sqrtexp (problem 3.4.4)

Time bar (total: 6.6s)

analyze2.0ms (0%)

Memory
2.5MiB live, 2.5MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample927.0ms (14.1%)

Memory
53.3MiB live, 952.4MiB allocated
Samples
454.0ms8 256×0valid
157.0ms2 694×0exit
Precisions
Click to see histograms. Total time spent on operations: 360.0ms
ival-expm1: 121.0ms (33.6% of total)
ival-mult: 77.0ms (21.4% of total)
ival-sqrt: 75.0ms (20.8% of total)
ival-div: 71.0ms (19.7% of total)
ival-true: 7.0ms (1.9% of total)
exact: 5.0ms (1.4% of total)
ival-assert: 3.0ms (0.8% of total)
Bogosity

preprocess397.0ms (6%)

Memory
6.9MiB live, 354.3MiB allocated
Algorithm
1×egg-herbie
Rules
15 394×lower-fma.f64
15 394×lower-fma.f32
2 850×lower--.f32
2 846×lower--.f64
2 458×lower-*.f32
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01229
13227
25527
38927
414313
525013
651313
7203913
8713613
01012
01712
12912
23512
34712
4737
51265
62035
76065
829265
967835
081975
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

explain189.0ms (2.9%)

Memory
5.9MiB live, 137.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1640-0-(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
1640-0-(-.f64 (exp.f64 x) #s(literal 1 binary64))
40-0-(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
00-0-(exp.f64 (*.f64 #s(literal 2 binary64) x))
00-0-#s(literal 1 binary64)
00-0-(*.f64 #s(literal 2 binary64) x)
00-0-(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
00-0-#s(literal 2 binary64)
00-0-(exp.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (exp.f64 x) #s(literal 1 binary64))cancellation1641
-.f64(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))cancellation1640
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/o30
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow4
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow4
↳(exp.f64 x)overflow3
↳(-.f64 (exp.f64 x) #s(literal 1 binary64))overflow3
/.f64(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))o/n10
↳(exp.f64 (*.f64 #s(literal 2 binary64) x))overflow4
↳(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))overflow4
Confusion
Predicted +Predicted -
+1670
-188
Precision
0.9940476190476191
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+16700
-1187
Precision?
0.9881656804733728
Recall?
1.0
Freqs
test
numberfreq
088
14
2164
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
38.0ms512×0valid
Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 24.0ms
ival-exp: 7.0ms (29.2% of total)
ival-expm1: 6.0ms (25.1% of total)
ival-div: 3.0ms (12.5% of total)
ival-mult: 3.0ms (12.5% of total)
ival-sqrt: 3.0ms (12.5% of total)
exact: 1.0ms (4.2% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶36.7%
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify368.0ms (5.6%)

Memory
1.5MiB live, 350.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff128
(*.f64 #s(literal 2 binary64) x)
✓cost-diff192
(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓cost-diff192
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓cost-diff7104
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Rules
15 394×lower-fma.f64
15 394×lower-fma.f32
2 850×lower--.f32
2 846×lower--.f64
2 458×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
01745
12945
23545
34745
47335
512631
620331
760631
8292631
9678331
0819727
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (+.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(exp.f64 (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(+.f64 x x)
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize49.0ms (0.7%)

Memory
-16.4MiB live, 22.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
✓accuracy98.7%
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓accuracy41.0%
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓accuracy40.9%
(-.f64 (exp.f64 x) #s(literal 1 binary64))
Samples
18.0ms256×0valid
Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-exp: 3.0ms (26.2% of total)
ival-expm1: 3.0ms (26.2% of total)
ival-div: 2.0ms (17.5% of total)
ival-mult: 2.0ms (17.5% of total)
ival-sqrt: 2.0ms (17.5% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
2.2MiB live, 2.2MiB allocated
Counts
4 → 48
Calls
Call 1
Inputs
#<alt (-.f64 (exp.f64 x) #s(literal 1 binary64))>
#<alt (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))>
#<alt (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))>
#<alt (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))>
Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms
x
@inf
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms
x
@0
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
0.0ms
x
@inf
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
0.0ms
x
@0
(- (exp x) 1)

rewrite344.0ms (5.2%)

