
Time bar (total: 2.3s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50% | 0% | 0% | 50% | 0% | 2 |
| 50% | 25% | 25% | 0% | 0% | 50% | 0% | 3 |
| 66.7% | 25% | 12.5% | 0% | 0% | 62.5% | 0% | 4 |
| 80% | 25% | 6.2% | 0% | 0% | 68.7% | 0% | 5 |
| 88.9% | 25% | 3.1% | 0% | 0% | 71.8% | 0% | 6 |
| 94.1% | 25% | 1.6% | 0% | 0% | 73.4% | 0% | 7 |
| 97% | 25% | 0.8% | 0% | 0% | 74.2% | 0% | 8 |
| 98.5% | 25% | 0.4% | 0% | 0% | 74.6% | 0% | 9 |
| 99.2% | 25% | 0.2% | 0% | 0% | 74.8% | 0% | 10 |
| 99.6% | 25% | 0.1% | 0% | 0% | 74.9% | 0% | 11 |
| 99.8% | 25% | 0% | 0% | 0% | 74.9% | 0% | 12 |
Compiled 9 to 8 computations (11.1% saved)
| 387.0ms | 8 250× | 0 | valid |
| 0.0ms | 10× | 0 | invalid |
| 0.0ms | 6× | 1 | valid |
ival-sqrt: 184.0ms (74.8% of total)ival-mult!: 32.0ms (13% of total)ival-sub!: 28.0ms (11.4% of total)adjust: 2.0ms (0.8% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 12 | 23 |
| 1 | 30 | 23 |
| 2 | 48 | 23 |
| 3 | 76 | 23 |
| 4 | 255 | 23 |
| 5 | 2233 | 23 |
| 1× | node-limit |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.1% | (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 12 to 12 computations (0% saved)
| Inputs |
|---|
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
| Outputs |
|---|
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (- x 1) #s(hole binary64 -1)) |
#s(approx (- x 1) #s(hole binary64 (- x 1))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sqrt x) #s(hole binary64 (sqrt x))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x)) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))) |
#s(approx (- x 1) #s(hole binary64 x)) |
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1))))) |
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | ((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x)) |
| 1.0ms | x | @ | 0 | ((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x)) |
| 1.0ms | x | @ | inf | ((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x)) |
| Inputs |
|---|
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (- x 1) #s(hole binary64 -1)) |
#s(approx (- x 1) #s(hole binary64 (- x 1))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (sqrt x) #s(hole binary64 (sqrt x))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x)) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))) |
#s(approx (- x 1) #s(hole binary64 x)) |
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1))))) |
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) |
(sqrt.f64 (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64))))) |
x |
#s(literal 1 binary64) |
(cosh.f64 #s(literal 0 binary64)) |
(exp.f64 #s(literal 0 binary64)) |
(pow.f64 x #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
#s(approx (sqrt (* (- x 1) x)) (sqrt.f64 (*.f64 x #s(literal -1 binary64)))) |
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x #s(literal -1 binary64))))) |
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (*.f64 x #s(literal -1 binary64))))) |
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (*.f64 x #s(literal -1 binary64))))) |
#s(approx (sqrt (- x 1)) (sqrt.f64 #s(literal -1 binary64))) |
#s(approx (sqrt (- x 1)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (- x 1) #s(literal -1 binary64)) |
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64))) |
#s(approx x x) |
#s(approx (sqrt x) (sqrt.f64 x)) |
#s(approx (sqrt (* (- x 1) x)) x) |
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (sqrt (* (- x 1) x)) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) |
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (sqrt (- x 1)) (sqrt.f64 x)) |
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)) |
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64))) x)) |
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64)))) x)) |
#s(approx (- x 1) x) |
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) |
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x))) |
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x))) |
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x))) x))) |
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) x))) x))) x))) |
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)))) |
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))) x))) |
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) x))) |
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))) x))) |
#s(approx (- x 1) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))) |
#s(approx (sqrt x) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)))) |
Compiled 486 to 228 computations (53.1% saved)
3 alts after pruning (3 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 37 | 3 | 40 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 38 | 3 | 41 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 97.7% | (*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
| ▶ | 50.5% | (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
| ▶ | 98.6% | #s(approx (sqrt (* (- x 1) x)) x) |
Compiled 18 to 18 computations (0% saved)
| Inputs |
|---|
#s(approx (sqrt (* (- x 1) x)) x) |
x |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(*.f64 (-.f64 x #s(literal 1 binary64)) x) |
(-.f64 x #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
(sqrt.f64 #s(approx (- x 1) x)) |
#s(approx (- x 1) x) |
(sqrt.f64 x) |
| Outputs |
|---|
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (* (- x 1) x) #s(hole binary64 (* -1 x))) |
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1)))) |
#s(approx (- x 1) #s(hole binary64 -1)) |
#s(approx (- x 1) #s(hole binary64 (- x 1))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt x) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 x)) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (* (- x 1) x) #s(hole binary64 (pow x 2))) |
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x))))) |
#s(approx (- x 1) #s(hole binary64 x)) |
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x)) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))))) |
