arccos

Time bar (total: 5.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze5.0ms (0.1%)

Memory
8.0MiB live, 8.0MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (22.4%)

Memory
40.4MiB live, 1 444.5MiB allocated
Samples
609.0ms8 256×0valid
1.0ms17×0invalid
Precisions
Click to see histograms. Total time spent on operations: 436.0ms
ival-sub: 96.0ms (22% of total)
ival-atan: 83.0ms (19% of total)
ival-mult: 64.0ms (14.7% of total)
ival-sqrt: 63.0ms (14.4% of total)
ival-add: 62.0ms (14.2% of total)
ival-div: 51.0ms (11.7% of total)
exact: 8.0ms (1.8% of total)
ival-true: 7.0ms (1.6% of total)
ival-assert: 3.0ms (0.7% of total)
Bogosity

explain96.0ms (1.9%)

Memory
1.5MiB live, 197.1MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 2 binary64)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
38.0ms512×0valid
Compiler

Compiled 147 to 40 computations (72.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-atan: 5.0ms (21.1% of total)
ival-add: 4.0ms (16.9% of total)
ival-mult: 4.0ms (16.9% of total)
ival-sqrt: 4.0ms (16.9% of total)
ival-div: 3.0ms (12.7% of total)
ival-sub: 3.0ms (12.7% of total)
exact: 1.0ms (4.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess31.0ms (0.6%)

Memory
-19.3MiB live, 51.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01124
13122
25922
310822
418122
534122
661622
764322
0911
01511
12411
23011
34111
46411
59811
613511
720811
833511
953011
1058011
058011
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify12.0ms (0.2%)

Memory
22.8MiB live, 22.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
cost-diff0
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
cost-diff0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
01544
12444
23044
34144
46444
59844
613544
720844
833544
953044
1058044
058044
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))

localize32.0ms (0.6%)

Memory
-16.0MiB live, 57.4MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy0.01953125
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy0.0234375
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy0.02734375
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Samples
24.0ms256×0valid
Compiler

Compiled 90 to 20 computations (77.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-add: 5.0ms (34.1% of total)
ival-div: 2.0ms (13.6% of total)
ival-mult: 2.0ms (13.6% of total)
ival-atan: 2.0ms (13.6% of total)
ival-sub: 2.0ms (13.6% of total)
ival-sqrt: 2.0ms (13.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
7.1MiB live, 7.1MiB allocated
Counts
4 → 23
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Calls

3 calls:

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

simplify124.0ms (2.5%)

Memory
16.2MiB live, 163.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107323
1276262
2763248
32118236
46223228
08109216
Stop Event
1×iter limit
1×node limit
Counts
23 → 23
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- (* 2 x) 2)))
(fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal -2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 2 binary64)) x #s(literal -2 binary64)) x #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- (* 2 (/ 1 x)) 1)
(-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal -1 binary64))) x)) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x))

rewrite126.0ms (2.5%)

Memory
4.2MiB live, 164.1MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01534
15234
233934
345958
098318
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 7
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(literal 1 binary64)))
(neg.f64 (atan.f64 (/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(neg.f64 (atan.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)

eval3.0ms (0.1%)

Memory
11.9MiB live, 11.9MiB allocated
Compiler

Compiled 421 to 138 computations (67.2% saved)

prune3.0ms (0.1%)

Memory
-29.4MiB live, 9.9MiB allocated
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New20424
Fresh000
Picked011
Done000
Total20525
Accuracy
100.0%
Counts
25 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶96.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶98.0%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 71 to 58 computations (18.3% saved)

simplify100.0ms (2%)

Memory
38.2MiB live, 76.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
cost-diff0
(atan.f64 #s(literal 1 binary64))
cost-diff0
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
cost-diff0
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff0
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
cost-diff0
(-.f64 #s(literal 1 binary64) x)
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027210
046210
168210
292210
3181210
4345210
5623210
61204210
72237210
82739210
92903210
102977210
113084210
123150210
133150210
03150210
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
#s(literal 1/2 binary64)
x
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)

localize69.0ms (1.4%)