Memory
6.4MiB live, 373.7MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 536×lower-fma.f64
4 536×lower-fma.f32
3 326×lower-*.f32
3 324×lower-*.f64
2 746×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01033
01733
16319
242919
3503619
0805115
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 688
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Outputs
(exp.f64 (*.f64 (neg.f64 (log.f64 (expm1.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (expm1.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) #s(literal -1 binary64))
(+.f64 (-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (exp.f64 x)))))
(-.f64 (/.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (expm1.f64 x) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (*.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (*.f64 (expm1.f64 x) (exp.f64 (+.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3/2 binary64))) (/.f64 (exp.f64 (*.f64 x #s(literal 3/2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
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(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(*.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(*.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (exp.f64 x))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (*.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (*.f64 (exp.f64 x) (expm1.f64 (+.f64 x x)))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 (expm1.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 (+.f64 x x))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 6 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x)) (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 6 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (exp.f64 (*.f64 x #s(literal 4 binary64)))) (exp.f64 (*.f64 #s(literal 4 binary64) (+.f64 x x)))))
(*.f64 (/.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x)) (-.f64 (exp.f64 (*.f64 #s(literal 4 binary64) (+.f64 x x))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64))) (exp.f64 (+.f64 x x))))
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 6 binary64))))) (fma.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (neg.f64 (expm1.f64 (+.f64 x x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(neg.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (expm1.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64)))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (expm1.f64 x) (exp.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 (exp.f64 (*.f64 x #s(literal 6 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (*.f64 (exp.f64 (*.f64 x #s(literal 4 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) #s(literal 1 binary64)) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 6 binary64))) (expm1.f64 x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(literal 1 binary64) (exp.f64 (log1p.f64 (exp.f64 x)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (sqrt.f64 (expm1.f64 (+.f64 x x))))
(*.f64 (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x))))
(*.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))

simplify411.0ms (6.2%)

Memory
17.3MiB live, 446.7MiB allocated
Algorithm
1×egg-herbie
Rules
15 504×lower-fma.f64
15 504×lower-fma.f32
4 704×lower-*.f64
4 704×lower-*.f32
2 492×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077444
1252410
2663410
31425404
42548324
55907289
08297234
Stop Event
1×iter limit
1×node limit
Counts
48 → 47
Calls
Call 1
Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (+.f64 x x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

eval130.0ms (2%)

Memory
-0.5MiB live, 124.7MiB allocated
Compiler

Compiled 16 857 to 2 362 computations (86% saved)

prune131.0ms (2%)

Memory
-11.4MiB live, 187.6MiB allocated
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New7269735
Fresh000
Picked101
Done000
Total7279736
Accuracy
100.0%
Counts
736 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶65.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶65.9%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶98.4%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
63.8%
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
▶70.2%
(sqrt.f64 #s(literal 2 binary64))
99.0%
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
Compiler

Compiled 156 to 116 computations (25.6% saved)

simplify398.0ms (6.1%)

Memory
6.3MiB live, 635.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 x x)
✓cost-diff0
(expm1.f64 (+.f64 x x))
✓cost-diff0
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓cost-diff7104
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓cost-diff0
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(exp.f64 x)
✓cost-diff0
(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓cost-diff0
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
Rules
16 482×lower-fma.f32
16 474×lower-fma.f64
2 548×lower-*.f64
2 548×lower-*.f32
2 468×lower--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02189
04183
17583
213583
323183
431383
543583
675683
7273583
8760183
0828883
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 x)
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (-.f64 (expm1.f64 x) #s(literal -2 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 (expm1.f64 x) #s(literal -2 binary64))
(exp.f64 x)
x
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (-.f64 (expm1.f64 x) #s(literal -2 binary64)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(-.f64 (expm1.f64 x) #s(literal -2 binary64))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 x)

localize72.0ms (1.1%)

Memory
14.6MiB live, 136.6MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(expm1.f64 (+.f64 x x))
✓accuracy100.0%
(expm1.f64 x)
✓accuracy100.0%
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓accuracy98.7%
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓accuracy100.0%
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.8%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.3%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓accuracy86.5%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(exp.f64 x)
✓accuracy100.0%
(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓accuracy100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
Samples
41.0ms245×0valid
2.0ms6×2valid
1.0ms5×1valid
Compiler

