Hyperbolic tangent

Time bar (total: 8.6s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
1.2MiB live, 1.2MiB allocated
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
100%100%0%0%0%0%0%2
Compiler

Compiled 15 to 9 computations (40% saved)

sample4.2s (48.3%)

Memory
46.3MiB live, 4 287.7MiB allocated
Samples
1.7s3 211×2valid
1.1s4 634×1valid
608.0ms7 793×0exit
26.0ms411×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.7s
ival-exp: 1.6s (59.5% of total)
adjust: 398.0ms (14.7% of total)
ival-add: 222.0ms (8.2% of total)
ival-div: 214.0ms (7.9% of total)
ival-sub: 164.0ms (6.1% of total)
ival-neg: 76.0ms (2.8% of total)
ival-true: 12.0ms (0.4% of total)
ival-assert: 7.0ms (0.3% of total)
Bogosity

explain212.0ms (2.5%)

Memory
-34.4MiB live, 356.8MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2480-0-(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
30-0-(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
00-0-(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
00-0-(exp.f64 x)
00-0-(exp.f64 (neg.f64 x))
00-0-(neg.f64 x)
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))cancellation2481
/.f64(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))o/o30
(exp.f64 x)overflow1
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))overflow3
(exp.f64 (neg.f64 x))overflow2
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))overflow3
(exp.f64 x)overflow1
(exp.f64 (neg.f64 x))overflow2
Confusion
Predicted +Predicted -
+2510
-05
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25100
-014
Precision?
0.996031746031746
Recall?
1.0
Freqs
test
numberfreq
05
1251
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
75.0ms166×2valid
61.0ms330×1valid
1.0ms16×0valid
Compiler

Compiled 83 to 25 computations (69.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 114.0ms
ival-exp: 72.0ms (63.3% of total)
adjust: 19.0ms (16.7% of total)
ival-div: 7.0ms (6.2% of total)
ival-add: 6.0ms (5.3% of total)
ival-sub: 5.0ms (4.4% of total)
ival-neg: 3.0ms (2.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

preprocess142.0ms (1.6%)

Memory
27.0MiB live, 166.8MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0927
13427
28727
335127
4367919
0713
01313
12613
26613
325813
416599
088379
Stop Event
iter limit
node limit
iter limit
node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
Symmetry

(negabs x)

Compiler

Compiled 13 to 7 computations (46.2% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
8.0%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 13 to 7 computations (46.2% saved)

simplify184.0ms (2.1%)

Memory
-22.3MiB live, 166.6MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(exp.f64 x)
cost-diff0
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
cost-diff2
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
cost-diff2
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0733
01333
12633
26633
325833
4165925
0883725
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Outputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (sinh.f64 x))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))

localize148.0ms (1.7%)

Memory
-11.5MiB live, 85.7MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(exp.f64 x)
accuracy0.00390625
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy0.7343832531524757
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy58.13887237207131
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Samples
66.0ms83×2valid
30.0ms165×1valid
1.0ms0valid
Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 86.0ms
ival-div: 36.0ms (41.9% of total)
ival-exp: 34.0ms (39.6% of total)
adjust: 10.0ms (11.6% of total)
ival-add: 3.0ms (3.5% of total)
ival-sub: 3.0ms (3.5% of total)
ival-neg: 1.0ms (1.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series3.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
Counts
4 → 23
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(exp.f64 x)
Outputs
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) (exp (neg x)))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(exp x)
(- (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))
1.0ms
x
@inf
((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))
1.0ms
x
@-inf
((- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (exp x))

simplify243.0ms (2.8%)

Memory
32.2MiB live, 118.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079210
1292210
2958200
33882200
08155179
Stop Event
iter limit
node limit
Counts
23 → 22
Calls
Call 1
Inputs
(* 2 x)
(* x (+ 2 (* 1/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
2
(+ 2 (pow x 2))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(- (exp x) (exp (neg x)))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(exp x)
(- (exp x) (exp (* -1 x)))
(+ (exp x) (exp (* -1 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/3 (pow x 2))))
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/3 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* 1/60 (pow x 2))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/60 binary64) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
(* x (+ 2 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/60 (* 1/2520 (pow x 2))))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2520 binary64) (*.f64 x x) #s(literal 1/60 binary64)) (*.f64 x x) #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (pow x 2))
(fma.f64 x x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* 1/12 (pow x 2)))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64) x) x #s(literal 2 binary64))
(+ 2 (* (pow x 2) (+ 1 (* (pow x 2) (+ 1/12 (* 1/360 (pow x 2)))))))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/360 binary64) (*.f64 x x) #s(literal 1/12 binary64)) x) x #s(literal 2 binary64))
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(- (exp x) (exp (neg x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+ (exp x) (exp (neg x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(exp x)
(exp.f64 x)
(- (exp x) (exp (* -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+ (exp x) (exp (* -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite256.0ms (3%)

