sqrt times

Time bar (total: 2.3s)

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory
1.6MiB live, 1.6MiB allocated; 0ms collecting garbage
Algorithm
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)

sample834.0ms (36.3%)

Memory
50.8MiB live, 644.6MiB allocated; 928ms collecting garbage
Samples
387.0ms8 250×0valid
0.0ms10×0invalid
0.0ms1valid
Precisions
Click to see histograms. Total time spent on operations: 246.0ms
ival-sqrt: 184.0ms (74.8% of total)
ival-mult!: 32.0ms (13% of total)
ival-sub!: 28.0ms (11.4% of total)
adjust: 2.0ms (0.8% of total)
Bogosity

preprocess192.0ms (8.3%)

Memory
-39.3MiB live, 49.2MiB allocated; 67ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01223
13023
24823
37623
425523
5223323
Stop Event
node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.1%
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Compiler

Compiled 12 to 12 computations (0% saved)

series6.0ms (0.2%)

Memory
5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Counts
6 → 32
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))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
1.0ms
x
@0
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))
1.0ms
x
@inf
((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) x 1 (sqrt x))

rewrite628.0ms (27.3%)

Memory
9.3MiB live, 135.8MiB allocated; 84ms collecting garbage
Counts
38 → 46
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))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x x) x) (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))))
x
#s(literal 1 binary64)
(cosh.f64 #s(literal 0 binary64))
(exp.f64 #s(literal 0 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
#s(approx (sqrt (* (- x 1) x)) (sqrt.f64 (*.f64 x #s(literal -1 binary64))))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 (*.f64 x #s(literal -1 binary64)))))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (*.f64 x #s(literal -1 binary64)))))
#s(approx (sqrt (* (- x 1) x)) (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (*.f64 x #s(literal -1 binary64)))))
#s(approx (sqrt (- x 1)) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (sqrt (- x 1)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (- x 1) #s(literal -1 binary64))
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (sqrt (* (- x 1) x)) x)
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
#s(approx (sqrt (* (- x 1) x)) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (sqrt (- x 1)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64)))) x))
#s(approx (- x 1) x)
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x)))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x)))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x))) x)))
#s(approx (sqrt (* (- x 1) x)) (neg.f64 (*.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) x))) x))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))) x)))
#s(approx (- x 1) (neg.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)))
#s(approx (sqrt x) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))

eval12.0ms (0.5%)

Memory
-42.3MiB live, 3.6MiB allocated; 6ms collecting garbage
Compiler

Compiled 486 to 228 computations (53.1% saved)

prune3.0ms (0.1%)

Memory
1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New37340
Fresh000
Picked101
Done000
Total38341
Accuracy
100.0%
Counts
41 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.7%
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
50.5%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
98.6%
#s(approx (sqrt (* (- x 1) x)) x)
Compiler

Compiled 18 to 18 computations (0% saved)

series6.0ms (0.3%)

Memory
2.4MiB live, 2.4MiB allocated; 0ms collecting garbage
Counts
10 → 48
Calls
Call 1
Inputs
#s(approx (sqrt (* (- x 1) x)) x)
x
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 #s(approx (- x 1) x))
#s(approx (- x 1) x)
(sqrt.f64 x)
Outputs
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (- x 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 x))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (* (- x 1) x) #s(hole binary64 (pow x 2)))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x)))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms
x
@inf
((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms
x
@0
((sqrt (* (- x 1) x)) x (sqrt (* (- x 1) x)) (* (- x 1) x) (- x 1) 1 (* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

rewrite585.0ms (25.5%)