Compiled 111 to 27 computations (75.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 31.0ms
ival-add: 8.0ms (26.1% of total)
ival-mult: 6.0ms (19.5% of total)
ival-sqrt: 6.0ms (19.5% of total)
ival-div: 3.0ms (9.8% of total)
ival-expm1: 3.0ms (9.8% of total)
ival-exp: 2.0ms (6.5% of total)
adjust: 1.0ms (3.3% of total)
ival-sub: 1.0ms (3.3% of total)
exact: 1.0ms (3.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory
-24.7MiB live, 13.6MiB allocated
Counts
14 → 156
Calls
Call 1
Inputs
#<alt (sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))>
#<alt (-.f64 (exp.f64 x) #s(literal -1 binary64))>
#<alt (exp.f64 x)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))>
#<alt (sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))>
#<alt (expm1.f64 x)>
#<alt (expm1.f64 (+.f64 x x))>
Outputs
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
Calls

39 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
1.0ms
x
@inf
(+ (* (/ x (sqrt 2)) (+ (* x 3/16) 1/2)) (sqrt 2))
1.0ms
x
@inf
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
1.0ms
x
@inf
(/ x (sqrt 2))
1.0ms
x
@-inf
(/ (- (exp (+ x x)) 1) (- (exp x) 1))

rewrite112.0ms (1.7%)

Memory
6.5MiB live, 85.6MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
744×lower-fma.f32
736×lower-fma.f64
702×lower-*.f64
702×lower-*.f32
610×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02172
04166
118066
0141066
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
14 → 268
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(exp.f64 x)
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(expm1.f64 x)
(expm1.f64 (+.f64 x x))
Outputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (*.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (*.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))
(exp.f64 x)
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64))) (sqrt.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x)))))
(/.f64 (sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal -4 binary64))) (sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(pow.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (neg.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))))
(+.f64 #s(literal 2 binary64) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) #s(literal 2 binary64))
(+.f64 (*.f64 x (*.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 2 binary64)))
(+.f64 (+.f64 #s(literal 2 binary64) (*.f64 x (*.f64 x #s(literal 1/2 binary64)))) x)
(-.f64 (/.f64 (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 x #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 x #s(literal 2 binary64)))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)) #s(literal -4 binary64))))
(/.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))) #s(literal 8 binary64)) (-.f64 (fma.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x) #s(literal 4 binary64)) (*.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (+.f64 x x))))
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(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (neg.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (*.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x))
(/.f64 (*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(expm1.f64 x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))
(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(/.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x)))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (expm1.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal 1 binary64))))
(+.f64 #s(literal -1 binary64) (exp.f64 (+.f64 x x)))
(+.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))
(-.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(-.f64 (/.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x)))))
(/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))
(*.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))

simplify448.0ms (6.8%)

Memory
-12.0MiB live, 441.1MiB allocated
Algorithm
1×egg-herbie
Rules
11 072×lower-fma.f64
11 072×lower-fma.f32
4 350×lower-*.f64
4 350×lower-*.f32
2 786×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01921393
16341212
219661138
357941134
08365951
Stop Event
1×iter limit
1×node limit
Counts
156 → 155
Calls
Call 1
Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal 1 binary64)) (/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal -3/4 binary64) (*.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* -1 (* x (sqrt 1/2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 x #s(literal 3/16 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 #s(literal 2 binary64) (fma.f64 x x x))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))

eval50.0ms (0.8%)

Memory
12.9MiB live, 91.0MiB allocated
Compiler

Compiled 6 179 to 792 computations (87.2% saved)

prune39.0ms (0.6%)

Memory
14.2MiB live, 91.2MiB allocated
Pruning

14 alts after pruning (10 fresh and 4 done)

PrunedKeptTotal
New4247431
Fresh134
Picked145
Done000
Total42614440
Accuracy
100.0%
Counts
440 → 14
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶64.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓65.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶65.6%
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
64.6%
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
64.1%
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
▶4.3%
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
4.1%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓65.9%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶4.3%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶63.8%
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 288 to 183 computations (36.5% saved)

simplify34.0ms (0.5%)