Memory
-7.7MiB live, 76.5MiB allocated
Localize:

Found 14 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
accuracy0.0
(atan.f64 #s(literal 1 binary64))
accuracy0.0
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy0.549688010105402
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy0.0
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
accuracy0.7627315562764668
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy0.0
(-.f64 #s(literal 1 binary64) x)
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy1.2657148489217518
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
Samples
42.0ms256×0valid
Compiler

Compiled 362 to 54 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 27.0ms
ival-mult: 10.0ms (37.1% of total)
ival-add: 7.0ms (26% of total)
ival-atan: 4.0ms (14.8% of total)
ival-div: 2.0ms (7.4% of total)
ival-sub: 2.0ms (7.4% of total)
ival-sqrt: 2.0ms (7.4% of total)
exact: 1.0ms (3.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series15.0ms (0.3%)

Memory
-32.8MiB live, 4.9MiB allocated
Counts
16 → 38
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* 1/2 x) 1)
1/2
(+ 1/2 (* -1/2 x))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
Calls

3 calls:

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

simplify191.0ms (3.8%)

Memory
11.7MiB live, 122.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124391
1338326
21132318
33815306
48000306
08010275
Stop Event
1×iter limit
1×node limit
Counts
38 → 38
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-1
(- (* 1/2 x) 1)
1/2
(+ 1/2 (* -1/2 x))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (/ 1 x)))
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (- 1/2 (/ 1 x)))
(* -1/2 x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- (/ 1 x) 1/2)))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- (* 1/2 x) 1)
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 x))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* 1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x)
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x)
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (- 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(* -1/2 x)
(*.f64 #s(literal -1/2 binary64) x)
(* x (- (* 1/2 (/ 1 x)) 1/2))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) x)
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1/2)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(* -1 (* x (- 1/2 (* 1/2 (/ 1 x)))))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))

rewrite351.0ms (7%)

Memory
15.2MiB live, 172.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027187
046187
1151187
21041187
08653187
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
16 → 251
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(atan.f64 #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
Outputs
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))) (+.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)))) (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 3 binary64)))) (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 (-.f64 #s(literal -1 binary64) x) (*.f64 x x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(neg.f64 (-.f64 x #s(literal 1 binary64)))
(fma.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 x (-.f64 x #s(literal 1 binary64))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (*.f64 x (-.f64 x #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal 1 binary64))
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(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (neg.f64 x) #s(literal -1/4 binary64)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/4 binary64) (*.f64 x x) (*.f64 (neg.f64 x) #s(literal -1/4 binary64)))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))))
(-.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))))
(+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) x #s(literal -1/2 binary64)))))
(+.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))

eval44.0ms (0.9%)

Memory
11.1MiB live, 86.3MiB allocated
Compiler

Compiled 9 331 to 1 647 computations (82.3% saved)

prune33.0ms (0.7%)

Memory
-14.5MiB live, 37.5MiB allocated
Pruning

7 alts after pruning (2 fresh and 5 done)

PrunedKeptTotal
New2722274
Fresh000
Picked044
Done011
Total2727279
Accuracy
100.0%
Counts
279 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓96.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶98.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
▶99.2%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓98.0%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 128 to 95 computations (25.8% saved)

simplify143.0ms (2.9%)

Memory
16.3MiB live, 208.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
cost-diff128
(-.f64 (neg.f64 x) #s(literal 1 binary64))
cost-diff1088
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
cost-diff8448
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027268
045268
173268
2122263
3343219
41345191
53768191
08159187
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(neg.f64 x)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
x
#s(literal 1/2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(-.f64 #s(literal -1 binary64) x)
(neg.f64 x)
#s(literal 1 binary64)

localize66.0ms (1.3%)

Memory
12.0MiB live, 171.4MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(neg.f64 x)
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
accuracy0.03125
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
accuracy1.2657148489217518
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
accuracy0.03515625
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
accuracy0.041347509768442016
(pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
accuracy0.549688010105402
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
Samples
46.0ms255×0valid
0.0ms1×1valid
Compiler

