sqrt times

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze1.0ms (0.1%)

Memory
1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample809.0ms (57.6%)

Memory
40.2MiB live, 632.3MiB allocated; 877ms collecting garbage
Samples
631.0ms8 242×0valid
1.0ms14×1valid
0.0ms7×0invalid
Precisions
Click to see histograms. Total time spent on operations: 496.0ms
ival-sqrt: 374.0ms (75.5% of total)
ival-mult!: 94.0ms (19% of total)
ival-sub!: 26.0ms (5.2% of total)
adjust: 2.0ms (0.4% of total)
Bogosity

preprocess117.0ms (8.3%)

Memory
-40.1MiB live, 50.3MiB allocated; 24ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01223
13023
24823
37623
425523
5223323
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 12 to 12 computations (0% saved)

series6.0ms (0.4%)

Memory
8.2MiB live, 8.2MiB allocated; 0ms collecting garbage
Counts
6 → 28
Calls
Call 1
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 (- 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 (* 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 (- 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)))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
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))

rewrite60.0ms (4.3%)

Memory
9.3MiB live, 53.5MiB allocated; 5ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0184720
0189568
01103547
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
34 → 40
Calls
Call 1
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 (- 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 (* 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 (- 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)))))
Outputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(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 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x) (sqrt.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 1/16 binary64))) (*.f64 x x))) (*.f64 x x) (sqrt.f64 (*.f64 #s(literal -1 binary64) 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 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 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 x (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) x (/.f64 #s(literal 1/2 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)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal -1/16 binary64) (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal -1 binary64)) #s(literal 1/16 binary64) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))))) x)))
#s(approx (- x 1) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))

eval4.0ms (0.3%)

Memory
5.6MiB live, 5.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 379 to 202 computations (46.7% saved)

prune4.0ms (0.3%)

Memory
6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New29534
Fresh000
Picked011
Done000
Total29635
Accuracy
100.0%
Counts
35 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶98.4%
(*.f64 #s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)) (sqrt.f64 x))
▶52.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶98.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
▶98.9%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
▶97.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
Compiler

Compiled 138 to 136 computations (1.4% saved)

series49.0ms (3.5%)

Memory
-17.5MiB live, 45.6MiB allocated; 65ms collecting garbage
Counts
39 → 84
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
(*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)
(+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
(neg.f64 (*.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(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(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))))
(sqrt.f64 (pow.f64 x #s(literal -5 binary64)))
(pow.f64 x #s(literal -5 binary64))
#s(literal -5 binary64)
#s(literal -1/8 binary64)
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
#s(literal -1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))
(sqrt.f64 (*.f64 (*.f64 x x) x))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ -1/8 (pow x 2))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ (- (* -1/2 x) 1/8) (pow x 2))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) (pow x 2))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ 1/8 (pow x 2))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) (pow x 2))))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (/ 1/8 x)))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (* -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 (* (- 1 (/ 1/2 x)) x) #s(hole binary64 -1/2))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (- x 1/2)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ -1/2 x)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ (- x 1/2) x)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 2))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* x (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))))) (pow x 2))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 5))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* x (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))))) (pow x 3))))
#s(approx (sqrt (pow x -5)) #s(hole binary64 (sqrt (/ 1 (pow x 5)))))
#s(approx (pow x -5) #s(hole binary64 (/ 1 (pow x 5))))
#s(approx (* -1/2 (/ 1 (sqrt (* (* x x) x)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ 1 (sqrt (* (* x x) x))) #s(hole binary64 (sqrt (/ 1 (pow x 3)))))
#s(approx (sqrt (* (* x x) x)) #s(hole binary64 (sqrt (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt 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 (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 1))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (- 1 (* 1/2 (/ 1 x)))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
#s(approx (neg (/ (+ (/ 1/8 x) 1/2) x)) #s(hole binary64 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 1/2))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ 1 x)))))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x)))))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
#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)) #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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (sqrt (/ 1 x)))) x)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (* 1/2 (sqrt (/ 1 (pow x 3))))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))))
#s(approx (sqrt (pow x -5)) #s(hole binary64 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))))
#s(approx (/ 1 (sqrt (* (* x x) x))) #s(hole binary64 (* -1 (sqrt (/ 1 (pow x 3))))))
#s(approx (sqrt (* (* x x) x)) #s(hole binary64 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))))
Calls