Memory
-3.6MiB live, 40.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(*.f64 x #s(literal 3/16 binary64))
✓cost-diff0
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
✓cost-diff0
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
✓cost-diff0
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓cost-diff0
(+.f64 x #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
Rules
1 136×lower-fma.f32
1 124×lower-fma.f64
478×lower-*.f32
472×lower-*.f64
250×associate-*l*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021112
042112
176112
2149112
3252112
4360112
5408112
6565112
7632112
8783112
0783112
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
#s(literal 1/2 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
x
(*.f64 x #s(literal 3/16 binary64))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
Outputs
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
#s(literal 1/2 binary64)
(*.f64 x x)
x
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
x
(*.f64 x #s(literal 3/16 binary64))
#s(literal 3/16 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize130.0ms (2%)

Memory
-31.1MiB live, 137.0MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓accuracy100.0%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 x #s(literal 3/16 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.9%
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
✓accuracy99.8%
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
✓accuracy100.0%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓accuracy100.0%
(+.f64 x #s(literal 2 binary64))
✓accuracy100.0%
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓accuracy100.0%
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.4%
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
Samples
51.0ms161×0invalid
16.0ms94×0valid
1.0ms1×5exit
Compiler

Compiled 126 to 28 computations (77.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 13.0ms (38.8% of total)
ival-add: 7.0ms (20.9% of total)
ival-sqrt: 5.0ms (14.9% of total)
const: 4.0ms (11.9% of total)
ival-div: 4.0ms (11.9% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
16.2MiB live, 16.2MiB allocated
Counts
15 → 168
Calls
Call 1
Inputs
#<alt (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))>
#<alt (sqrt.f64 (+.f64 x #s(literal 2 binary64)))>
#<alt (+.f64 x #s(literal 2 binary64))>
#<alt (sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))>
#<alt (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)>
#<alt (*.f64 x x)>
#<alt (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x (*.f64 x #s(literal 3/16 binary64)))>
#<alt (*.f64 x #s(literal 3/16 binary64))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))>
Outputs
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* 3/16 x)>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 3/16 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (* 3/16 x)>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
Calls

42 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(sqrt (+ x 2))
0.0ms
x
@0
(/ (* x (* x 3/16)) (sqrt 2))
0.0ms
x
@inf
(sqrt (+ x 2))
0.0ms
x
@inf
(/ (* x (* x 3/16)) (sqrt 2))
0.0ms
x
@-inf
(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))

rewrite327.0ms (5%)

Memory
28.0MiB live, 492.1MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 768×lower-fma.f32
5 756×lower-fma.f64
4 358×lower-/.f32
4 352×lower-/.f64
3 820×lower-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02185
04285
118285
2142685
0822185
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
15 → 480
Calls
Call 1
Inputs
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+.f64 x #s(literal 2 binary64))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(*.f64 x x)
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 x #s(literal 3/16 binary64)))
(*.f64 x #s(literal 3/16 binary64))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/256 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 9/256 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) (neg.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))))
(/.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 27/4096 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 3/32 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/256 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (neg.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
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(*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (neg.f64 (fma.f64 (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 x x) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))))))
(+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))
(+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64))
(+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(-.f64 (/.f64 #s(literal 9/256 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (neg.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))) (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (*.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (*.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(*.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(*.f64 (-.f64 #s(literal 9/256 binary64) (*.f64 (*.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))

simplify394.0ms (6%)

Memory
-5.1MiB live, 629.3MiB allocated
Algorithm
1×egg-herbie
Rules
13 948×lower-fma.f64
13 948×lower-fma.f32
5 568×lower-*.f64
5 568×lower-*.f32
1 884×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02351416
17131376
221381309
367041291
083231214
Stop Event
1×iter limit
1×node limit
Counts
168 → 165
Calls
Call 1
Inputs
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(+ 1/2 (* 3/16 x))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(* 3/16 x)
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
Outputs
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (*.f64 x x)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (*.f64 x x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (*.f64 x x)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (/.f64 (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (*.f64 x x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(*.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 x (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal -1/32 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x #s(literal 1/128 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))))
(* -1 (* x (sqrt 1/2)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* 1/8 (/ 1 (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (* x (pow (sqrt 1/2) 5)))) (* 1/8 (/ 1 (pow (sqrt 1/2) 3)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(neg.f64 (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))) (-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* 1/2 (pow x 2))
(*.f64 #s(literal 1/2 binary64) (*.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(*.f64 x (*.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 (pow x 2))
(*.f64 #s(literal 3/16 binary64) (*.f64 x x))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (*.f64 x x))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (*.f64 x x)))) (*.f64 x x))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x))) x)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

eval101.0ms (1.5%)

