Linear.Quaternion:$clog from linear-1.19.1.3
Time bar (total: 1.6s)
| 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 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 3 |
| 50% | 50% | 50% | 0.1% | 0% | 0% | 0% | 4 |
| 62.5% | 62.4% | 37.5% | 0.1% | 0% | 0% | 0% | 5 |
| 66.7% | 62.4% | 31.2% | 0.1% | 0% | 6.2% | 0% | 6 |
| 75% | 65.6% | 21.9% | 0.1% | 0% | 12.5% | 0% | 7 |
| 80% | 68.7% | 17.2% | 0.1% | 0% | 14% | 0% | 8 |
| 85.7% | 70.2% | 11.7% | 0.1% | 0% | 18% | 0% | 9 |
| 88.9% | 71.8% | 9% | 0.1% | 0% | 19.1% | 0% | 10 |
| 92.3% | 72.6% | 6% | 0.1% | 0% | 21.3% | 0% | 11 |
| 94.1% | 73.4% | 4.6% | 0.1% | 0% | 22% | 0% | 12 |
Compiled 8 to 7 computations (12.5% saved)
| 530.0ms | 8 256× | 0 | valid |
| 12.0ms | 315× | 0 | invalid |
ival-mult!: 99.0ms (45.3% of total)ival-sqrt: 95.0ms (43.5% of total)ival-add!: 22.0ms (10.1% of total)adjust: 2.0ms (0.9% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 17 | 40 |
| 1 | 42 | 40 |
| 2 | 107 | 40 |
| 3 | 185 | 40 |
| 4 | 418 | 40 |
| 5 | 2020 | 40 |
| 6 | 4663 | 40 |
| 1× | node-limit |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 71.7% | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
(abs x)
Compiled 10 to 10 computations (0% saved)
| Inputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) y)) |
(+.f64 (*.f64 x x) y) |
(*.f64 x x) |
x |
y |
| Outputs |
|---|
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt y))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 y)) |
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2)))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))) |
#s(approx y #s(hole binary64 y)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | y | @ | -inf | ((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y) |
| 2.0ms | x | @ | inf | ((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y) |
| 2.0ms | x | @ | -inf | ((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y) |
| 1.0ms | y | @ | inf | ((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y) |
| 1.0ms | x | @ | 0 | ((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 170 | 765 |
| 0 | 173 | 698 |
| 0 | 526 | 666 |
| 0 | 3639 | 599 |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | unsound |
| 1× | iter-limit |
| Inputs |
|---|
(sqrt.f64 (+.f64 (*.f64 x x) y)) |
(+.f64 (*.f64 x x) y) |
(*.f64 x x) |
x |
y |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt y))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 y)) |
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2)))) |
#s(approx (* x x) #s(hole binary64 (pow x 2))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2)))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))) |
#s(approx y #s(hole binary64 y)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))))) |
| Outputs |
|---|
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) |
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) |
(sqrt.f64 (fma.f64 x x y)) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 y y)) (-.f64 (*.f64 x x) y)) |
(/.f64 (-.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 y (*.f64 x x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) (*.f64 (*.f64 y y) y)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 (*.f64 x x) y)))) |
(/.f64 (fma.f64 (*.f64 y y) y (pow.f64 (*.f64 x x) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 y (*.f64 x x))))) |
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x y) |
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) y) |
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) y) |
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y) |
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) y) |
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) y) |
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) y) |
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64) y) |
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) y) |
(fma.f64 (fabs.f64 x) (fabs.f64 x) y) |
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) y) |
(fma.f64 (neg.f64 x) (neg.f64 x) y) |
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) y) |
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y) |
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y) |
(fma.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 x)) y) |
(fma.f64 x x y) |
(-.f64 y (*.f64 (neg.f64 x) x)) |
(+.f64 (*.f64 x x) y) |
(+.f64 y (*.f64 x x)) |
(*.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x) |
(*.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x)) |
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x)) |
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64))) |
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x))) |
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x))) |
