(/.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 y))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 (-.f64 #s(literal 0 binary64) y)))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(pow.f64 y #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 y) #s(literal -2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 y y) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y)) |
(*.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 1 binary64)) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) y)) |
(*.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) |
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) |
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64))) |
(/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)) (sqrt.f64 y)) |
(/.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (sqrt.f64 y)) |
(/.f64 (*.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(*.f64 (sqrt.f64 y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 y)) (sqrt.f64 y))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 (sqrt.f64 y) x))) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (sqrt.f64 y)) |
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (*.f64 (sqrt.f64 y) x)) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)))) |
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)))) |
(*.f64 (/.f64 x (sqrt.f64 y)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 y) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(*.f64 (*.f64 (sqrt.f64 y) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) |
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (sqrt.f64 y) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 y))) |
(*.f64 (*.f64 (sqrt.f64 y) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x) |
(*.f64 (*.f64 (sqrt.f64 y) (/.f64 x (sqrt.f64 y))) #s(literal 1/2 binary64)) |
(*.f64 (*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64))) |
| 1× | egg-herbie |
| 13 426× | accelerator-lowering-fma.f32 |
| 13 426× | accelerator-lowering-fma.f64 |
| 4 642× | *-lowering-*.f32 |
| 4 642× | *-lowering-*.f64 |
| 4 014× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 359 | 2044 |
| 1 | 1074 | 1931 |
| 2 | 3288 | 1839 |
| 3 | 7603 | 1839 |
| 0 | 8745 | 1732 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y))) |
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y))))))) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))) |
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) |
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
(sqrt (/ 1 y)) |
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* 3/8 (* x (sqrt (/ 1 (pow y 5)))))))) |
(+ (sqrt (/ 1 y)) (* x (+ (* -1/2 (sqrt (/ 1 (pow y 3)))) (* x (+ (* -5/16 (* x (sqrt (/ 1 (pow y 7))))) (* 3/8 (sqrt (/ 1 (pow y 5))))))))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))))) |
(+ (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ (* 1/4 (* x (pow y 2))) (pow y 3)))) (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2)))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (pow y 2))) (* 1/2 (* (sqrt (/ 1 x)) (+ (* -1/4 (/ (* x (pow y 2)) (pow (sqrt -1) 2))) (pow y 3))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* -1/2 (* (sqrt (/ 1 (pow x 3))) y))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 3/8 (* (sqrt (/ 1 (pow x 5))) y))))) |
(+ (sqrt (/ 1 x)) (* y (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* y (+ (* -5/16 (* (sqrt (/ 1 (pow x 7))) y)) (* 3/8 (sqrt (/ 1 (pow x 5))))))))) |
(sqrt (/ 1 y)) |
(+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))) |
(+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/2 (* (sqrt (/ 1 (pow y 7))) (+ (* 1/4 (* (pow x 2) y)) (pow x 3)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/2 (* (pow x 2) (sqrt y))) (* 1/2 (* (sqrt (/ 1 y)) (+ (* -1/4 (/ (* (pow x 2) y) (pow (sqrt -1) 2))) (pow x 3))))) (pow y 3))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))) |
(/ 1 y) |
(+ (* -1 (/ x (pow y 2))) (/ 1 y)) |
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)) |
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)) |
(/ 1 x) |
(/ (+ 1 (* -1 (/ y x))) x) |
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x) |
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x) |
(/ 1 x) |
(* -1 (/ (- (/ y x) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x)) |
(/ 1 x) |
(+ (* -1 (/ y (pow x 2))) (/ 1 x)) |
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x)) |
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x)) |
(/ 1 y) |
(/ (+ 1 (* -1 (/ x y))) y) |
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y) |
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y) |
(/ 1 y) |
(* -1 (/ (- (/ x y) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y)) |
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y)) |
y |
(+ x y) |
(+ x y) |
(+ x y) |
x |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
(* x (+ 1 (/ y x))) |
x |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
(* -1 (* x (- (* -1 (/ y x)) 1))) |
x |
(+ x y) |
(+ x y) |
(+ x y) |
y |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
(* y (+ 1 (/ x y))) |
y |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* -1 (* y (- (* -1 (/ x y)) 1))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 y)) |
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) |
(fma.f64 x (fma.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 x #s(literal 1/16 binary64)) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (sqrt.f64 y)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))) |
