arccos

Time bar (total: 4.1s)

start0.0ms (0%)

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

analyze5.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (27.8%)

Memory
26.9MiB live, 1 281.8MiB allocated; 342ms collecting garbage
Samples
859.0ms8 256×0valid
1.0ms20×0invalid
Precisions
Click to see histograms. Total time spent on operations: 475.0ms
ival-div: 109.0ms (22.9% of total)
ival-sqrt: 88.0ms (18.5% of total)
ival-atan: 84.0ms (17.7% of total)
ival-sub: 75.0ms (15.8% of total)
ival-mult: 58.0ms (12.2% of total)
ival-add: 42.0ms (8.8% of total)
exact: 8.0ms (1.7% of total)
ival-true: 6.0ms (1.3% of total)
adjust: 3.0ms (0.6% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain98.0ms (2.4%)

Memory
-20.7MiB live, 169.0MiB allocated; 19ms collecting garbage
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
39.0ms512×0valid
Compiler

Compiled 103 to 31 computations (69.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-atan: 5.0ms (22.1% of total)
ival-sqrt: 4.0ms (17.7% of total)
ival-div: 3.0ms (13.2% of total)
ival-add: 3.0ms (13.2% of total)
ival-mult: 3.0ms (13.2% of total)
ival-sub: 3.0ms (13.2% of total)
exact: 1.0ms (4.4% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess14.0ms (0.3%)

Memory
21.4MiB live, 21.4MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01126
12526
23026
33226
43726
53926
64226
74526
84626
95026
105626
116226
126626
0911
01511
12411
02411
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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
Compiler

Compiled 11 to 9 computations (18.2% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated; 0ms collecting garbage
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)

simplify3.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
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
02444
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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) #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 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))))
(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 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

localize33.0ms (0.8%)

Memory
-3.6MiB live, 40.1MiB allocated; 11ms collecting garbage
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)))))
accuracy0.0
(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))))
accuracy0.01171875
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Samples
25.0ms256×0valid
Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-mult: 8.0ms (44.3% of total)
ival-div: 2.0ms (11.1% of total)
ival-atan: 2.0ms (11.1% of total)
ival-sub: 2.0ms (11.1% of total)
ival-sqrt: 2.0ms (11.1% of total)
ival-add: 1.0ms (5.5% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
5.0MiB live, 5.0MiB allocated; 0ms collecting garbage
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)))

simplify120.0ms (3%)

Memory
15.4MiB live, 201.3MiB allocated; 26ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107324
1307262
21011242
33679224
08337217
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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(fma.f64 (-.f64 (*.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 (/.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 (* x (sqrt -1)))))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (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 (/.f64 (-.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) x) #s(literal 1 binary64))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x) #s(literal 1 binary64))
(* 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 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (*.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 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal -2 binary64) x) #s(literal -2 binary64)) x) #s(literal 1 binary64))
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
(-.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) x)) x) #s(literal 1 binary64))

rewrite131.0ms (3.2%)

Memory
-47.5MiB live, 199.1MiB allocated; 37ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01534
15034
227326
329565
092045
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 6
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
#s(literal 2 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)

eval11.0ms (0.3%)

Memory
22.6MiB live, 22.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 415 to 143 computations (65.5% saved)

prune4.0ms (0.1%)

Memory
9.1MiB live, 9.1MiB allocated; 0ms collecting garbage
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New18523
Fresh000
Picked011
Done000
Total18624
Accuracy
100.0%
Counts
24 → 6
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)))))
▶99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶98.5%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
▶20.7%
#s(literal 2 binary64)
Compiler

Compiled 155 to 123 computations (20.6% saved)

simplify245.0ms (6.1%)

Memory
6.9MiB live, 99.8MiB allocated; 6ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
cost-diff1
(fma.f64 (-.f64 (*.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))))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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-diff1
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029256
048256
171256
292256
3134256
4245256
5395256
6666256
71165256
81614256
92139256
102602256
113199256
123759256
134631256
145632256
155851256
165853256
175857256
185865256
195865256
205865256
215969256
226293256
236293256
06293247
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))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64))
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(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 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))))
(fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64))
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 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))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(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 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
#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(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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)

localize70.0ms (1.7%)

Memory
2.0MiB live, 145.0MiB allocated; 10ms collecting garbage
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
accuracy0.0
(*.f64 #s(literal 1/2 binary64) x)
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64))))
accuracy0.3511305809649088
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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)))
accuracy0.5611458286928591
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
accuracy0.9863306833278052
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64))))
accuracy0.24439060818109667
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
Samples
45.0ms256×0valid
Compiler

