arccos

Time bar (total: 5.0s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze5.0ms (0.1%)

Memory
6.3MiB live, 6.3MiB 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)

sample1.5s (31%)

Memory
13.6MiB live, 1 393.4MiB allocated
Samples
914.0ms8 256×0valid
1.0ms18×0invalid
Precisions
Click to see histograms. Total time spent on operations: 681.0ms
ival-atan: 167.0ms (24.5% of total)
ival-sqrt: 154.0ms (22.6% of total)
ival-mult: 105.0ms (15.4% of total)
ival-div: 96.0ms (14.1% of total)
ival-sub: 92.0ms (13.5% of total)
ival-add: 51.0ms (7.5% of total)
exact: 7.0ms (1% of total)
ival-true: 6.0ms (0.9% of total)
ival-assert: 3.0ms (0.4% of total)
Bogosity

explain92.0ms (1.9%)

Memory
17.1MiB live, 202.9MiB 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
35.0ms512×0valid
Compiler

Compiled 147 to 40 computations (72.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-atan: 4.0ms (18.6% of total)
ival-sqrt: 4.0ms (18.6% of total)
ival-div: 3.0ms (13.9% of total)
ival-add: 3.0ms (13.9% of total)
ival-mult: 3.0ms (13.9% of total)
ival-sub: 3.0ms (13.9% of total)
exact: 1.0ms (4.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess29.0ms (0.6%)

Memory
11.5MiB live, 47.5MiB 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
1.2MiB live, 1.2MiB 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)

simplify14.0ms (0.3%)

Memory
-22.8MiB live, 13.4MiB 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 (0.7%)

Memory
6.4MiB live, 55.1MiB 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)))))
accuracy0.0078125
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
accuracy0.0078125
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy0.015625
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Samples
25.0ms256×0valid
Compiler

Compiled 90 to 20 computations (77.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-sqrt: 8.0ms (42.9% of total)
ival-atan: 4.0ms (21.5% of total)
ival-div: 2.0ms (10.7% of total)
ival-mult: 2.0ms (10.7% of total)
ival-sub: 2.0ms (10.7% of total)
ival-add: 1.0ms (5.4% 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
5.7MiB live, 5.7MiB 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)))

simplify123.0ms (2.5%)

Memory
14.2MiB live, 169.5MiB 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))

rewrite90.0ms (1.8%)

Memory
-6.7MiB live, 106.4MiB 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
3.7MiB live, 3.7MiB allocated
Compiler

Compiled 421 to 138 computations (67.2% saved)

prune2.0ms (0%)

Memory
3.3MiB live, 3.3MiB 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
▶98.8%
(*.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)))))
▶99.5%
(*.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)))))
▶99.5%
(*.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)))))
▶99.3%
(*.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)

simplify238.0ms (4.8%)

Memory
-6.4MiB live, 35.8MiB 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)

localize73.0ms (1.5%)

Memory
-14.7MiB live, 60.5MiB 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)))))
accuracy0.0078125
(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))))
accuracy0.3028261106046903
#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)))))
accuracy0.0078125
(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))))
accuracy0.35719677793405163
#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))))
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy0.4412387562351594
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
Samples
49.0ms256×0valid
Compiler

Compiled 362 to 54 computations (85.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-add: 10.0ms (27.6% of total)
ival-mult: 10.0ms (27.6% of total)
ival-sqrt: 9.0ms (24.8% of total)
ival-atan: 3.0ms (8.3% of total)
ival-div: 2.0ms (5.5% of total)
ival-sub: 2.0ms (5.5% of total)
exact: 1.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
4.7MiB live, 4.7MiB 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))

simplify198.0ms (4%)

Memory
23.4MiB live, 99.7MiB 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))

rewrite186.0ms (3.7%)

Memory
10.4MiB live, 206.4MiB 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))

eval43.0ms (0.9%)