Memory
18.3MiB live, 131.0MiB allocated
Compiler

Compiled 14 745 to 1 626 computations (89% saved)

prune100.0ms (1.5%)

Memory
-19.2MiB live, 155.4MiB allocated
Pruning

20 alts after pruning (14 fresh and 6 done)

PrunedKeptTotal
New69110701
Fresh145
Picked235
Done134
Total69520715
Accuracy
100.0%
Counts
715 → 20
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓64.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.5%
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
64.6%
(fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
1.0%
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x #s(literal 1/128 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
▶64.6%
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
▶64.6%
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
4.3%
(/.f64 (*.f64 (*.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶2.5%
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
62.7%
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
4.1%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
▶4.3%
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
3.1%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓65.9%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓4.3%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓63.8%
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
▶2.5%
(sqrt.f64 x)
✓70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 464 to 304 computations (34.5% saved)

simplify26.0ms (0.4%)

Memory
-24.8MiB live, 20.5MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff0
(*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓cost-diff1984
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff0
(*.f64 x x)
✓cost-diff0
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
✓cost-diff0
(*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))
✓cost-diff0
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff0
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
✓cost-diff0
(sqrt.f64 x)
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff1344
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
Rules
736×lower-fma.f32
724×lower-fma.f64
238×lower-*.f32
224×lower-*.f64
188×lower-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
023166
047162
1101158
2223156
3326156
4367156
5396156
6402156
7407156
8408156
0408152
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
x
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 3/16 binary64)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))
x
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(*.f64 x x)
#s(literal 7/192 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
x
(*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 7/192 binary64)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
Outputs
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
#s(literal 3/16 binary64)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 3/16 binary64)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))
(*.f64 x (*.f64 x (*.f64 x #s(literal 7/192 binary64))))
x
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(*.f64 x (*.f64 x #s(literal 7/192 binary64)))
(*.f64 x x)
#s(literal 7/192 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 7/192 binary64)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)

localize100.0ms (1.5%)

Memory
24.4MiB live, 181.9MiB allocated
Localize:

Found 17 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.9%
(*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.7%
(*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))
✓accuracy99.9%
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.9%
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy99.9%
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
✓accuracy99.8%
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 x)
✓accuracy100.0%
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓accuracy100.0%
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.7%
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.4%
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
Samples
38.0ms161×0invalid
22.0ms94×0valid
1.0ms1×5exit
Compiler

Compiled 180 to 31 computations (82.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
ival-mult: 20.0ms (48% of total)
ival-add: 9.0ms (21.6% of total)
ival-div: 5.0ms (12% of total)
const: 4.0ms (9.6% of total)
ival-sqrt: 4.0ms (9.6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory
-22.6MiB live, 16.1MiB allocated
Counts
14 → 144
Calls
Call 1
Inputs
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))>
#<alt (sqrt.f64 x)>
#<alt (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (*.f64 (*.f64 x x) #s(literal 7/192 binary64))>
#<alt (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))>
#<alt (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
Outputs
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (pow x 2))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (pow x 3))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ x (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
Calls

36 calls:

TimeVariablePointExpression
2.0ms
x
@0
(* (* x x) 7/192)
2.0ms
x
@inf
(* (* x x) 7/192)
1.0ms
x
@0
(/ (* x (* (* x x) 7/192)) (sqrt 2))
0.0ms
x
@inf
(/ (* x (* (* x x) 7/192)) (sqrt 2))
0.0ms
x
@-inf
(sqrt x)

rewrite370.0ms (5.6%)

Memory
27.6MiB live, 466.4MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 974×lower-/.f32
4 968×lower-/.f64
4 638×lower-*.f32
4 624×lower-*.f64
4 064×lower-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02294
04494
117790
2149888
0874088
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
14 → 339
Calls
Call 1
Inputs
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(sqrt.f64 x)
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (*.f64 x x) #s(literal 7/192 binary64))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64)))
(*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 3 binary64))))
(neg.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))))
(pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -3 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))
(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 x #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (neg.f64 (*.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))
(+.f64 (*.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 2 binary64) (fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (/.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))))))
(fma.f64 x (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) x (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
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(/.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64))) (neg.f64 (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)))) (neg.f64 (neg.f64 (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))) (neg.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (fma.f64 (*.f64 #s(literal 27/4096 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 8 binary64)))) (fma.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
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(*.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64) #s(literal 4 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
(*.f64 (fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))

simplify310.0ms (4.7%)