Compiled 183 to 23 computations (87.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-mult: 9.0ms (31.1% of total)
ival-sub: 7.0ms (24.2% of total)
ival-add: 5.0ms (17.3% of total)
ival-atan: 3.0ms (10.4% of total)
ival-div: 2.0ms (6.9% of total)
ival-sqrt: 2.0ms (6.9% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Counts
17 → 30
Calls
Call 1
Inputs
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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))) #s(literal 1 binary64))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 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))))
(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)
(fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
-1
(- (* 1/2 x) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(* 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)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -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)))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) 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))))
Calls

3 calls:

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

simplify158.0ms (3.9%)

Memory
-27.8MiB live, 197.9MiB allocated; 39ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105364
1290302
2940282
33348271
09581266
Stop Event
1×iter limit
1×node limit
Counts
30 → 30
Calls
Call 1
Inputs
-1
(- (* 1/2 x) 1)
(- (* x (+ 1/2 (* -1/2 x))) 1)
(* 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)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(* -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)))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) 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))))
Outputs
-1
#s(literal -1 binary64)
(- (* 1/2 x) 1)
(-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(- (* x (+ 1/2 (* -1/2 x))) 1)
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(*.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #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 (-.f64 (*.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 (-.f64 (*.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 (* -1/2 x)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(* -1/2 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) x) x)
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (*.f64 x x))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+.f64 (/.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 (* x (sqrt -1)))))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #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 (*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) x)
(* (pow x 2) (- (+ 1/2 (/ 1 (pow x 2))) (/ 1 x)))
(*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x))
(* (pow x 2) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/2))
(*.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x) #s(literal 1/2 binary64)) (*.f64 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 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #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 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))
(* -1 (* x (- 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x))
(* (pow x 2) (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (*.f64 x x))

rewrite257.0ms (6.3%)

Memory
32.1MiB live, 183.2MiB allocated; 156ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029221
048242
1150242
2989162
08752162
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
17 → 303
Calls
Call 1
Inputs
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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))) #s(literal 1 binary64))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
#s(approx (sqrt (/ (- 1 x) (+ 1 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))))
(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)
(fma.f64 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)
Outputs
(*.f64 (/.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (/.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))) (*.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))))) (*.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (fma.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (fma.f64 (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (neg.f64 x) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (*.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (neg.f64 x) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 2 binary64)))))
(neg.f64 (neg.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
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(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(-.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 0 binary64))) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 3 binary64)) (fma.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))) #s(literal 0 binary64))))
(+.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(+.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(+.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(+.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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))) (-.f64 #s(literal 1 binary64) x))) (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))) #s(literal 1 binary64))) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
(+.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #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 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #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 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x)
(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x))
(*.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
(*.f64 x (*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))))
(*.f64 x (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal 1/4 binary64) x) x (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))))
(/.f64 (neg.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (*.f64 x (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))))
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x)))
(/.f64 (*.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) (-.f64 (*.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (*.f64 x (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x)))
(fma.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))) x (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))) x))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 x (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))) (*.f64 x (/.f64 #s(literal 1/8 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x)))))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) (*.f64 #s(literal 1/2 binary64) x))
(-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x #s(literal -1/2 binary64)))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (neg.f64 x) (*.f64 x #s(literal -1/2 binary64))))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))) x) (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x))) x))
(+.f64 (*.f64 x (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x)))) (*.f64 x (/.f64 #s(literal 1/8 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) x)))))
(+.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))

eval34.0ms (0.8%)

Memory
6.5MiB live, 51.8MiB allocated; 4ms collecting garbage
Compiler

Compiled 8 594 to 1 274 computations (85.2% saved)

prune7.0ms (0.2%)

Memory
-30.9MiB live, 14.4MiB allocated; 3ms collecting garbage
Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New2261227
Fresh000
Picked055
Done011
Total2267233
Accuracy
100.0%
Counts
233 → 7
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)))))
✓99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓98.5%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
✓20.7%
#s(literal 2 binary64)
Compiler

Compiled 104 to 81 computations (22.1% saved)

simplify256.0ms (6.3%)

Memory
5.5MiB live, 285.6MiB allocated; 67ms collecting garbage
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))
cost-diff0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
cost-diff0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
cost-diff5
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
Iterations

Useful iterations: 12 (0.0ms)

IterNodesCost
01481
02081
13781
26581
311581
416281
518281
618381
718981
820181
921581
1023181
1127181
1240961
1387761
14449361
0841561
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
(+.f64 #s(literal 1 binary64) x)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (neg.f64 (-.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
(neg.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))

localize41.0ms (1%)

Memory
9.6MiB live, 53.9MiB allocated; 22ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
accuracy0.0078125
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
accuracy0.0234375
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
accuracy0.5611458286928591
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))
Samples
22.0ms256×0valid
Compiler

