arccos

Time bar (total: 4.3s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze5.0ms (0.1%)

Memory
3.0MiB live, 3.0MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
33.3%25%50%0%0%25%0%4
60%37.5%25%0%0%37.5%0%5
77.8%43.7%12.5%0%0%43.7%0%6
88.2%46.9%6.2%0%0%46.9%0%7
93.9%48.4%3.1%0%0%48.4%0%8
96.9%49.2%1.6%0%0%49.2%0%9
98.4%49.6%0.8%0%0%49.6%0%10
99.2%49.8%0.4%0%0%49.8%0%11
99.6%49.9%0.2%0%0%49.9%0%12
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample999.0ms (23.2%)

Memory
36.3MiB live, 1 243.2MiB allocated
Samples
712.0ms8 256×0valid
1.0ms23×0invalid
Precisions
Click to see histograms. Total time spent on operations: 447.0ms
ival-sqrt: 94.0ms (21% of total)
ival-sub: 92.0ms (20.6% of total)
ival-atan: 79.0ms (17.7% of total)
ival-div: 59.0ms (13.2% of total)
ival-mult: 59.0ms (13.2% of total)
ival-add: 47.0ms (10.5% of total)
exact: 7.0ms (1.6% of total)
ival-true: 6.0ms (1.3% of total)
ival-assert: 3.0ms (0.7% of total)
Bogosity

explain95.0ms (2.2%)

Memory
1.4MiB live, 238.0MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
00-0-#s(literal 1 binary64)
00-0-(-.f64 #s(literal 1 binary64) x)
00-0-(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
00-0-(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
00-0-(+.f64 #s(literal 1 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
00-0-#s(literal 2 binary64)
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
37.0ms512×0valid
Compiler

Compiled 103 to 31 computations (69.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 22.0ms
ival-atan: 5.0ms (22.5% of total)
ival-sqrt: 4.0ms (18% of total)
ival-div: 3.0ms (13.5% of total)
ival-add: 3.0ms (13.5% of total)
ival-mult: 3.0ms (13.5% of total)
ival-sub: 3.0ms (13.5% of total)
exact: 1.0ms (4.5% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess16.0ms (0.4%)

Memory
-2.7MiB live, 43.8MiB allocated
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
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

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

Compiled 11 to 9 computations (18.2% saved)

simplify3.0ms (0.1%)

Memory
6.7MiB live, 6.7MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0944
01544
12444
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))

localize29.0ms (0.7%)

Memory
18.5MiB live, 65.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
accuracy0.0
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
accuracy0.01953125
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
accuracy0.0234375
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Samples
22.0ms256×0valid
Compiler

Compiled 46 to 11 computations (76.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-sub: 4.0ms (27.3% of total)
ival-div: 3.0ms (20.5% of total)
ival-mult: 2.0ms (13.7% 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)
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
8.1MiB live, 8.1MiB allocated
Counts
4 → 23
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Outputs
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
(+ 1 (* -2 x))
(+ 1 (* x (- (* 2 x) 2)))
(+ 1 (* x (- (* x (+ 2 (* -2 x))) 2)))
(sqrt -1)
(+ (sqrt -1) (/ 1 (* x (sqrt -1))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (/ 1 (* x (sqrt -1)))))
(+ (sqrt -1) (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* (pow x 2) (sqrt -1)))) (+ (* 1/2 (/ (- 2 (* -1 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (pow (sqrt -1) 2)))) (* (pow x 3) (sqrt -1)))) (/ 1 (* x (sqrt -1))))))
-1
(- (* 2 (/ 1 x)) 1)
(- (* 2 (/ 1 x)) (+ 1 (/ 2 (pow x 2))))
(- (+ (* 2 (/ 1 x)) (* 2 (/ 1 (pow x 3)))) (+ 1 (/ 2 (pow x 2))))
(* 2 (atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x))))))
(atan (sqrt (/ (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(+ (sqrt -1) (* -1 (/ (- (* 1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (* x (sqrt -1)))) (/ 1 (sqrt -1))) x)))
(+ (sqrt -1) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (+ 2 (/ 1 (pow (sqrt -1) 2))) (sqrt -1))) (* 1/2 (/ (+ 2 (+ (* 2 (/ 1 (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 4)))) (* x (sqrt -1))))) x)) (/ 1 (sqrt -1))) x)))
(- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* 2 (/ 1 x)) 2) x)) 2) x)) 1)
Calls