Memory
-18.0MiB live, 216.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
01312
15012
239512
3619612
0920112
Stop Event
iter limit
node limit
iter limit
Counts
4 → 636
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(exp.f64 x)
Outputs
(*.f64 (/.f64 (neg.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))) (neg.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (sinh.f64 x))
(*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)))) (fma.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))) (+.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(*.f64 (/.f64 (neg.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (neg.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x))))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (cosh.f64 x)) (sinh.f64 x))
(*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -2 binary64) (sinh.f64 (neg.f64 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(*.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))))
(*.f64 #s(literal 1 binary64) (*.f64 (sinh.f64 x) #s(literal 2 binary64)))
(*.f64 (cosh.f64 x) (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (cosh.f64 x)))
(*.f64 (sinh.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 (/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (sinh.f64 x))
(*.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (tanh.f64 x))
(*.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (cosh.f64 x)) #s(literal 2 binary64))
(/.f64 (sinh.f64 (*.f64 #s(literal -2 binary64) x)) (neg.f64 (cosh.f64 x)))
(/.f64 (*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 2 binary64)))) (fma.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64) #s(literal 1 binary64)))
(/.f64 (*.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))) (+.f64 (pow.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal 6 binary64)))) (fma.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) (-.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (neg.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
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(/.f64 (fma.f64 (sinh.f64 x) #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64)))) (neg.f64 (-.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 (*.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (-.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (cosh.f64 x) (sinh.f64 x))))
(/.f64 (-.f64 (*.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (sinh.f64 x) #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (-.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (sinh.f64 x))) #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (fma.f64 (sinh.f64 x) (sinh.f64 x) (-.f64 (pow.f64 (cosh.f64 x) #s(literal 2 binary64)) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(/.f64 (+.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (pow.f64 (cosh.f64 x) #s(literal 3 binary64))) (-.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (cosh.f64 x) (sinh.f64 x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(fma.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal -3 binary64) x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) #s(literal 2 binary64)) (cosh.f64 x))
(fma.f64 (/.f64 (*.f64 (sinh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (sinh.f64 x))
(fma.f64 #s(literal 1 binary64) (cosh.f64 x) (sinh.f64 x))
(fma.f64 #s(literal 1 binary64) (sinh.f64 x) (cosh.f64 x))
(fma.f64 (cosh.f64 x) #s(literal 1 binary64) (sinh.f64 x))
(fma.f64 (sinh.f64 x) #s(literal 1 binary64) (cosh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (sinh.f64 x) #s(literal 2 binary64)) (cosh.f64 x))
(fma.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (sinh.f64 x))
(-.f64 (cosh.f64 x) (sinh.f64 (neg.f64 x)))
(exp.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(exp.f64 x)
(+.f64 (/.f64 (pow.f64 (cosh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (cosh.f64 x) (sinh.f64 x)))) (/.f64 (pow.f64 (sinh.f64 x) #s(literal 3 binary64)) (-.f64 (cosh.f64 (*.f64 #s(literal 2 binary64) x)) (*.f64 (cosh.f64 x) (sinh.f64 x)))))
(+.f64 (cosh.f64 x) (sinh.f64 x))
(+.f64 (sinh.f64 x) (cosh.f64 x))

eval126.0ms (1.5%)

Memory
17.5MiB live, 201.3MiB allocated
Compiler

Compiled 19 340 to 1 974 computations (89.8% saved)

prune50.0ms (0.6%)

Memory
-43.7MiB live, 37.1MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New6983701
Fresh000
Picked101
Done000
Total6993702
Accuracy
100.0%
Counts
702 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.8%
(/.f64 (sinh.f64 x) (cosh.f64 x))
100.0%
(tanh.f64 x)
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify100.0ms (1.2%)

Memory
35.3MiB live, 127.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cosh.f64 x)
cost-diff0
(sinh.f64 x)
cost-diff3
(/.f64 (sinh.f64 x) (cosh.f64 x))
cost-diff0
(tanh.f64 x)
cost-diff0
(pow.f64 x #s(literal 3 binary64))
cost-diff0
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
cost-diff0
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01645
02331
15331
214031
357331
4415031
0926631
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
#s(literal -1/3 binary64)
(tanh.f64 x)
x
(/.f64 (sinh.f64 x) (cosh.f64 x))
(sinh.f64 x)
x
(cosh.f64 x)
Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
#s(literal -1/3 binary64)
(tanh.f64 x)
x
(/.f64 (sinh.f64 x) (cosh.f64 x))
(tanh.f64 x)
(sinh.f64 x)
x
(cosh.f64 x)

localize127.0ms (1.5%)