3 calls:

TimeVariablePointExpression
30.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) (neg (/ (+ (/ 1/8 x) 1/2) x)) (/ (+ (/ 1/8 x) 1/2) x) (+ (/ 1/8 x) 1/2) (/ 1/8 x) 1/8 x 1/2 1 (* (sqrt (- x 1)) (sqrt x)) (neg (* -1 x)) (* -1 x) -1 (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) (/ 1/2 x) (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (sqrt (pow x -5)) (pow x -5) -5 -1/8 (* -1/2 (/ 1 (sqrt (* (* x x) x)))) -1/2 (/ 1 (sqrt (* (* x x) x))) (sqrt (* (* x x) x)) (* (* x x) x) (* x x) (/ 1 (sqrt x)) (sqrt x))
11.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) (neg (/ (+ (/ 1/8 x) 1/2) x)) (/ (+ (/ 1/8 x) 1/2) x) (+ (/ 1/8 x) 1/2) (/ 1/8 x) 1/8 x 1/2 1 (* (sqrt (- x 1)) (sqrt x)) (neg (* -1 x)) (* -1 x) -1 (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) (/ 1/2 x) (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (sqrt (pow x -5)) (pow x -5) -5 -1/8 (* -1/2 (/ 1 (sqrt (* (* x x) x)))) -1/2 (/ 1 (sqrt (* (* x x) x))) (sqrt (* (* x x) x)) (* (* x x) x) (* x x) (/ 1 (sqrt x)) (sqrt x))
5.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) (neg (/ (+ (/ 1/8 x) 1/2) x)) (/ (+ (/ 1/8 x) 1/2) x) (+ (/ 1/8 x) 1/2) (/ 1/8 x) 1/8 x 1/2 1 (* (sqrt (- x 1)) (sqrt x)) (neg (* -1 x)) (* -1 x) -1 (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (- 1 (/ 1/2 x)) (/ 1/2 x) (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (sqrt (pow x -5)) (pow x -5) -5 -1/8 (* -1/2 (/ 1 (sqrt (* (* x x) x)))) -1/2 (/ 1 (sqrt (* (* x x) x))) (sqrt (* (* x x) x)) (* (* x x) x) (* x x) (/ 1 (sqrt x)) (sqrt x))

rewrite69.0ms (4.9%)