(*.f64 x (fma.f64 y (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) y)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))) |
(*.f64 x (fma.f64 (*.f64 y y) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) y (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x)) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(-.f64 #s(literal 0 binary64) (*.f64 x (fma.f64 y (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y y)) #s(literal 1/8 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x)) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (*.f64 y (*.f64 y y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (*.f64 y (*.f64 y y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (*.f64 y (*.f64 y y)))) y) |
(sqrt y) |
(sqrt.f64 y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(*.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (-.f64 #s(literal 0 binary64) y)) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (-.f64 #s(literal 0 binary64) y)) |
(* -1 (* y (+ (* -1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (-.f64 #s(literal 0 binary64) y)) |
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(* 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) |
Compiled 12 902 to 1 867 computations (85.5% saved)
5 alts after pruning (2 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 676 | 2 | 678 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 2 | 3 |
| Done | 0 | 1 | 1 |
| Total | 677 | 5 | 682 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 98.5% | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
| ✓ | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
| ▶ | 96.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 97.1% | (sqrt.f64 y) |
Compiled 38 to 26 computations (31.6% saved)
| 1× | egg-herbie |
Found 6 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | cost-diff | 0 | (sqrt.f64 y) |
| ✓ | cost-diff | 0 | (/.f64 x (sqrt.f64 y)) |
| ✓ | cost-diff | 0 | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) y) |
| ✓ | cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
| ✓ | cost-diff | 0 | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
| 12× | *-lowering-*.f32 |
| 12× | *-lowering-*.f64 |
| 10× | /-lowering-/.f32 |
| 10× | /-lowering-/.f64 |
| 8× | accelerator-lowering-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 33 |
| 1 | 17 | 33 |
| 2 | 21 | 33 |
| 3 | 22 | 33 |
| 0 | 22 | 32 |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/ 1 (sqrt (/ 1 y))) |
1 |
(sqrt (/ 1 y)) |
(/ 1 y) |
y |
(+ (* (/ x (sqrt y)) 1/2) (sqrt y)) |
(/ x (sqrt y)) |
x |
(sqrt y) |
y |
1/2 |
| Outputs |
|---|
(/ 1 (sqrt (/ 1 y))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
1 |
#s(literal 1 binary64) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
y |
(+ (* (/ x (sqrt y)) 1/2) (sqrt y)) |
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)) |
(/ x (sqrt y)) |
(/.f64 x (sqrt.f64 y)) |
x |
(sqrt y) |
(sqrt.f64 y) |
y |
1/2 |
#s(literal 1/2 binary64) |
Found 6 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| ✓ | accuracy | 100.0% | (sqrt.f64 y) |
| ✓ | accuracy | 100.0% | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
| ✓ | accuracy | 99.7% | (/.f64 x (sqrt.f64 y)) |
| ✓ | accuracy | 100.0% | (/.f64 #s(literal 1 binary64) y) |
| ✓ | accuracy | 99.8% | (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
| ✓ | accuracy | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
| 22.0ms | 256× | 0 | valid |
Compiled 34 to 13 computations (61.8% saved)
ival-div: 5.0ms (35.5% of total)ival-add: 3.0ms (21.3% of total)ival-sqrt: 3.0ms (21.3% of total)ival-mult: 2.0ms (14.2% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#<alt (/ 1 (sqrt (/ 1 y)))> |
#<alt (sqrt (/ 1 y))> |
#<alt (/ 1 y)> |
#<alt (+ (* (/ x (sqrt y)) 1/2) (sqrt y))> |
#<alt (/ x (sqrt y))> |
#<alt (sqrt y)> |
| Outputs |
|---|
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (* -1 (sqrt y))> |
#<alt (* -1 (sqrt y))> |
#<alt (* -1 (sqrt y))> |
#<alt (* -1 (sqrt y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (sqrt (/ 1 y))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (/ 1 y)> |
#<alt (sqrt y)> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))> |
#<alt (* 1/2 (* x (sqrt (/ 1 y))))> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)> |
#<alt (sqrt y)> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (* x (sqrt (/ 1 y)))> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (sqrt y)> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))> |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | y | @ | -inf | (/ 1 (sqrt (/ 1 y))) |
| 1.0ms | y | @ | -inf | (+ (* (/ x (sqrt y)) 1/2) (sqrt y)) |
| 0.0ms | x | @ | 0 | (/ x (sqrt y)) |
| 0.0ms | y | @ | -inf | (/ x (sqrt y)) |
| 0.0ms | x | @ | -inf | (/ x (sqrt y)) |
| 1× | batch-egg-rewrite |
| 3 576× | accelerator-lowering-fma.f32 |
| 3 576× | accelerator-lowering-fma.f64 |
| 2 440× | *-lowering-*.f32 |
| 2 440× | *-lowering-*.f64 |
| 1 744× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 11 | 32 |
| 1 | 54 | 23 |
| 2 | 333 | 23 |
| 0 | 4117 | 22 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (sqrt (/ 1 y))) |
(sqrt (/ 1 y)) |
(/ 1 y) |
(+ (* (/ x (sqrt y)) 1/2) (sqrt y)) |
(/ x (sqrt y)) |
(sqrt y) |
| Outputs |
|---|
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)) #s(literal -1/2 binary64))) |
(fabs.f64 (sqrt.f64 y)) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(sqrt.f64 y) |
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(/.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64))) |