Memory
14.1MiB live, 155.8MiB allocated
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(cosh.f64 x)
accuracy0.0078125
(sinh.f64 x)
accuracy0.7343832531524757
(/.f64 (sinh.f64 x) (cosh.f64 x))
accuracy0.01171875
(tanh.f64 x)
accuracy0.00390625
(pow.f64 x #s(literal 3 binary64))
accuracy0.01171875
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy1.586464407051171
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
Samples
59.0ms83×2valid
56.0ms165×1valid
1.0ms0valid
Compiler

Compiled 41 to 18 computations (56.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 98.0ms
ival-exp: 36.0ms (36.6% of total)
adjust: 19.0ms (19.3% of total)
ival-pow: 13.0ms (13.2% of total)
ival-add: 10.0ms (10.2% of total)
ival-div: 5.0ms (5.1% of total)
const: 4.0ms (4.1% of total)
ival-sub: 3.0ms (3.1% of total)
ival-cosh: 2.0ms (2% of total)
ival-mult: 2.0ms (2% of total)
ival-tanh: 1.0ms (1% of total)
ival-sinh: 1.0ms (1% of total)
ival-neg: 1.0ms (1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series26.0ms (0.3%)

Memory
-16.1MiB live, 30.0MiB allocated
Counts
7 → 20
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(pow.f64 x #s(literal 3 binary64))
(tanh.f64 x)
(/.f64 (sinh.f64 x) (cosh.f64 x))
(sinh.f64 x)
(cosh.f64 x)
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 3)
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
Calls

3 calls:

TimeVariablePointExpression
18.0ms
x
@-inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (sinh x) (cosh x)) (sinh x) (cosh x))
6.0ms
x
@inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (sinh x) (cosh x)) (sinh x) (cosh x))
2.0ms
x
@0
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (sinh x) (cosh x)) (sinh x) (cosh x))

simplify143.0ms (1.7%)

Memory
-11.8MiB live, 175.7MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083217
1283205
2870205
33586205
08147189
Stop Event
iter limit
node limit
Counts
20 → 19
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 3)
(* x (+ 1 (* 1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* x (+ 1 (* 1/6 (pow x 2))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(* x (+ 1 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/5040 (pow x 2))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (/ 1 (exp x))) (+ (exp x) (/ 1 (exp x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* 1/2 (- (exp x) (/ 1 (exp x))))
(*.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) #s(literal 1/2 binary64))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(fma.f64 #s(literal 1/2 binary64) (exp.f64 x) (/.f64 #s(literal 1/2 binary64) (exp.f64 x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))

rewrite188.0ms (2.2%)

Memory
52.2MiB live, 223.0MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
02326
19426
268626
0853426
Stop Event
iter limit
node limit
iter limit
Counts
7 → 398
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(pow.f64 x #s(literal 3 binary64))
(tanh.f64 x)
(/.f64 (sinh.f64 x) (cosh.f64 x))
(sinh.f64 x)
(cosh.f64 x)
Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))) (*.f64 (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)))) (+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))) (-.f64 (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64))))))))
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(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))
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(sinh.f64 x)
(neg.f64 (sinh.f64 (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64))) #s(literal 2 binary64))))
(-.f64 (/.f64 (-.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 (neg.f64 x)) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (cosh.f64 x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)))) #s(literal 2 binary64)))
(-.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))) (/.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))))
(+.f64 (/.f64 (-.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (-.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)))
(+.f64 (/.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) (sinh.f64 x))
(*.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) (cosh.f64 x))
(*.f64 #s(literal 2 binary64) (/.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (*.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))) (sinh.f64 (neg.f64 x)))
(/.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)) (-.f64 (*.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))) (*.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64))))))
(/.f64 (fma.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (exp.f64 x))) #s(literal 4 binary64))
(/.f64 (fma.f64 (exp.f64 x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (exp.f64 (neg.f64 x)))) #s(literal 4 binary64))
(/.f64 (*.f64 (cosh.f64 x) (sinh.f64 x)) (sinh.f64 x))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) (neg.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(neg.f64 (neg.f64 (cosh.f64 x)))
(cosh.f64 (neg.f64 x))
(cosh.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (-.f64 (sinh.f64 x) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64))))
(+.f64 (/.f64 (+.f64 (exp.f64 (neg.f64 x)) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 2 binary64)) (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))) (/.f64 (neg.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 x)) #s(literal 2 binary64))))
(+.f64 (/.f64 (+.f64 (exp.f64 x) (cosh.f64 x)) #s(literal 2 binary64)) (/.f64 (sinh.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 (neg.f64 x)) (exp.f64 x)) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (+.f64 (sinh.f64 x) (exp.f64 (neg.f64 x))) #s(literal 2 binary64)))
(+.f64 (/.f64 (cosh.f64 x) #s(literal 2 binary64)) (/.f64 (cosh.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)) (/.f64 (exp.f64 x) #s(literal 2 binary64)))
(+.f64 (/.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (exp.f64 (neg.f64 x)) #s(literal 2 binary64)))