3 calls:

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

simplify139.0ms (3.2%)

Memory
-3.8MiB live, 235.7MiB allocated
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))

rewrite136.0ms (3.2%)

Memory
4.7MiB live, 190.9MiB allocated
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)

eval3.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated
Compiler

Compiled 415 to 143 computations (65.5% saved)

prune4.0ms (0.1%)

Memory
9.0MiB live, 9.0MiB allocated
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)))))
▶99.1%
(*.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)))))
▶99.0%
(*.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)))))
▶98.9%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶98.2%
(*.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)

simplify252.0ms (5.8%)

Memory
-15.0MiB live, 122.2MiB allocated
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)

localize65.0ms (1.5%)

Memory
-9.0MiB live, 92.3MiB allocated
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)
accuracy0.0
(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))))
accuracy0.6668471168959585
#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))))
accuracy0.0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x)))
accuracy0.7156907091583697
#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))))
accuracy0.0
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64)))
accuracy1.1757650253138703
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) #s(literal 1 binary64))
accuracy0.00390625
(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))
accuracy0.00390625
(-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
accuracy0.01171875
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
accuracy0.6118832999400914
#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
40.0ms256×0valid
Compiler

Compiled 183 to 23 computations (87.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-mult: 9.0ms (37.9% of total)
ival-add: 5.0ms (21.1% of total)
ival-sub: 4.0ms (16.9% of total)
ival-div: 2.0ms (8.4% of total)
ival-atan: 2.0ms (8.4% of total)
ival-sqrt: 2.0ms (8.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory
9.3MiB live, 9.3MiB allocated
Counts
18 → 37
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)
(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 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)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* (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))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
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) 1/2) x) 1) x) 1) (* 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) 1/2) x) 1) x) 1) (* 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) 1/2) x) 1) x) 1) (* 1/2 x))

simplify239.0ms (5.5%)

Memory
-8.9MiB live, 161.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125459
1363388
21297366
34992355
08420350
Stop Event
1×iter limit
1×node limit
Counts
37 → 37
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)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* (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))))
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
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) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.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 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) x)
(* -1/2 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (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)) (neg.f64 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 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal -1/2 binary64) #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 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) x)
(* -1 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))

rewrite200.0ms (4.6%)

Memory
-14.1MiB live, 215.5MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029232
048253
1150253
2989173
08752173
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 343
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)
(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 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))))
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(fma.f64 (/.f64 x (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 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.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 1 binary64))
(fma.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(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))
(fma.f64 #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)) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal 1 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))) #s(literal 1 binary64))
(fma.f64 x (-.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 #s(literal 1 binary64) (-.f64 #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)) x))) (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (-.f64 #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)) x))))
(-.f64 (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (-.f64 (*.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))) (pow.f64 (-.f64 (*.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 -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))) (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))))
(+.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))))
(+.f64 (/.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))) (pow.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (*.f64 (-.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))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (neg.f64 x)) (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))))
(+.f64 #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)) x))
(*.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)))

eval63.0ms (1.4%)

Memory
8.1MiB live, 53.5MiB allocated
Compiler

Compiled 11 332 to 1 541 computations (86.4% saved)

prune58.0ms (1.3%)