Compiled 452 to 56 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-mult: 9.0ms (26.8% of total)
ival-add: 6.0ms (17.9% of total)
ival-div: 5.0ms (14.9% of total)
ival-sub: 4.0ms (11.9% of total)
ival-pow2: 3.0ms (8.9% of total)
ival-atan: 2.0ms (6% of total)
ival-sqrt: 2.0ms (6% of total)
ival-neg: 2.0ms (6% of total)
exact: 1.0ms (3% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
-23.2MiB live, 15.7MiB allocated
Counts
11 → 37
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
(pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(neg.f64 x)
Outputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
-1
(- (* -1 x) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(* -1 x)
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
Calls

3 calls:

TimeVariablePointExpression
3.0ms
x
@0
((/ (- (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) 1) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))
1.0ms
x
@inf
((/ (- (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) 1) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))
1.0ms
x
@-inf
((/ (- (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) 1) (+ (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) -1)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))) (/ (+ (* x x) -1) (- (neg x) 1)) (- (neg x) 1) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (sqrt (/ (- 1 x) (+ 1 x))) (neg x))

simplify280.0ms (5.6%)

Memory
10.4MiB live, 203.9MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0155471
1444402
21367385
34744369
08522355
Stop Event
1×iter limit
1×node limit
Counts
37 → 37
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
-1
(- (* -1 x) 1)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(* -1 x)
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/4 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 5/4 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
(* -1 x)
(neg.f64 x)
(* -1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (+.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* 1/4 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4 binary64))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 5/4 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) x) x) #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 5/4 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) (pow.f64 x #s(literal 6 binary64)))

rewrite288.0ms (5.8%)

Memory
10.2MiB live, 322.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027211
045211
1186135
21402134
09152130
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
11 → 458
Calls
Call 1
Inputs
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))))
(pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
(neg.f64 x)
Outputs
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(-.f64 x #s(literal 1 binary64))
(+.f64 (neg.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 x)))
(+.f64 #s(literal -1 binary64) (neg.f64 x))
(+.f64 x #s(literal -1 binary64))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (*.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64)) x) #s(literal 1 binary64)) x)
(*.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64))) #s(literal 1 binary64)) x)
(*.f64 (pow.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)))
(*.f64 (*.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64)) x) x)
(*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64))) x)
(*.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) x) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)))
(*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x)) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x)))
(*.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64)) (*.f64 x x))
(*.f64 (*.f64 x x) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) (pow.f64 (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) (*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 1 binary64)))
(*.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x))
(*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (pow.f64 (*.f64 x (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)) #s(literal 1 binary64)))
(*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (*.f64 x (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)))
(*.f64 x (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)) #s(literal 1 binary64)))
(*.f64 x (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)))
(pow.f64 (*.f64 (neg.f64 x) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))
(exp.f64 (fma.f64 (log.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (log.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) x)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(*.f64 (neg.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 0 binary64) (neg.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (+.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 3 binary64)))))
(neg.f64 x)
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (fma.f64 x x (*.f64 #s(literal 0 binary64) x)))))
(-.f64 #s(literal 0 binary64) x)
(+.f64 #s(literal 0 binary64) (neg.f64 x))

eval77.0ms (1.5%)

Memory
13.9MiB live, 177.4MiB allocated
Compiler

Compiled 19 493 to 2 820 computations (85.5% saved)

prune79.0ms (1.6%)

Memory
-11.4MiB live, 32.7MiB allocated
Pruning

7 alts after pruning (2 fresh and 5 done)

PrunedKeptTotal
New4842486
Fresh000
Picked202
Done055
Total4867493
Accuracy
100.0%
Counts
493 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓96.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
▶98.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓98.0%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 142 to 108 computations (23.9% saved)

simplify190.0ms (3.8%)