Memory
-31.1MiB live, 89.0MiB allocated
Compiler

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

prune5.0ms (0.1%)

Memory
18.5MiB live, 18.5MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New2731274
Fresh000
Picked044
Done011
Total2736279
Accuracy
100.0%
Counts
279 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.8%
(*.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)))))
✓99.5%
(*.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)))))
✓99.5%
(*.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)))))
▶99.3%
(*.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))))))
✓99.3%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 92 to 74 computations (19.6% saved)

simplify154.0ms (3.1%)

Memory
14.4MiB live, 242.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 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)))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01581
02281
13881
25276
39276
417556
541656
6149456
7524956
8715256
0803156
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 (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 (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)

localize43.0ms (0.9%)

Memory
-21.2MiB live, 100.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(neg.f64 x)
accuracy0.0078125
(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)))))
accuracy0.01171875
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64)))
accuracy0.4412387562351594
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (neg.f64 x) #s(literal 1 binary64))))
Samples
30.0ms256×0valid
Compiler

Compiled 136 to 33 computations (75.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-div: 6.0ms (26.8% of total)
ival-add: 4.0ms (17.8% of total)
ival-mult: 3.0ms (13.4% of total)
ival-sub: 3.0ms (13.4% of total)
ival-atan: 2.0ms (8.9% of total)
ival-sqrt: 2.0ms (8.9% of total)
ival-neg: 1.0ms (4.5% 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
8.8MiB live, 8.8MiB allocated
Counts
6 → 20
Calls
Call 1
Inputs
(/.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)))))
#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
(- (* -1 x) 1)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 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 (- 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)))
Calls

3 calls:

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

simplify146.0ms (3%)

Memory
13.8MiB live, 213.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
087251
1223190
2645182
31710174
44957164
08104160
Stop Event
1×iter limit
1×node limit
Counts
20 → 20
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
-1
(- (* -1 x) 1)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* -1 (* x (+ 1 (/ 1 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 (- 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)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
-1
#s(literal -1 binary64)
(- (* -1 x) 1)
(-.f64 #s(literal -1 binary64) x)
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.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 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (+ 1 (/ 1 x))))
(-.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)))))
(-.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 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 #s(literal -1 binary64)))
(* -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 x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)))) #s(literal 2 binary64))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.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))

rewrite103.0ms (2.1%)

Memory
-13.8MiB live, 185.3MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01573
02273
19549
272326
01091126
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 647
Calls
Call 1
Inputs
(/.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)))))
#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
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)))) (-.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64))) (fma.f64 x x x)))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
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x

eval98.0ms (2%)

Memory
11.9MiB live, 250.5MiB allocated
Compiler

Compiled 22 316 to 3 375 computations (84.9% saved)

prune10.0ms (0.2%)

Memory
0.6MiB live, 38.6MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New6601661
Fresh000
Picked101
Done055
Total6616667
Accuracy
100.0%
Counts
667 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.8%
(*.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)))))
✓99.5%
(*.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)))))
✓99.5%
(*.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)))))
▶99.3%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
✓99.3%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 91 to 72 computations (20.9% saved)

simplify332.0ms (6.7%)

Memory
12.6MiB live, 210.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.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)) (-.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)) (-.f64 #s(literal -1 binary64) x)))))
cost-diff1088
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01473
02073
13473
24573
37973
413873
531153
6111353
7384353
8546453
9669353
10741853
11797853
0800153
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 (fma.f64 x x #s(literal -1 binary64)) (-.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)) (-.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
(/.f64 (fma.f64 x 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 #s(literal -1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.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 (fma.f64 x x #s(literal -1 binary64)) (-.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 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) x)

localize135.0ms (2.7%)

Memory
-23.6MiB live, 136.8MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
accuracy0.01171875
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))
accuracy0.4412387562351594
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
Samples
45.0ms256×0valid
Compiler