Memory
-22.7MiB live, 22.1MiB allocated
Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New2731274
Fresh000
Picked055
Done011
Total2737280
Accuracy
100.0%
Counts
280 → 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)))))
✓99.1%
(*.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)))))
✓99.0%
(*.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)))))
✓98.9%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
▶99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))))
✓98.2%
(*.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 107 to 84 computations (21.5% saved)

simplify294.0ms (6.8%)

Memory
29.1MiB live, 118.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
017112
025112
139112
257112
396112
4202112
5367112
6648112
71130112
81287112
91736108
102444108
112932108
123374108
134007108
145537108
156225108
166229108
176229108
186231108
196235108
206243108
216243108
226243108
236347108
246764108
256764108
06764102
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))
(+.f64 (*.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))
(*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 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)
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
x
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))))
(*.f64 (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))) #s(literal 2 binary64))
#s(literal 2 binary64)
(atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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))) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64)))))
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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(approx (sqrt (/ (- 1 x) (+ 1 x))) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal -1 binary64))))
(+.f64 (*.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))
(*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/2 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)) x)
(*.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x)
(-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #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 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64))
x
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
#s(literal 1 binary64)

localize58.0ms (1.3%)

Memory
-12.5MiB live, 75.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
accuracy0.01171875
(*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
accuracy0.015625
(*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
accuracy0.6118832999400914
#s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))
Samples
27.0ms256×0valid
Compiler

Compiled 80 to 19 computations (76.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-mult: 6.0ms (32.9% of total)
ival-add: 3.0ms (16.5% of total)
ival-sub: 3.0ms (16.5% of total)
ival-div: 2.0ms (11% of total)
ival-atan: 2.0ms (11% of total)
ival-sqrt: 2.0ms (11% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
5.2MiB live, 5.2MiB allocated
Counts
7 → 33
Calls
Call 1
Inputs
(+.f64 (*.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))
(-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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))) (+.f64 (*.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(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))
(*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
(*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
Outputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-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 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* 1/2 x)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (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 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* (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)))
Calls

3 calls:

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

simplify265.0ms (6.1%)

Memory
-37.2MiB live, 287.3MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116418
1338347
21227329
34727320
08049314
Stop Event
1×iter limit
1×node limit
Counts
33 → 33
Calls
Call 1
Inputs
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/2 x))) 1)))
-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 x)
(* x (- (* 1/2 x) 1))
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(* 1/2 x)
(* x (+ 1/2 (* -1/2 x)))
(* -1/2 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(* -1/2 (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 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(* (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)))
Outputs
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
#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 x)
(neg.f64 x)
(* x (- (* 1/2 x) 1))
(*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
(* x (- (* x (+ 1/2 (* -1/2 x))) 1))
(*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
(* 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 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/2 binary64))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/2))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/2 (/ 1 (pow x 2)))))
(*.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x)) (pow.f64 x #s(literal 3 binary64)))
(* -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) (/.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) (*.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 (* (pow x 3) (- 1/2 (* 1/2 (/ 1 x)))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* -1 (* (pow x 3) (+ 1/2 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))
(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) #s(literal -1/2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (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)) (neg.f64 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 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) x) #s(literal -1/2 binary64) #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))

rewrite191.0ms (4.4%)