(pow.f64 y #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 y)) |
(*.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 y) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 y)) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(exp.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 y) #s(literal 0 binary64))) |
(exp.f64 (*.f64 (log.f64 y) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64)) #s(literal -1 binary64))) |
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 y)) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
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(*.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)) (/.f64 (-.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (sqrt.f64 y)) (-.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) (sqrt.f64 y)))) |
(*.f64 (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y)))) |
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y)) (*.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y))))) |
(*.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y)) (/.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y)) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y)))) |
(*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y) (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64) (sqrt.f64 y)))) |
(*.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y))))) |
(*.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y))) y) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64) (sqrt.f64 y)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y))) (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y))))) |
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64) (sqrt.f64 y))) (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y)) |
(*.f64 (+.f64 y (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) y))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))))) |
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y) (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y)) (fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) (sqrt.f64 y))) |
(*.f64 (/.f64 (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y)))) (fma.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (*.f64 y (*.f64 (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))))) (/.f64 (*.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) (*.f64 y (*.f64 y y))))) (fma.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (-.f64 (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y))) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y y)))) |
(*.f64 (/.f64 (fma.f64 y (sqrt.f64 y) (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y)))) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y y)) (*.f64 y (*.f64 (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64))))))) (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) (fma.f64 (sqrt.f64 y) (*.f64 (/.f64 x (sqrt.f64 y)) #s(literal -1/2 binary64)) y))) |
(*.f64 (/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y)) y) (-.f64 (/.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (*.f64 y (sqrt.f64 y))) (*.f64 y (sqrt.f64 y)))) (fma.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) y) (fma.f64 (sqrt.f64 y) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y)) y))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 y) x)) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x (sqrt.f64 y)))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) (neg.f64 (/.f64 x (sqrt.f64 y)))) |
(neg.f64 (neg.f64 (/.f64 x (sqrt.f64 y)))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 y) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 y) x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (/.f64 #s(literal 1 binary64) x)) |
(/.f64 x (sqrt.f64 y)) |
(/.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 y) x))) |
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (neg.f64 (/.f64 x (sqrt.f64 y))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (sqrt.f64 y)) |
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) x) #s(literal -1 binary64)) |
(/.f64 (/.f64 x #s(literal 1 binary64)) (sqrt.f64 y)) |
(/.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64))) |
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (sqrt.f64 y)) |
(/.f64 (*.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
(pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 y))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) |
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(*.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1 binary64)) |
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (sqrt.f64 y)))) |
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 y)) (-.f64 #s(literal 0 binary64) x)) |
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(*.f64 (pow.f64 y #s(literal -1/4 binary64)) (*.f64 (pow.f64 y #s(literal -1/4 binary64)) x)) |
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(*.f64 (/.f64 x (pow.f64 y #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64)))) |
(*.f64 (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 y) x) #s(literal -1/2 binary64))) |
(*.f64 (*.f64 x (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64))) |
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 y) #s(literal 0 binary64))) |
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)) #s(literal -1/2 binary64))) |
(fabs.f64 (sqrt.f64 y)) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(sqrt.f64 y) |
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) |
(/.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 y))) |