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | ((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x)) |
| 1.0ms | x | @ | inf | ((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x)) |
| 1.0ms | x | @ | 0 | ((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x)) |
| Inputs |
|---|
#s(approx (sqrt (* (- x 1) x)) x) |
x |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(*.f64 (-.f64 x #s(literal 1 binary64)) x) |
(-.f64 x #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
(sqrt.f64 #s(approx (- x 1) x)) |
#s(approx (- x 1) x) |
(sqrt.f64 x) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx x #s(hole binary64 x)) |
#s(approx (* (- x 1) x) #s(hole binary64 (* -1 x))) |
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1)))) |
#s(approx (- x 1) #s(hole binary64 -1)) |
#s(approx (- x 1) #s(hole binary64 (- x 1))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1)))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5))))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))))) |
#s(approx (sqrt x) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 x)) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (* (- x 1) x) #s(hole binary64 (pow x 2))) |
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x))))) |
#s(approx (- x 1) #s(hole binary64 x)) |
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x)) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 x))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 x))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))) |
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))))))) |
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2)))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))) |
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2))))) |
| Outputs |
|---|
#s(approx (sqrt (* x (- x 1))) x) |
x |
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(pow.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1/2 binary64)) |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(*.f64 (-.f64 x #s(literal 1 binary64)) x) |
(*.f64 x (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64))))) |
#s(literal 1 binary64) |
(cosh.f64 #s(literal 0 binary64)) |
(exp.f64 #s(literal 0 binary64)) |
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
(sqrt.f64 #s(approx (- x 1) x)) |
#s(approx (- x 1) x) |
(pow.f64 x #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
#s(approx (sqrt (* x (- x 1))) (sqrt.f64 (neg.f64 x))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x)))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x)))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x)))) |
#s(approx x x) |
#s(approx (* x (- x 1)) (neg.f64 x)) |
#s(approx (* x (- x 1)) (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
#s(approx (- x 1) #s(literal -1 binary64)) |
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64))) |
#s(approx (sqrt (* x (- x 1))) (sqrt.f64 (neg.f64 x))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x)))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x)))) |
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x)))) |
#s(approx (sqrt (- x 1)) (sqrt.f64 #s(literal -1 binary64))) |
#s(approx (sqrt (- x 1)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))) |
#s(approx (sqrt x) (sqrt.f64 x)) |
#s(approx (sqrt (* x (- x 1))) x) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (* x (- x 1)) (*.f64 x x)) |
#s(approx (* x (- x 1)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x))) |
#s(approx (- x 1) x) |
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) |
#s(approx (sqrt (* x (- x 1))) x) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x)) |
#s(approx (sqrt (- x 1)) (sqrt.f64 x)) |
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)) |
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)) |
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)) |
#s(approx (sqrt (* x (- x 1))) (neg.f64 x)) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/16 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)))) |
#s(approx (- x 1) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x))))) |
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) x))) x))))) |
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)))) |
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))) |
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))) |
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/16 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))) |
#s(approx (sqrt x) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)))) |
Compiled 560 to 251 computations (55.2% saved)
3 alts after pruning (0 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 50 | 0 | 50 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 3 | 3 |
| Done | 0 | 0 | 0 |
| Total | 50 | 3 | 53 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 97.7% | (*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
| ✓ | 50.5% | (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
| ✓ | 98.6% | #s(approx (sqrt (* (- x 1) x)) x) |
Compiled 36 to 34 computations (5.6% saved)
| Inputs |
|---|
#s(approx (sqrt (* (- x 1) x)) x) |
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
2 calls:
| 2.0ms | x |
| 2.0ms | (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 99.1% | 1 | x |
Compiled 7 to 7 computations (0% saved)
Total -31.9b remaining (-3516.8%)
Threshold costs -31.9b (-3516.8%)
| Inputs |
|---|
#s(approx (sqrt (* (- x 1) x)) x) |
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x)) |
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x)) |
| Outputs |
|---|
#s(approx (sqrt (* (- x 1) x)) x) |
2 calls:
| 1.0ms | (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.6% | 1 | (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 98.6% | 1 | x |
Compiled 7 to 7 computations (0% saved)
| 1× | done |
Compiled 11 to 11 computations (0% saved)
Compiled 17 to 17 computations (0% saved)
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