Memory
35.8MiB live, 176.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017103
025103
198103
266982
3757482
0866979
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 188
Calls
Call 1
Inputs
(+.f64 (*.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))
(-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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))) (+.f64 (*.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(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))
(*.f64 (-.f64 (*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
(*.f64 (fma.f64 x #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)
Outputs
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 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 (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)))) (fma.f64 (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 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 (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 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (fma.f64 (-.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 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x))))
(*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 6 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) (-.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (pow.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x) #s(literal 4 binary64))))
(*.f64 (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 (*.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 (-.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 (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64))
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(*.f64 #s(literal 1 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)) x))
(*.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)
(*.f64 x (fma.f64 #s(literal -1/2 binary64) x #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) x) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) x) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (*.f64 (neg.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 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))))
(/.f64 (*.f64 x (-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) x)))
(/.f64 (*.f64 x (neg.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (*.f64 x (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/2 binary64))) (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) (-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.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)) (pow.f64 (*.f64 #s(literal 1/2 binary64) 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 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 1/2 binary64) 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 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #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 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 #s(literal -1/2 binary64) x) #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 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64)))
(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 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))) x (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 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 (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 #s(literal -1/2 binary64) x) x (*.f64 #s(literal 1/2 binary64) x))
(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 #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))
(fma.f64 x (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))) (*.f64 x (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64)))))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(-.f64 (*.f64 (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) #s(literal 1/2 binary64)))
(-.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 (neg.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 (*.f64 #s(literal 1/2 binary64) x) x))
(+.f64 (*.f64 (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))) x) (*.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64))) x))
(+.f64 (*.f64 x (/.f64 (pow.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64)))) (*.f64 x (/.f64 #s(literal 1/8 binary64) (fma.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/4 binary64)))))
(+.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)))

eval52.0ms (1.2%)

Memory
-1.9MiB live, 44.0MiB allocated
Compiler

Compiled 10 281 to 1 477 computations (85.6% saved)

prune24.0ms (0.6%)

Memory
-29.6MiB live, 16.7MiB allocated
Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New2180218
Fresh000
Picked011
Done066
Total2187225
Accuracy
100.0%
Counts
225 → 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)))))
✓99.1%
(*.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)))))
✓99.0%
(*.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)))))
✓98.9%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (-.f64 #s(literal 1 binary64) x))))
✓99.1%
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))))
✓98.2%
(*.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 214 to 127 computations (40.7% saved)

regimes10.0ms (0.2%)

Memory
27.3MiB live, 27.3MiB allocated
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 (-.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)))))
(*.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)

regimes12.0ms (0.3%)

Memory
-17.2MiB live, 25.3MiB allocated
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 (-.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)))))
Outputs
(*.f64 #s(literal 2 binary64) (atan.f64 #s(approx (sqrt (/ (- 1 x) (+ 1 x))) (+.f64 (*.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)))))
Calls

5 calls:

5.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
2.0ms
x
2.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
(atan.f64 (sqrt.f64 (/.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)

regimes8.0ms (0.2%)

Memory
22.3MiB live, 22.3MiB allocated
Counts
5 → 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)))))
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:

2.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.1%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)

regimes16.0ms (0.4%)

Memory
-30.6MiB live, 19.2MiB allocated
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:

10.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
2.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
Results
AccuracySegmentsBranch
99.0%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
99.0%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
99.0%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
99.0%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
99.0%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory
15.6MiB live, 15.6MiB allocated
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:

2.0ms
x
1.0ms
(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
1.0ms
(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
1.0ms
(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
98.9%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
98.9%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.9%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.9%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.9%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory
15.8MiB live, 15.8MiB allocated
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:

1.0ms
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
(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
98.2%1(/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
98.2%1(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
98.2%1(atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
98.2%1(*.f64 #s(literal 2 binary64) (atan.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
98.2%1x
Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes7.0ms (0.2%)

Memory
-27.7MiB live, 14.2MiB allocated
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
(*.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
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)

simplify12.0ms (0.3%)

Memory
40.4MiB live, 40.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042107
155107
262107
366107
470107
586107
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))) (+.f64 (*.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)))))
(*.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))) (+.f64 (*.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)))))
(*.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)

derivations996.0ms (23.1%)

Memory
-40.2MiB live, 395.2MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0935
01534
15034
227326
329565
092045
029232
048253
1150253
2989173
08752173
0107324
1307262
21011242
33679224
08337217
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 107 to 43 computations (59.8% saved)

preprocess38.0ms (0.9%)

Memory
43.6MiB live, 85.6MiB allocated
Compiler

Compiled 236 to 104 computations (55.9% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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