Memory
10.4MiB live, 360.0MiB allocated
Algorithm
1×egg-herbie
Rules
10 228×lower-fma.f64
10 228×lower-fma.f32
4 002×lower-*.f64
4 002×lower-*.f32
1 268×lower-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0891019
12811019
2808981
32327954
45582944
08339902
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
Calls
Call 1
Inputs
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ x (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (pow x 2))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (pow x 3))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ x (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
Outputs
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (pow x 2))
(*.f64 #s(literal 7/192 binary64) (*.f64 x x))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (pow x 3))
(*.f64 x (*.f64 #s(literal 7/192 binary64) (*.f64 x x)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ x (sqrt 2)))
(/.f64 (*.f64 x #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 #s(literal 7/192 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))

eval117.0ms (1.8%)

Memory
-21.6MiB live, 146.5MiB allocated
Compiler

Compiled 13 387 to 1 260 computations (90.6% saved)

prune71.0ms (1.1%)

Memory
-12.8MiB live, 144.7MiB allocated
Pruning

22 alts after pruning (12 fresh and 10 done)

PrunedKeptTotal
New6334637
Fresh189
Picked145
Done066
Total63522657
Accuracy
100.0%
Counts
657 → 22
Alt Table
Click to see full alt table
StatusAccuracyProgram
64.6%
(fma.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
✓64.6%
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
64.5%
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
1.0%
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x #s(literal 1/128 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
✓64.6%
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
4.3%
(/.f64 (*.f64 (*.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓2.5%
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
3.1%
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
62.7%
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
2.8%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
4.1%
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
2.5%
(*.f64 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓4.3%
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
3.1%
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
2.9%
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
64.3%
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓65.9%
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓4.3%
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
✓100.0%
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓63.8%
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
✓2.5%
(sqrt.f64 x)
✓70.2%
(sqrt.f64 #s(literal 2 binary64))
Compiler

Compiled 645 to 302 computations (53.2% saved)

regimes26.0ms (0.4%)

Memory
9.6MiB live, 46.6MiB allocated
Counts
31 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (*.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x #s(literal 1/128 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
Calls

3 calls:

10.0ms
x
7.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
100.0%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes22.0ms (0.3%)

Memory
15.1MiB live, 53.9MiB allocated
Accuracy

Total -44.6b remaining (-234.2%)

Threshold costs -44.6b (-234.2%)

Counts
27 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(*.f64 (*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) x)
(/.f64 (*.f64 x (*.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (*.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))
(*.f64 (*.f64 x (*.f64 x #s(literal 7/192 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 x (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 (*.f64 x (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 2 binary64) x)))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 (fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (*.f64 x (*.f64 #s(literal 7/192 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) x) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 (*.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x #s(literal 1/128 binary64)) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x x) #s(literal -1/32 binary64)))) (sqrt.f64 x))
Outputs
(sqrt.f64 #s(literal 2 binary64))
Calls

3 calls:

7.0ms
x
7.0ms
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
6.0ms
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
70.2%1x
70.2%1(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
70.2%1(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify5.0ms (0.1%)

Memory
13.2MiB live, 13.2MiB allocated
Algorithm
1×egg-herbie
Rules
4×+-commutative_binary64
4×sub-neg_binary64
2×neg-sub0_binary64
2×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
197
2137
3147
4157
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
Outputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))

soundness293.0ms (4.4%)

Memory
-15.8MiB live, 244.8MiB allocated
Rules
15 504×lower-fma.f64
15 504×lower-fma.f32
4 704×lower-*.f64
4 704×lower-*.f32
4 536×lower-fma.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01033
01733
16319
242919
3503619
0805115
077444
1252410
2663410
31425404
42548324
55907289
08297234
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess54.0ms (0.8%)

Memory
12.9MiB live, 51.4MiB allocated
Compiler

Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...