eval32.0ms (0.4%)

Memory
2.5MiB live, 48.6MiB allocated
Compiler

Compiled 8 097 to 952 computations (88.2% saved)

prune38.0ms (0.4%)

Memory
-39.6MiB live, 22.0MiB allocated
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2771278
Fresh000
Picked123
Done000
Total2783281
Accuracy
100.0%
Counts
281 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.8%
(/.f64 (sinh.f64 x) (cosh.f64 x))
100.0%
(tanh.f64 x)
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
Compiler

Compiled 29 to 18 computations (37.9% saved)

simplify92.0ms (1.1%)

Memory
2.8MiB live, 95.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 x #s(literal -1/3 binary64))
cost-diff0
(*.f64 x x)
cost-diff0
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
cost-diff2
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
01638
13938
212236
344136
4200032
0921630
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
(*.f64 x x)
x
(*.f64 x #s(literal -1/3 binary64))
#s(literal -1/3 binary64)
Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(*.f64 x x)
x
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)

localize102.0ms (1.2%)

Memory
26.1MiB live, 120.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 x x)
accuracy0.00390625
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
accuracy0.37890625
(*.f64 x #s(literal -1/3 binary64))
accuracy1.586464407051171
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
Samples
52.0ms83×2valid
40.0ms165×1valid
1.0ms0valid
Compiler

Compiled 32 to 14 computations (56.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 79.0ms
ival-exp: 34.0ms (43.3% of total)
adjust: 23.0ms (29.3% of total)
ival-div: 5.0ms (6.4% of total)
ival-mult: 5.0ms (6.4% of total)
ival-add: 4.0ms (5.1% of total)
const: 4.0ms (5.1% of total)
ival-sub: 3.0ms (3.8% of total)
ival-neg: 1.0ms (1.3% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series3.0ms (0%)

Memory
5.5MiB live, 5.5MiB allocated
Counts
4 → 11
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 2)
(* -1/3 x)
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3))
1.0ms
x
@-inf
((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3))
1.0ms
x
@0
((+ (* (* x x) (* x -1/3)) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3))

simplify110.0ms (1.3%)

Memory
-4.9MiB live, 125.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045106
1128100
2322100
31206100
43783100
0811196
Stop Event
iter limit
node limit
Counts
11 → 10
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(pow x 2)
(* -1/3 x)
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64))) x)
(pow x 2)
(*.f64 x x)
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite670.0ms (7.8%)

Memory
-179.5MiB live, 147.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01236
01625
17523
261223
0845921
Stop Event
iter limit
node limit
iter limit
Counts
4 → 83
Calls
Call 1
Inputs
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
Outputs
(*.f64 (/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (pow.f64 (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) #s(literal 2 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64)))))))
(*.f64 (/.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64) (pow.f64 (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) (*.f64 (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (-.f64 (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))))
(*.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
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(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/3 binary64)) x)
(fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) x x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 (neg.f64 x) (*.f64 (*.f64 #s(literal 1/3 binary64) x) x) x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) (*.f64 x x) x)
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (*.f64 x x) (*.f64 #s(literal -1/3 binary64) x) x)
(fma.f64 x (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)))
(-.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))) (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 x x (-.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 x x (-.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(+.f64 (/.f64 (*.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (+.f64 x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))))
(+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)
(+.f64 x (*.f64 (neg.f64 (*.f64 #s(literal 1/3 binary64) x)) (*.f64 x x)))
(+.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 #s(literal -1/3 binary64) x)
(*.f64 x #s(literal -1/3 binary64))

eval12.0ms (0.1%)

Memory
-24.8MiB live, 20.8MiB allocated
Compiler

Compiled 3 670 to 374 computations (89.8% saved)

prune4.0ms (0%)