Memory
12.6MiB live, 58.4MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03652217
04121773
019001744
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
123 → 238
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
(*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x)
(+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))
(neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x))
(/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)
(+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
(neg.f64 (*.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(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(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))))
(sqrt.f64 (pow.f64 x #s(literal -5 binary64)))
(pow.f64 x #s(literal -5 binary64))
#s(literal -5 binary64)
#s(literal -1/8 binary64)
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
#s(literal -1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))
(sqrt.f64 (*.f64 (*.f64 x x) x))
(*.f64 (*.f64 x x) x)
(*.f64 x x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ -1/8 (pow x 2))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ (- (* -1/2 x) 1/8) (pow x 2))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) (pow x 2))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ 1/8 (pow x 2))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) (pow x 2))))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (/ 1/8 x)))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (/ (+ 1/8 (* 1/2 x)) x)))
#s(approx x #s(hole binary64 x))
#s(approx (* -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 (* (- 1 (/ 1/2 x)) x) #s(hole binary64 -1/2))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(hole binary64 (- x 1/2)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ -1/2 x)))
#s(approx (- 1 (/ 1/2 x)) #s(hole binary64 (/ (- x 1/2) x)))
#s(approx (/ 1/2 x) #s(hole binary64 (/ 1/2 x)))
#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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 3))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 2))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* x (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))))) (pow x 2))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (* -1/8 (sqrt (/ 1 (pow x 5))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) (pow x 3))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* -1/8 (sqrt x)) (* x (+ (sqrt (pow x 3)) (* -1/2 (sqrt x))))) (pow x 3))))
#s(approx (sqrt (pow x -5)) #s(hole binary64 (sqrt (/ 1 (pow x 5)))))
#s(approx (pow x -5) #s(hole binary64 (/ 1 (pow x 5))))
#s(approx (* -1/2 (/ 1 (sqrt (* (* x x) x)))) #s(hole binary64 (* -1/2 (sqrt (/ 1 (pow x 3))))))
#s(approx (/ 1 (sqrt (* (* x x) x))) #s(hole binary64 (sqrt (/ 1 (pow x 3)))))
#s(approx (sqrt (* (* x x) x)) #s(hole binary64 (sqrt (pow x 3))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt 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 (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 1))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (- 1 (* 1/2 (/ 1 x)))))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(hole binary64 (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
#s(approx (neg (/ (+ (/ 1/8 x) 1/2) x)) #s(hole binary64 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 1/2))
#s(approx (+ (/ 1/8 x) 1/2) #s(hole binary64 (+ 1/2 (* 1/8 (/ 1 x)))))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x)))))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
#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)) #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 (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* x (+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (sqrt (/ 1 x)))) x)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) #s(hole binary64 (+ (sqrt (/ 1 x)) (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (* 1/2 (sqrt (/ 1 (pow x 3))))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) #s(hole binary64 (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))))
#s(approx (sqrt (pow x -5)) #s(hole binary64 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))))
#s(approx (/ 1 (sqrt (* (* x x) x))) #s(hole binary64 (* -1 (sqrt (/ 1 (pow x 3))))))
#s(approx (sqrt (* (* x x) x)) #s(hole binary64 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))))
Outputs
#s(approx (sqrt (* (- x 1) x)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) x))
(*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) x)
(*.f64 x (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) x))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))))
(+.f64 (*.f64 x #s(literal 1 binary64)) (*.f64 x (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))))
(+.f64 (neg.f64 (neg.f64 x)) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))) #s(literal 1 binary64)) (-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)))) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))))
(/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))) (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))))))
(fma.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) #s(literal -1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
(/.f64 (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) x)
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))
(neg.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
(/.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (neg.f64 x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(+.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) x) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/8 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/8 binary64) x) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64))
(*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1/8 binary64) (neg.f64 x))
(/.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 x))
(*.f64 #s(literal 1 binary64) x)
(neg.f64 (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
#s(literal -1 binary64)
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(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 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))))
(-.f64 x #s(literal 1 binary64))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x)
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))))
(-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x)))
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#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (/.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (sqrt.f64 (*.f64 (*.f64 x x) x))) x (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)))
#s(approx (sqrt (pow x -5)) (pow.f64 x #s(literal -5/2 binary64)))
#s(approx (pow x -5) (pow.f64 x #s(literal -5 binary64)))
#s(approx (* -1/2 (/ 1 (sqrt (* (* x x) x)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
#s(approx (/ 1 (sqrt (* (* x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))
#s(approx (sqrt (* (* x x) x)) (sqrt.f64 (*.f64 (*.f64 x x) x)))
#s(approx (* (* x x) x) (*.f64 (*.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx (/ 1 (sqrt x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) #s(literal 1 binary64))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)))
#s(approx (neg (/ (+ (/ 1/8 x) 1/2) x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)))
#s(approx (/ (+ (/ 1/8 x) 1/2) x) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))
#s(approx (+ (/ 1/8 x) 1/2) #s(literal 1/2 binary64))
#s(approx (+ (/ 1/8 x) 1/2) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
#s(approx (* (- x 1) x) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x)))
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal -1/16 binary64) (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1/8 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (fma.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64))) x))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (neg.f64 x)))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64))))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (*.f64 (neg.f64 x) (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) #s(literal 1 binary64))))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64))))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) x)) 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 1)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (pow.f64 x #s(literal -7 binary64)))) #s(literal -1 binary64) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/2 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))))
#s(approx (* (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) x) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal -1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) x)) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))))
#s(approx (+ (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (/ 1 (sqrt x))) (+.f64 (neg.f64 (/.f64 (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64))) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))
#s(approx (+ (* (sqrt (pow x -5)) -1/8) (* -1/2 (/ 1 (sqrt (* (* x x) x))))) (neg.f64 (/.f64 (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) #s(literal 1/8 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64))) x)))
#s(approx (sqrt (pow x -5)) (*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal -1 binary64)))
#s(approx (/ 1 (sqrt (* (* x x) x))) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))))
#s(approx (sqrt (* (* x x) x)) (*.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1 binary64)))