Memory
-16.5MiB live, 223.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
cost-diff0
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
037342
055342
187337
2139337
3355337
41232337
53132337
66002337
08112337
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64))
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal -1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64))
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal -1 binary64) x)

localize116.0ms (2.3%)

Memory
8.4MiB live, 207.6MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
accuracy0.0234375
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
accuracy0.03125
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
accuracy1.2657148489217518
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
accuracy0.02734375
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
accuracy0.03515625
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
accuracy0.549688010105402
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
accuracy1.3287742276399952
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x))
Samples
80.0ms255×0valid
0.0ms1×1valid
Compiler

Compiled 542 to 73 computations (86.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-neg: 29.0ms (45.1% of total)
ival-mult: 11.0ms (17.1% of total)
ival-add: 6.0ms (9.3% of total)
ival-div: 5.0ms (7.8% of total)
ival-sub: 5.0ms (7.8% of total)
ival-pow2: 3.0ms (4.7% of total)
ival-atan: 2.0ms (3.1% of total)
ival-sqrt: 2.0ms (3.1% of total)
exact: 1.0ms (1.6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
16.6MiB live, 16.6MiB allocated
Counts
11 → 41
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
x
(* x (+ 1 (* -1 x)))
-1
(- (* -1 x) 1)
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
Calls

3 calls:

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

simplify265.0ms (5.3%)

Memory
-2.0MiB live, 232.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0158486
1455417
21377400
34755384
08175371
Stop Event
1×iter limit
1×node limit
Counts
41 → 40
Calls
Call 1
Inputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 x)))
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
x
(* x (+ 1 (* -1 x)))
-1
(- (* -1 x) 1)
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1 x)
(* x (- (/ 1 x) 1))
(* 1/4 (pow x 6))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 x))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* -1 (* x (- 1 (/ 1 x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 x)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)
(* (pow x 2) (+ 1 (* x (- (* 5/4 x) 1))))
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 5/4 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
(* (pow x 2) (+ 1 (* x (- (* x (+ 5/4 (* -1/2 x))) 1))))
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 5/4 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) x) x)
x
(* x (+ 1 (* -1 x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(* -1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64))))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* 1/4 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/4 binary64))
(* (pow x 6) (- 1/4 (* 1/2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/2 binary64) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (- (+ 1/4 (/ 5/4 (pow x 2))) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3)))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 5/4 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 x) 1))
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.f64 #s(literal -1 binary64) x)
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64))))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal -1 binary64)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(fma.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x)) x))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) x) x) #s(literal 1/2 binary64)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* (pow x 6) (+ 1/4 (* -1 (/ (- 1/2 (* 5/4 (/ 1 x))) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 5/4 binary64) x)) x)) (pow.f64 x #s(literal 6 binary64)))
(* (pow x 6) (+ 1/4 (* -1 (/ (+ 1/2 (* -1 (/ (- 5/4 (/ 1 x)) x))) x))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 5/4 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x)) (pow.f64 x #s(literal 6 binary64)))

rewrite318.0ms (6.4%)