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x))) |
(*.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64)) |
(*.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64))) |
(*.f64 (fabs.f64 x) (fabs.f64 x)) |
(*.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64))) |
(*.f64 (neg.f64 x) (neg.f64 x)) |
(*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x)) |
(*.f64 #s(literal 1 binary64) (*.f64 x x)) |
(*.f64 (*.f64 x x) #s(literal 1 binary64)) |
(*.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 x))) |
(*.f64 x x) |
(pow.f64 (fabs.f64 x) #s(literal 2 binary64)) |
(pow.f64 (neg.f64 x) #s(literal 2 binary64)) |
(pow.f64 x #s(literal 2 binary64)) |
(neg.f64 (*.f64 (neg.f64 x) x)) |
(fabs.f64 (*.f64 x x)) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) |
x |
y |
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64)) x) x (sqrt.f64 y))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x) x (sqrt.f64 y))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 y #s(literal -5/2 binary64)) x) x) #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) #s(literal -1/8 binary64))) x) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 y))) |
#s(approx (+ (* x x) y) y) |
#s(approx (+ (* x x) y) (fma.f64 x x y)) |
#s(approx (* x x) (*.f64 x x)) |
#s(approx x x) |
#s(approx (sqrt (+ (* x x) y)) x) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64))) x x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (*.f64 y (/.f64 (*.f64 y y) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x x)) |
#s(approx (+ (* x x) y) (*.f64 x x)) |
#s(approx (+ (* x x) y) (*.f64 (*.f64 (+.f64 (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) x) x)) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 x) (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)))) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64))) x x))) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 (*.f64 y y) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x x))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (/.f64 y (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) y x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)) |
#s(approx y y) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (pow.f64 y #s(literal -5/2 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) y)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal -5/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (pow.f64 y #s(literal -7/2 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y)) |
#s(approx (+ (* x x) y) (fma.f64 (/.f64 (*.f64 x x) y) y y)) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (neg.f64 (sqrt.f64 y)))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)) (pow.f64 y #s(literal -5/2 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal -5/2 binary64))) (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) (fma.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal -7/2 binary64))) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))) |
#s(approx (+ (* x x) y) (*.f64 (neg.f64 y) (-.f64 (/.f64 (*.f64 (neg.f64 x) x) y) #s(literal 1 binary64)))) |
Compiled 643 to 292 computations (54.6% saved)
4 alts after pruning (4 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 76 | 4 | 80 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 77 | 4 | 81 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 71.7% | (sqrt.f64 (fma.f64 x x y)) |
| ▶ | 39.4% | (sqrt.f64 #s(approx (+ (* x x) y) y)) |
| ▶ | 1.3% | #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
| ▶ | 62.6% | #s(approx (sqrt (+ (* x x) y)) x) |
Compiled 23 to 23 computations (0% saved)
| Inputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
x |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
(neg.f64 x) |
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
#s(approx (+ (* x x) y) y) |
y |
(sqrt.f64 (fma.f64 x x y)) |
(fma.f64 x x y) |
| Outputs |
|---|
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt y))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (neg x) #s(hole binary64 (* -1 x))) |
#s(approx (+ (* x x) y) #s(hole binary64 y)) |
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2)))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2)))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))) |
#s(approx y #s(hole binary64 y)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))))) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | ((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y)) |
| 1.0ms | y | @ | -inf | ((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y)) |
| 1.0ms | x | @ | inf | ((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y)) |
| 0.0ms | y | @ | inf | ((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y)) |