eval56.0ms (4%)

Memory
-15.8MiB live, 29.9MiB allocated; 5ms collecting garbage
Compiler

Compiled 2 530 to 1 177 computations (53.5% saved)

prune6.0ms (0.4%)

Memory
9.4MiB live, 9.4MiB allocated; 0ms collecting garbage
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New2074211
Fresh000
Picked325
Done011
Total2107217
Accuracy
100.0%
Counts
217 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓52.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓98.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
▶97.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
▶98.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
▶1.1%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
▶51.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
Compiler

Compiled 81 to 81 computations (0% saved)

series5.0ms (0.3%)

Memory
7.2MiB live, 7.2MiB allocated; 0ms collecting garbage
Counts
17 → 28
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x))
(/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)
(-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64))
(*.f64 (-.f64 x #s(literal 1/2 binary64)) x)
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
(neg.f64 (neg.f64 x))
(neg.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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 -1/8))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* -1/2 x) 1/8)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* x (- x 1/2)) 1/8)))
#s(approx (* (- x 1/2) x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (- x 1/2) x) #s(hole binary64 (* x (- x 1/2))))
#s(approx (- x 1/2) #s(hole binary64 -1/2))
#s(approx (- x 1/2) #s(hole binary64 (- x 1/2)))
#s(approx x #s(hole binary64 x))
#s(approx (neg x) #s(hole binary64 (* -1 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 (- (* (- x 1/2) x) 1/8) #s(hole binary64 (pow x 2)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* (- x 1/2) x) (- x 1/2) x 1/2 1/8 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) -1/2 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (* (sqrt (- x 1)) (sqrt x)) (neg (neg x)) (neg x))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* (- x 1/2) x) (- x 1/2) x 1/2 1/8 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) -1/2 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (* (sqrt (- x 1)) (sqrt x)) (neg (neg x)) (neg x))
1.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* (- x 1/2) x) (- x 1/2) x 1/2 1/8 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) -1/2 (* (sqrt (- x 1)) (sqrt x)) (* (- 1 (/ 1/2 x)) x) (* (sqrt (- x 1)) (sqrt x)) (neg (neg x)) (neg x))

rewrite62.0ms (4.4%)