Memory
-46.3MiB live, 272.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037274
055274
1208269
21453227
09244221
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
11 → 238
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
Outputs
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x))) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x))) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x))) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)) (+.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x))) (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 (/.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 (/.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -2 binary64)) (/.f64 (/.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))))
(*.f64 (fma.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) (neg.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal 2 binary64))))
(*.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)))))
(*.f64 (-.f64 (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) (+.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal -1 binary64)) (pow.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 2 binary64))))))
(*.f64 (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64)))
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(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal 1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))))
(neg.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(-.f64 (/.f64 (*.f64 x x) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) (pow.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal -1 binary64) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) (/.f64 (*.f64 x x) (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(*.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x)))
#s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (fma.f64 x x x) x))
(*.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 x (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 x (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 x (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 x (pow.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) x) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) x) (pow.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64))))))
(*.f64 (-.f64 x #s(literal -1 binary64)) x)
(*.f64 x (-.f64 #s(literal -1 binary64) x))
(*.f64 x (-.f64 x #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x x))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x (*.f64 x x)))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal 4 binary64))) (-.f64 (neg.f64 x) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x (*.f64 (neg.f64 x) x)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 x x (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) x)) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (neg.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))) (neg.f64 (fma.f64 x x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) x) (-.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(/.f64 (*.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))) (-.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x)) (fma.f64 x x x))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))))
(/.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal -1 binary64)) (*.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x #s(literal -1 binary64)) (*.f64 x (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) (*.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x x) (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 x x))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (neg.f64 x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) x)
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x (neg.f64 x))
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 x x))
(fma.f64 (*.f64 (neg.f64 x) x) (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) (neg.f64 x))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) x)
(fma.f64 (neg.f64 x) (neg.f64 x) (neg.f64 x))
(fma.f64 (neg.f64 x) (neg.f64 x) x)
(fma.f64 (neg.f64 x) #s(literal 1 binary64) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) x (*.f64 x x))
(fma.f64 x #s(literal -1 binary64) (*.f64 x x))
(fma.f64 x x (neg.f64 x))
(fma.f64 x x x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (neg.f64 x) x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) (neg.f64 x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) x)
(fma.f64 #s(literal 1 binary64) (neg.f64 x) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) x (*.f64 (neg.f64 x) x))
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x x)) (/.f64 (*.f64 x x) (fma.f64 x x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (*.f64 x x) (neg.f64 x))
(-.f64 (*.f64 x x) x)
(-.f64 (neg.f64 x) (*.f64 (neg.f64 x) x))
(-.f64 x (*.f64 (neg.f64 x) x))
(+.f64 (*.f64 x x) (neg.f64 x))
(+.f64 (*.f64 x x) x)
(+.f64 (neg.f64 x) (*.f64 x x))
(+.f64 x (*.f64 (neg.f64 x) x))
(+.f64 x (*.f64 x x))
(*.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
#s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))) #s(literal -1 binary64))
(/.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64)))
(neg.f64 (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))

eval43.0ms (0.9%)

Memory
4.2MiB live, 113.9MiB allocated
Compiler

Compiled 15 085 to 1 759 computations (88.3% saved)

prune10.0ms (0.2%)

Memory
-17.5MiB live, 30.6MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New2670267
Fresh000
Picked022
Done055
Total2677274
Accuracy
100.0%
Counts
274 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓96.6%
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
✓100.0%
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓98.8%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
✓98.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
✓98.0%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 341 to 182 computations (46.6% saved)

regimes13.0ms (0.3%)

Memory
32.9MiB live, 32.9MiB allocated
Counts
9 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(approx (pow (* (+ (* (+ (* -1/2 x) 1/2) x) -1) x) 2) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal -1 binary64))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
Calls

5 calls:

3.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
100.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
100.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
100.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes12.0ms (0.2%)

Memory
-11.0MiB live, 28.3MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(approx (- (neg x) 1) (-.f64 #s(literal -1 binary64) x))))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Calls

5 calls:

4.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.1%1x
99.1%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.1%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.1%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.1%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes16.0ms (0.3%)

Memory
-23.2MiB live, 16.0MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
Calls

5 calls:

11.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.8%1x
98.8%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.8%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.8%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.8%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory
13.9MiB live, 13.9MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Calls

5 calls:

1.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
98.0%1x
98.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory
12.0MiB live, 12.0MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Calls

5 calls:

1.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
96.6%1x
96.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
96.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
96.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
96.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify98.0ms (2%)

Memory
-3.6MiB live, 74.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03271
14271
25071
36371
49271
513471
623671
750771
8496771
9646471
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (atan.f64 #s(literal 1 binary64)) #s(literal 2 binary64))

soundness519.0ms (10.4%)

Memory
-13.6MiB live, 262.4MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01534
15234
233934
345958
098318
0107323
1276262
2763248
32118236
46223228
08109216
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 100 to 59 computations (41% saved)

preprocess77.0ms (1.5%)

Memory
-0.8MiB live, 82.2MiB allocated
Compiler

Compiled 164 to 84 computations (48.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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