Memory
38.0MiB live, 130.1MiB allocated; 14ms collecting garbage
Counts
58 → 67
Calls
Call 1
Inputs
#s(approx (sqrt (* (- x 1) x)) x)
x
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(-.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 #s(approx (- x 1) x))
#s(approx (- x 1) x)
(sqrt.f64 x)
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (* (- x 1) x) #s(hole binary64 (* -1 x)))
#s(approx (* (- x 1) x) #s(hole binary64 (* x (- x 1))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 x))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (* (- x 1) x) #s(hole binary64 (pow x 2)))
#s(approx (* (- x 1) x) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 x)))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))))
#s(approx (sqrt (* (- x 1) x)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
Outputs
#s(approx (sqrt (* x (- x 1))) x)
x
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(pow.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1 binary64) #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 x (*.f64 x x)) (pow.f64 #s(literal 1 binary64) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1 binary64) #s(literal 1 binary64) (*.f64 x #s(literal 1 binary64)))))
#s(literal 1 binary64)
(cosh.f64 #s(literal 0 binary64))
(exp.f64 #s(literal 0 binary64))
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 #s(approx (- x 1) x))
#s(approx (- x 1) x)
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
#s(approx (sqrt (* x (- x 1))) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx x x)
#s(approx (* x (- x 1)) (neg.f64 x))
#s(approx (* x (- x 1)) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (- x 1) #s(literal -1 binary64))
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64)))
#s(approx (sqrt (* x (- x 1))) (sqrt.f64 (neg.f64 x)))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (* x (- x 1))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) (neg.f64 #s(literal 5 binary64))))) (*.f64 x x) (*.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (*.f64 x x) (sqrt.f64 (neg.f64 x))))
#s(approx (sqrt (- x 1)) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (sqrt (- x 1)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/16 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 1/8 binary64) #s(literal 1 binary64)) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) x (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx (sqrt (* x (- x 1))) x)
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (sqrt (* x (- x 1))) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (* x (- x 1)) (*.f64 x x))
#s(approx (* x (- x 1)) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x x)))
#s(approx (- x 1) x)
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x))
#s(approx (sqrt (* x (- x 1))) x)
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (sqrt (* x (- x 1))) (*.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64)) x))
#s(approx (sqrt (* x (- x 1))) (*.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) #s(literal 1/8 binary64)) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x)) x))
#s(approx (sqrt (- x 1)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (sqrt (- x 1)) (*.f64 (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/16 binary64) (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) #s(literal -1/8 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x))
#s(approx (sqrt (* x (- x 1))) (neg.f64 x))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) #s(literal 1 binary64)) x))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (+.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/16 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) x)) #s(literal 1 binary64))))
#s(approx (- x 1) (*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) x)))))
#s(approx (sqrt (* x (- x 1))) (*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (/.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x) #s(literal -1/16 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) x))) x)))))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))
#s(approx (sqrt (- x 1)) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 5 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (*.f64 (sqrt.f64 (pow.f64 x (neg.f64 #s(literal 7 binary64)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/16 binary64) (fma.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))))
#s(approx (sqrt x) (neg.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))

eval6.0ms (0.2%)

Memory
7.9MiB live, 7.9MiB allocated; 0ms collecting garbage
Compiler

Compiled 560 to 251 computations (55.2% saved)

prune4.0ms (0.2%)

Memory
-49.3MiB live, 3.9MiB allocated; 4ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New50050
Fresh000
Picked033
Done000
Total50353
Accuracy
100.0%
Counts
53 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
97.7%
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
50.5%
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
98.6%
#s(approx (sqrt (* (- x 1) x)) x)
Compiler

Compiled 36 to 34 computations (5.6% saved)

regimes4.0ms (0.2%)

Memory
6.7MiB live, 6.7MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (* (- x 1) x)) x)
(*.f64 (sqrt.f64 #s(approx (- x 1) x)) (sqrt.f64 x))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Calls

2 calls:

2.0ms
x
2.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
Results
AccuracySegmentsBranch
99.1%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
99.1%1x
Compiler

Compiled 7 to 7 computations (0% saved)

regimes3.0ms (0.1%)

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

Total -31.9b remaining (-3516.8%)

Threshold costs -31.9b (-3516.8%)

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

2 calls:

1.0ms
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms
x
Results
AccuracySegmentsBranch
98.6%1(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
98.6%1x
Compiler

Compiled 7 to 7 computations (0% saved)

derivations0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Stop Event
done
Compiler

Compiled 11 to 11 computations (0% saved)

preprocess15.0ms (0.6%)

Memory
26.4MiB live, 26.4MiB allocated; 0ms collecting garbage
Compiler

Compiled 17 to 17 computations (0% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...