Memory
-19.8MiB live, 26.2MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0164734
0174624
0887618
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
45 → 54
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x))
(/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)
(-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64))
(*.f64 (-.f64 x #s(literal 1/2 binary64)) x)
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
(neg.f64 (neg.f64 x))
(neg.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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 -1/8))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* -1/2 x) 1/8)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* x (- x 1/2)) 1/8)))
#s(approx (* (- x 1/2) x) #s(hole binary64 (* -1/2 x)))
#s(approx (* (- x 1/2) x) #s(hole binary64 (* x (- x 1/2))))
#s(approx (- x 1/2) #s(hole binary64 -1/2))
#s(approx (- x 1/2) #s(hole binary64 (- x 1/2)))
#s(approx x #s(hole binary64 x))
#s(approx (neg x) #s(hole binary64 (* -1 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 (- (* (- x 1/2) x) 1/8) #s(hole binary64 (pow x 2)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x))
(/.f64 (neg.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64))) (neg.f64 x))
(/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)
(-.f64 (/.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) x) (/.f64 #s(literal 1/8 binary64) x))
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) (*.f64 (-.f64 x #s(literal 1/2 binary64)) x)) #s(literal 1/64 binary64)) (fma.f64 (-.f64 x #s(literal 1/2 binary64)) x #s(literal 1/8 binary64)))
(/.f64 (-.f64 (pow.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1/512 binary64)) (fma.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) (+.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)))))
(-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64))
(*.f64 (-.f64 x #s(literal 1/2 binary64)) x)
(*.f64 x (-.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) (fma.f64 x x (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(literal 1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (neg.f64 x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 1/16 binary64))) (*.f64 x x))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(literal -1/8 binary64) x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x))
#s(approx (- (* (- x 1/2) x) 1/8) #s(literal -1/8 binary64))
#s(approx (- (* (- x 1/2) x) 1/8) (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)))
#s(approx (- (* (- x 1/2) x) 1/8) (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)))
#s(approx (* (- x 1/2) x) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* (- x 1/2) x) (*.f64 (-.f64 x #s(literal 1/2 binary64)) x))
#s(approx (- x 1/2) #s(literal -1/2 binary64))
#s(approx (- x 1/2) (-.f64 x #s(literal 1/2 binary64)))
#s(approx x x)
#s(approx (neg x) (neg.f64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x))
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x)))
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (*.f64 (neg.f64 x) (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))))

eval4.0ms (0.3%)

Memory
6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 438 to 243 computations (44.5% saved)

prune2.0ms (0.2%)

Memory
4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New39241
Fresh000
Picked224
Done123
Total42648
Accuracy
100.0%
Counts
48 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓52.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓98.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
✓51.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
▶49.5%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
▶97.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 76 to 76 computations (0% saved)

series3.0ms (0.2%)

Memory
4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Counts
7 → 23
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x))
(/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x))
(*.f64 x 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 x #s(hole binary64 x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 -1/8))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* -1/2 x) 1/8)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* x (- x 1/2)) 1/8)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) x (* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* x x))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) x (* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* x x))
1.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) x (* (sqrt (- x 1)) (sqrt x)) (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/ (- (* (- x 1/2) x) 1/8) x) (- (* (- x 1/2) x) 1/8) (* x x))

rewrite47.0ms (3.3%)

Memory
-1.4MiB live, 49.2MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0148637
0150541
0847535
Stop Event
1×iter-limit
1×iter-limit
1×node-limit
1×iter-limit
Counts
30 → 36
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x))
(/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x))
(*.f64 x 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 x #s(hole binary64 x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ -1/8 x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* -1/2 x) 1/8) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (/ (- (* x (- x 1/2)) 1/8) x)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 -1/8))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* -1/2 x) 1/8)))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (- (* x (- x 1/2)) 1/8)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#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 (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (- 1 (* 1/2 (/ 1 x))))))
#s(approx (- (* (- x 1/2) x) 1/8) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) 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 (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) #s(hole binary64 (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x))
(/.f64 (neg.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x))) (neg.f64 x))
(/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (sqrt.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) (*.f64 x x) (sqrt.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (*.f64 (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -5 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal 1/16 binary64))) (*.f64 x x))) (*.f64 x x) (sqrt.f64 (*.f64 #s(literal -1 binary64) x))))
#s(approx x x)
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(literal -1/8 binary64) x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x))
#s(approx (- (* (- x 1/2) x) 1/8) #s(literal -1/8 binary64))
#s(approx (- (* (- x 1/2) x) 1/8) (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)))
#s(approx (- (* (- x 1/2) x) 1/8) (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x)) x))
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x)))
#s(approx (- (* (- x 1/2) x) 1/8) (*.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x)) #s(literal 1 binary64)) (*.f64 x x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) #s(literal 1/2 binary64)) x)) #s(literal -1 binary64)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (neg.f64 (*.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) x)))

eval3.0ms (0.2%)