| 0.0ms | x | @ | 0 | ((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 173 | 761 |
| 0 | 176 | 692 |
| 0 | 527 | 660 |
| 0 | 3643 | 624 |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | iter-limit |
| 1× | unsound |
| 1× | iter-limit |
| Inputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
x |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
(neg.f64 x) |
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
#s(approx (+ (* x x) y) y) |
y |
(sqrt.f64 (fma.f64 x x y)) |
(fma.f64 x x y) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (sqrt y))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (neg x) #s(hole binary64 (* -1 x))) |
#s(approx (+ (* x x) y) #s(hole binary64 y)) |
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2)))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 x)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (pow x 2))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2)))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))) |
#s(approx y #s(hole binary64 y)) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))) |
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1))))) |
| Outputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
x |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
(*.f64 #s(literal -1 binary64) x) |
(*.f64 x #s(literal -1 binary64)) |
(neg.f64 x) |
(*.f64 (pow.f64 #s(approx (+ (* x x) y) y) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (* x x) y) y) #s(literal 1/4 binary64))) |
(pow.f64 #s(approx (+ (* x x) y) y) #s(literal 1/2 binary64)) |
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
(exp.f64 (*.f64 (log.f64 #s(approx (+ (* x x) y) y)) #s(literal 1/2 binary64))) |
#s(approx (+ (* x x) y) y) |
y |
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) |
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64)) |
(sqrt.f64 (fma.f64 x x y)) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 y y)) (-.f64 (*.f64 x x) y)) |
(/.f64 (-.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 y (*.f64 x x))) |
(/.f64 (+.f64 (pow.f64 (*.f64 x x) #s(literal 3 binary64)) (*.f64 (*.f64 y y) y)) (fma.f64 (*.f64 x x) (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 (*.f64 x x) y)))) |
(/.f64 (fma.f64 (*.f64 y y) y (pow.f64 (*.f64 x x) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 y (*.f64 x x))))) |
(fma.f64 (*.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x) y) |
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x y) |
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) y) |
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y) |
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) y) |
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) y) |
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) y) |
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64) y) |
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 1 binary64)) y) |
(fma.f64 (fabs.f64 x) (fabs.f64 x) y) |
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) y) |
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y) |
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y) |
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) y) |
(fma.f64 (neg.f64 x) (neg.f64 x) y) |
(fma.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 x)) y) |
(fma.f64 x x y) |
(-.f64 y (*.f64 (neg.f64 x) x)) |
(+.f64 (*.f64 x x) y) |
(+.f64 y (*.f64 x x)) |
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64)) x) x (sqrt.f64 y))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x) x (sqrt.f64 y))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (pow.f64 y #s(literal -5/2 binary64)) x) x) #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) #s(literal -1/8 binary64))) x) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 y))) |
#s(approx x x) |
#s(approx (neg x) (neg.f64 x)) |
#s(approx (+ (* x x) y) y) |
#s(approx (+ (* x x) y) (fma.f64 x x y)) |
#s(approx (sqrt (+ (* x x) y)) x) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64))) x x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (*.f64 y (/.f64 (*.f64 y y) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x x)) |
#s(approx (+ (* x x) y) (*.f64 x x)) |
#s(approx (+ (* x x) y) (*.f64 (*.f64 (+.f64 (/.f64 y (*.f64 x x)) #s(literal 1 binary64)) x) x)) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x))) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64))) x x))) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (fma.f64 (fma.f64 (*.f64 y (/.f64 (*.f64 y y) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (*.f64 y y) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64) (*.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x x))) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (/.f64 y (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) y x)) |