Compiled 53 to 14 computations (73.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-div: 3.0ms (20.5% of total)
ival-mult: 3.0ms (20.5% of total)
ival-sub: 3.0ms (20.5% of total)
ival-atan: 2.0ms (13.7% of total)
ival-sqrt: 2.0ms (13.7% of total)
ival-add: 1.0ms (6.8% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Counts
4 → 17
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.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
((/ (- 1 (* x x)) (+ 1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))))
1.0ms
x
@-inf
((/ (- 1 (* x x)) (+ 1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))))
1.0ms
x
@0
((/ (- 1 (* x x)) (+ 1 x)) (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))) (sqrt (/ (- 1 x) (+ 1 x))))

simplify142.0ms (3.5%)

Memory
10.3MiB live, 197.7MiB allocated; 56ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083252
1233190
2805174
32800164
09063161
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 (-.f64 (*.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 (-.f64 (*.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 (-.f64 (/.f64 #s(literal 1 binary64) x) #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 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
(+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1/2 binary64)) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (- 1 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 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 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #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 (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x))

rewrite234.0ms (5.8%)

Memory
-18.0MiB live, 187.1MiB allocated; 53ms collecting garbage
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01467
02043
17443
249431
3732231
0811531
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 357
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))
Outputs
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) 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))))) (fma.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) x) (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (fma.f64 x x x) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) 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 (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 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (*.f64 x x) #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(*.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 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(*.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #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)))))
(*.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (*.f64 x (/.f64 x (fma.f64 x 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))
(/.f64 (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (fma.f64 x x x) x)) (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (fma.f64 x x #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 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.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 #s(literal -1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) 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 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (pow.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))) (*.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (pow.f64 (*.f64 (neg.f64 x) (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (neg.f64 x) (/.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) 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))))) (neg.f64 (fma.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) x) (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)))))
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(+.f64 (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (/.f64 x (-.f64 #s(literal 1 binary64) x)))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (neg.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (neg.f64 (*.f64 x (/.f64 x (fma.f64 x x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) x)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (neg.f64 x) (/.f64 x (-.f64 #s(literal 1 binary64) x))))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (neg.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 x))
(+.f64 #s(literal 1 binary64) x)
(atan2.f64 (*.f64 #s(literal 2 binary64) #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (pow.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(-.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64)) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64))) (/.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) #s(literal 0 binary64))))
(+.f64 (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))))
(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))

eval102.0ms (2.5%)

Memory
11.8MiB live, 111.3MiB allocated; 11ms collecting garbage
Compiler

Compiled 12 448 to 1 790 computations (85.6% saved)

prune11.0ms (0.3%)

Memory
-16.3MiB live, 28.6MiB allocated; 5ms collecting garbage
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New3710371
Fresh000
Picked011
Done066
Total3717378
Accuracy
100.0%
Counts
378 → 7
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)))))
✓99.6%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓98.5%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
✓20.7%
#s(literal 2 binary64)
Compiler

Compiled 208 to 122 computations (41.3% saved)

regimes10.0ms (0.2%)

Memory
19.3MiB live, 19.3MiB allocated; 0ms collecting garbage
Counts
7 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
(*.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:

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

Compiled 36 to 28 computations (22.2% saved)

regimes11.0ms (0.3%)

Memory
-30.3MiB live, 15.9MiB allocated; 3ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
Calls

5 calls:

4.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
2.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.6%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
99.6%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.6%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.6%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.6%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes7.0ms (0.2%)

Memory
16.1MiB live, 16.1MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x #s(literal 1 binary64)))))
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
(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))
Results
AccuracySegmentsBranch
99.5%1(/.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(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
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%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.2%)

Memory
16.6MiB live, 16.7MiB allocated; 0ms collecting garbage
Counts
3 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 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))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
Calls

5 calls:

1.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(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
99.1%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
99.1%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.1%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.1%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.1%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes10.0ms (0.2%)

Memory
-29.7MiB live, 15.6MiB allocated; 3ms collecting garbage
Counts
2 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
Calls

5 calls:

5.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
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))
Results
AccuracySegmentsBranch
98.5%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
98.5%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.5%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.5%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.5%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory
14.3MiB live, 14.3MiB allocated; 0ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 2 binary64)
Outputs
#s(literal 2 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 (-.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
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
20.7%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
20.7%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
20.7%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
20.7%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
20.7%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify11.0ms (0.3%)

Memory
17.0MiB live, 17.0MiB allocated; 0ms collecting garbage
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03483
14683
25383
35783
46183
57683
Stop Event
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)))))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (fma.f64 (-.f64 (*.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 (-.f64 (*.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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #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 (-.f64 (*.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 (-.f64 (*.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 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))))
#s(literal 2 binary64)

derivations843.0ms (20.8%)

Memory
-39.1MiB live, 208.9MiB allocated; 32ms collecting garbage
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01534
15034
227326
329565
092045
0107324
1307262
21011242
33679224
08337217
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 83 to 35 computations (57.8% saved)

preprocess36.0ms (0.9%)

Memory
21.6MiB live, 64.1MiB allocated; 7ms collecting garbage
Compiler

Compiled 188 to 88 computations (53.2% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...