Compiled 123 to 30 computations (75.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 38.0ms
exact: 16.0ms (42.1% of total)
ival-add: 7.0ms (18.4% of total)
ival-div: 4.0ms (10.5% of total)
ival-mult: 3.0ms (7.9% of total)
ival-sub: 3.0ms (7.9% of total)
ival-atan: 2.0ms (5.3% of total)
ival-sqrt: 2.0ms (5.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series2.0ms (0%)

Memory
6.0MiB live, 6.0MiB allocated
Counts
4 → 17
Calls
Call 1
Inputs
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.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 #s(literal -1 binary64) x)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
Outputs
1
(+ 1 (* -1 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* x (- (/ 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 (* 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)))
Calls

3 calls:

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

simplify137.0ms (2.8%)

Memory
19.4MiB live, 218.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083242
1208181
2618175
31615167
45558157
08131153
Stop Event
1×iter limit
1×node limit
Counts
17 → 17
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(* -1 x)
(* x (- (/ 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 (* 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)))
Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* 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 (* 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 x)
(neg.f64 x)
(* x (- (/ 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)))))
(-.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 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) x) (+.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) (sqrt.f64 #s(literal -1 binary64)))
(* -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 #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))

rewrite221.0ms (4.4%)

Memory
-46.3MiB live, 206.6MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01463
02063
18843
266943
0854343
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 351
Calls
Call 1
Inputs
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.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 #s(literal -1 binary64) x)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))
Outputs
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x x) (-.f64 (fma.f64 x x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.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 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)) x))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) x)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal -1 binary64) x) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (pow.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 (+.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64)) x))
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(+.f64 (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)) (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal -1 binary64)) x #s(literal 1 binary64)))))
(+.f64 (neg.f64 x) #s(literal 1 binary64))
(+.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (*.f64 x x) (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))))
(+.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 (-.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (*.f64 x x)))
(+.f64 (pow.f64 (-.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal -1 binary64))))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal -1 binary64) x)) (-.f64 x #s(literal -1 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal -1 binary64)) (/.f64 x (-.f64 #s(literal -1 binary64) x))))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(*.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))

eval96.0ms (1.9%)

Memory
32.0MiB live, 152.5MiB allocated
Compiler

Compiled 11 697 to 1 810 computations (84.5% saved)

prune9.0ms (0.2%)

Memory
-6.1MiB live, 31.5MiB allocated
Pruning

6 alts after pruning (0 fresh and 6 done)

PrunedKeptTotal
New3630363
Fresh000
Picked011
Done055
Total3636369
Accuracy
100.0%
Counts
369 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.8%
(*.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)))))
✓99.5%
(*.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)))))
✓99.5%
(*.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)))))
✓99.3%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal -1 binary64) x)))))
✓99.3%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Compiler

Compiled 203 to 117 computations (42.4% saved)

regimes12.0ms (0.2%)

Memory
-10.0MiB live, 28.6MiB allocated
Counts
7 → 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)) (-.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)))))
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:

4.0ms
(atan.f64 (sqrt.f64 (/.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
(/.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
-18.1MiB live, 27.1MiB 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)) (-.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
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
(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))
Results
AccuracySegmentsBranch
99.5%1x
99.5%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.5%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.5%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.5%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes7.0ms (0.1%)

Memory
21.9MiB live, 21.9MiB 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:

1.0ms
x
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) 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
(/.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
99.5%1x
99.5%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.5%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.5%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.5%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
-17.4MiB live, 22.0MiB 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:

2.0ms
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
99.3%1x
99.3%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.3%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.3%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.3%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
17.3MiB live, 17.3MiB 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
(/.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
98.8%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)

simplify86.0ms (1.7%)

Memory
4.4MiB live, 83.6MiB 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))

soundness549.0ms (11.1%)

Memory
-15.9MiB live, 262.0MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

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

Compiled 100 to 59 computations (41% saved)

preprocess113.0ms (2.3%)

Memory
-1.2MiB 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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