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) y)) (sqrt.f64 #s(literal -1 binary64))) |
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1/4 binary64))) (pow.f64 y #s(literal -1/4 binary64))) |
(pow.f64 y #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 y)) |
(*.f64 (sqrt.f64 y) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 y) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 y))) |
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) #s(literal -1 binary64)) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (*.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (/.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 y)) |
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 y #s(literal -1/4 binary64)) #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 (sqrt.f64 y))) |
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 1/4 binary64))) (pow.f64 y #s(literal 1/4 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) y))) |
| 1× | egg-herbie |
| 3 710× | accelerator-lowering-fma.f32 |
| 3 710× | accelerator-lowering-fma.f64 |
| 3 668× | *-lowering-*.f32 |
| 3 668× | *-lowering-*.f64 |
| 1 282× | /-lowering-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 46 | 570 |
| 1 | 123 | 558 |
| 2 | 341 | 554 |
| 3 | 888 | 554 |
| 4 | 1892 | 554 |
| 5 | 4398 | 554 |
| 6 | 5622 | 554 |
| 7 | 6512 | 554 |
| 8 | 7040 | 554 |
| 9 | 7422 | 554 |
| 10 | 7963 | 554 |
| 0 | 8116 | 536 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(* -1 (sqrt y)) |
(* -1 (sqrt y)) |
(* -1 (sqrt y)) |
(* -1 (sqrt y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(sqrt (/ 1 y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(/ 1 y) |
(sqrt y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(sqrt y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(* x (sqrt (/ 1 y))) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(sqrt y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(* -1 (sqrt y)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 y)) |
(* -1 (sqrt y)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 y)) |
(* -1 (sqrt y)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 y)) |
(* -1 (sqrt y)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(sqrt (/ 1 y)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) y)) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(* (sqrt (/ 1 y)) (pow (sqrt -1) 2)) |
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(/ 1 y) |
(/.f64 #s(literal 1 binary64) y) |
(sqrt y) |
(sqrt.f64 y) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y)))))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 y)) |
(* 1/2 (* x (sqrt (/ 1 y)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64)) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y) |
(/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y) |
(/.f64 (fma.f64 (sqrt.f64 y) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) y) |
(sqrt y) |
(sqrt.f64 y) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) |
(fma.f64 y (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(* x (sqrt (/ 1 y))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) x #s(literal 0 binary64)) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(sqrt y) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
(* -1 (* (sqrt y) (pow (sqrt -1) 2))) |
(sqrt.f64 y) |
Compiled 6 687 to 787 computations (88.2% saved)
5 alts after pruning (0 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 438 | 0 | 438 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 3 | 3 |
| Total | 438 | 5 | 443 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 98.5% | (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
| ✓ | 99.5% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
| ✓ | 96.7% | (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
| ✓ | 100.0% | (sqrt.f64 (+.f64 x y)) |
| ✓ | 97.1% | (sqrt.f64 y) |
Compiled 78 to 43 computations (44.9% saved)
| Inputs |
|---|
(sqrt.f64 y) |
(sqrt.f64 (+.f64 x y)) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)))) |
(fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 y)) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
4 calls:
| 2.0ms | (+.f64 x y) |
| 2.0ms | x |
| 2.0ms | (sqrt.f64 (+.f64 x y)) |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | (sqrt.f64 (+.f64 x y)) |
| 100.0% | 1 | (+.f64 x y) |
Compiled 17 to 11 computations (35.3% saved)
Total -0.0b remaining (-0%)
Threshold costs -0b (-0%)
| Inputs |
|---|
(sqrt.f64 y) |
| Outputs |
|---|
(sqrt.f64 y) |
4 calls:
| 1.0ms | (sqrt.f64 (+.f64 x y)) |
| 1.0ms | (+.f64 x y) |
| 1.0ms | x |
| 1.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.1% | 1 | x |
| 97.1% | 1 | y |
| 97.1% | 1 | (sqrt.f64 (+.f64 x y)) |
| 97.1% | 1 | (+.f64 x y) |
Compiled 17 to 11 computations (35.3% saved)
| 1× | egg-herbie |
| 2× | +-commutative_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 6 |
| 1 | 6 | 6 |
| 1× | saturated |
| Inputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 y) |
| Outputs |
|---|
(sqrt.f64 (+.f64 x y)) |
(sqrt.f64 y) |
| 28 536× | accelerator-lowering-fma.f32 |
| 28 536× | accelerator-lowering-fma.f64 |
| 5 638× | *-lowering-*.f32 |
| 5 638× | *-lowering-*.f64 |
| 2 832× | +-lowering-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 156 | 630 |
| 1 | 454 | 600 |
| 2 | 1425 | 582 |
| 3 | 4619 | 570 |
| 0 | 8274 | 534 |
| 1× | done |
| 1× | iter limit |
| 1× | node limit |
Compiled 12 to 8 computations (33.3% saved)
(sort x y)
Compiled 52 to 34 computations (34.6% saved)
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