Memory
7.2MiB live, 7.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 338 to 190 computations (43.8% saved)

prune4.0ms (0.3%)

Memory
8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New29029
Fresh000
Picked022
Done044
Total29635
Accuracy
100.0%
Counts
35 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.2%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓52.3%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓98.4%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
✓51.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
✓49.5%
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
✓97.2%
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Compiler

Compiled 175 to 154 computations (12% saved)

regimes11.0ms (0.8%)

Memory
-21.2MiB live, 22.7MiB allocated; 5ms collecting garbage
Counts
12 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 (-.f64 (*.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
(*.f64 #s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (*.f64 x x) x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Calls

2 calls:

7.0ms
x
4.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.2%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.2%1x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes6.0ms (0.4%)

Memory
14.4MiB live, 14.4MiB allocated; 0ms collecting garbage
Counts
8 → 2
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
Outputs
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) x))
Calls

2 calls:

3.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms
x
Results
AccuracySegmentsBranch
100.0%2(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
100.0%2x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes5.0ms (0.4%)

Memory
13.5MiB live, 13.5MiB allocated; 0ms collecting garbage
Counts
7 → 2
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
Outputs
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Calls

2 calls:

2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms
x
Results
AccuracySegmentsBranch
100.0%2(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
100.0%2x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes8.0ms (0.6%)

Memory
-30.4MiB live, 13.1MiB allocated; 6ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (+ (neg (/ (+ (/ 1/8 x) 1/2) x)) 1) x) (/.f64 #s(approx (- (* (- x 1/2) x) 1/8) (*.f64 x x)) x)))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) (-.f64 x #s(literal 1/2 binary64))))
Calls

2 calls:

5.0ms
x
2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
98.4%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
98.4%1x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0.2%)

Memory
9.5MiB live, 9.5MiB allocated; 0ms collecting garbage
Accuracy

Total -61.5b remaining (-3405%)

Threshold costs -61.5b (-3405%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(approx (* (- 1 (/ 1/2 x)) x) #s(literal -1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (neg.f64 (neg.f64 x)))
Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
Calls

2 calls:

1.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
97.2%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
97.2%1x
Compiler

Compiled 7 to 7 computations (0% saved)

bsearch3.0ms (0.2%)

Memory
7.4MiB live, 7.4MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
2.0ms
8170285.19823038
125853683.37118278
Samples
1.0ms32×0valid
Compiler

Compiled 44 to 48 computations (-9.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-sub!: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
ival-mult!: 0.0ms (0% of total)

bsearch4.0ms (0.3%)

Memory
12.3MiB live, 12.3MiB allocated; 0ms collecting garbage
Algorithm
1×binary-search
Stop Event
1×predicate-same
Steps
TimeLeftRight
4.0ms
419972027495181.7
8008293924474688.0
Samples
1.0ms32×0valid
1.0ms16×1valid
Compiler

Compiled 46 to 52 computations (-13% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.0ms
ival-sqrt: 1.0ms (71.7% of total)
adjust: 0.0ms (0% of total)
ival-sub!: 0.0ms (0% of total)
ival-mult!: 0.0ms (0% of total)

derivations19.0ms (1.4%)

Memory
-10.0MiB live, 33.9MiB allocated; 8ms collecting garbage
Stop Event
1×done
Compiler

Compiled 37 to 32 computations (13.5% saved)

preprocess35.0ms (2.5%)

Memory
-15.6MiB live, 86.7MiB allocated; 18ms collecting garbage
Compiler

Compiled 43 to 38 computations (11.6% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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