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 x x) x))) y (/.f64 #s(literal 1/2 binary64) x)) y x)) |
#s(approx y y) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 (pow.f64 y #s(literal -5/2 binary64)) #s(literal -1/8 binary64)) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) y)) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (+.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal -5/2 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (pow.f64 y #s(literal -7/2 binary64)) #s(literal 1/16 binary64)) (*.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (*.f64 x x)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y)) |
#s(approx (+ (* x x) y) (fma.f64 (/.f64 (*.f64 x x) y) y y)) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (neg.f64 (sqrt.f64 y)))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)) (pow.f64 y #s(literal -5/2 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))))) |
#s(approx (sqrt (+ (* x x) y)) (*.f64 (neg.f64 y) (fma.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal -7/2 binary64))) (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (fma.f64 (*.f64 (neg.f64 (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/8 binary64)) (pow.f64 y #s(literal -5/2 binary64)) (fma.f64 (*.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) y))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))))) |
#s(approx (+ (* x x) y) (*.f64 (neg.f64 y) (-.f64 (/.f64 (*.f64 (neg.f64 x) x) y) #s(literal 1 binary64)))) |
Compiled 551 to 234 computations (57.5% saved)
4 alts after pruning (0 fresh and 4 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 62 | 0 | 62 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 4 | 4 |
| Done | 0 | 0 | 0 |
| Total | 62 | 4 | 66 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 71.7% | (sqrt.f64 (fma.f64 x x y)) |
| ✓ | 39.4% | (sqrt.f64 #s(approx (+ (* x x) y) y)) |
| ✓ | 1.3% | #s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
| ✓ | 62.6% | #s(approx (sqrt (+ (* x x) y)) x) |
Compiled 43 to 38 computations (11.6% saved)
| Inputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
(sqrt.f64 (fma.f64 x x y)) |
(sqrt.f64 (+.f64 (*.f64 x x) y)) |
| Outputs |
|---|
(sqrt.f64 (fma.f64 x x y)) |
#s(approx (sqrt (+ (* x x) y)) x) |
5 calls:
| 2.0ms | y |
| 2.0ms | x |
| 2.0ms | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 2.0ms | (+.f64 (*.f64 x x) y) |
| 2.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 2 | (*.f64 x x) |
| 100.0% | 2 | (+.f64 (*.f64 x x) y) |
| 100.0% | 2 | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 100.0% | 2 | x |
| 83.3% | 2 | y |
Compiled 13 to 16 computations (-23.1% saved)
| Inputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
| Outputs |
|---|
(sqrt.f64 #s(approx (+ (* x x) y) y)) |
#s(approx (sqrt (+ (* x x) y)) x) |
4 calls:
| 54.0ms | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 1.0ms | x |
| 1.0ms | (+.f64 (*.f64 x x) y) |
| 1.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 88.9% | 2 | (*.f64 x x) |
| 74.6% | 2 | (+.f64 (*.f64 x x) y) |
| 74.6% | 2 | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 88.9% | 2 | x |
Compiled 12 to 14 computations (-16.7% saved)
Total -39.2b remaining (-163.6%)
Threshold costs -39.2b (-163.6%)
| Inputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x)) |
| Outputs |
|---|
#s(approx (sqrt (+ (* x x) y)) x) |
5 calls:
| 1.0ms | x |
| 1.0ms | y |
| 1.0ms | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 1.0ms | (+.f64 (*.f64 x x) y) |
| 1.0ms | (*.f64 x x) |
| Accuracy | Segments | Branch |
|---|---|---|
| 62.6% | 1 | (+.f64 (*.f64 x x) y) |
| 62.6% | 1 | (sqrt.f64 (+.f64 (*.f64 x x) y)) |
| 62.6% | 1 | y |
| 62.6% | 1 | (*.f64 x x) |
| 62.6% | 1 | x |
Compiled 13 to 16 computations (-23.1% saved)
| 1× | binary-search |
| 1× | predicate-same |
| Time | Left | Right |
|---|---|---|
| 1.0ms | 3.41263107419282e+150 | 4.992326222766559e+150 |
| 1.0ms | 16× | 0 | valid |
Compiled 19 to 22 computations (-15.8% saved)
adjust: 0.0ms (0% of total)ival-add!: 0.0ms (0% of total)ival-sqrt: 0.0ms (0% of total)ival-mult!: 0.0ms (0% of total)| 1× | binary-search |
| 1× | narrow-enough |
| Time | Left | Right |
|---|---|---|
| 6.0ms | 5.402378812091585e-35 | 1.6878407703228967e-34 |
| 3.0ms | 80× | 0 | valid |
| 0.0ms | 12× | 0 | invalid |
Compiled 69 to 80 computations (-15.9% saved)
ival-sqrt: 1.0ms (74% of total)adjust: 0.0ms (0% of total)ival-add!: 0.0ms (0% of total)ival-mult!: 0.0ms (0% of total)| 1× | done |
Compiled 18 to 16 computations (11.1% saved)
Compiled 83 to 77 computations (7.2% saved)
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