Memory
11.4MiB live, 11.4MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New91192
Fresh000
Picked011
Done022
Total91495
Accuracy
100.0%
Counts
95 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.8%
(/.f64 (sinh.f64 x) (cosh.f64 x))
100.0%
(tanh.f64 x)
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
Compiler

Compiled 51 to 31 computations (39.2% saved)

simplify160.0ms (1.9%)

Memory
21.7MiB live, 126.1MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal -1/3 binary64) x)
cost-diff0
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
cost-diff0
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
cost-diff2
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01342
01742
13742
29642
334940
4190636
0896034
Stop Event
iter limit
node limit
iter limit
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
x
#s(literal 1 binary64)
Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
#s(literal -1/3 binary64)
x
#s(literal 1 binary64)

localize160.0ms (1.9%)

Memory
-37.7MiB live, 158.9MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
accuracy0.015625
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
accuracy0.37890625
(*.f64 #s(literal -1/3 binary64) x)
accuracy1.586464407051171
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
Samples
92.0ms83×2valid
54.0ms165×1valid
1.0ms0valid
Compiler

Compiled 37 to 15 computations (59.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 135.0ms
ival-exp: 56.0ms (41.4% of total)
ival-add: 35.0ms (25.9% of total)
ival-mult: 18.0ms (13.3% of total)
adjust: 14.0ms (10.4% of total)
ival-div: 4.0ms (3% of total)
const: 4.0ms (3% of total)
ival-sub: 3.0ms (2.2% of total)
ival-neg: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory
8.1MiB live, 8.1MiB allocated
Counts
4 → 14
Calls
Call 1
Inputs
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* -1/3 x)
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x))
1.0ms
x
@inf
((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x))
1.0ms
x
@0
((* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x))

simplify139.0ms (1.6%)

Memory
2.4MiB live, 143.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046127
1130121
2324121
31203121
43795121
08028116
Stop Event
iter limit
node limit
Counts
14 → 13
Calls
Call 1
Inputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
1
(+ 1 (* -1/3 (pow x 2)))
(* -1/3 x)
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
Outputs
x
(* x (+ 1 (* -1/3 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -17/315 binary64) (-.f64 (*.f64 #s(literal 2/15 binary64) (*.f64 x x)) #s(literal 1/3 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/3 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* -1/3 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))
(* -1/3 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64)) x) x)
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)))

rewrite210.0ms (2.4%)

Memory
19.6MiB live, 213.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01339
01728
17428
256626
3780726
0808824
Stop Event
iter limit
node limit
iter limit
Counts
4 → 106
Calls
Call 1
Inputs
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) x)
Outputs
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (-.f64 (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x) (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64))) (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) x) (-.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64))))
(*.f64 (/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64))) (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (/.f64 x (-.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (/.f64 x (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(*.f64 (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64))) x) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))
(/.f64 (*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64))) x) (neg.f64 (-.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) x) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)))) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))
(/.f64 (*.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)))) (neg.f64 (-.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))))
(/.f64 (*.f64 x (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))) (*.f64 x x)) (-.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x))
(/.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))
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(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64))) (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) #s(literal -1 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (-.f64 (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64))) (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 4 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (*.f64 #s(literal -1/3 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1/3 binary64) x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 3/2 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal -1/3 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/27 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 #s(literal -1/27 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (/.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(fma.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (*.f64 #s(literal 1/3 binary64) x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))
(fma.f64 (*.f64 x #s(literal -1/3 binary64)) x #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/3 binary64) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64)) (-.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))) (pow.f64 (-.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(+.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))))
(+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/9 binary64) (fma.f64 (*.f64 #s(literal 1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 (*.f64 x #s(literal -1/3 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (*.f64 #s(literal 1/3 binary64) x)) x))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x #s(literal -1/3 binary64)) x))
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/3 binary64)))
(*.f64 (*.f64 x #s(literal -1/3 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal -1/3 binary64))
(*.f64 #s(literal -1/3 binary64) x)

eval27.0ms (0.3%)

Memory
-11.8MiB live, 34.5MiB allocated
Compiler

Compiled 4 436 to 498 computations (88.8% saved)

prune4.0ms (0%)

Memory
10.6MiB live, 10.6MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1171118
Fresh000
Picked011
Done033
Total1175122
Accuracy
100.0%
Counts
122 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.8%
(/.f64 (sinh.f64 x) (cosh.f64 x))
100.0%
(tanh.f64 x)
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
97.5%
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
Compiler

Compiled 185 to 86 computations (53.5% saved)

regimes4.0ms (0.1%)

Memory
8.9MiB live, 8.9MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(/.f64 (sinh.f64 x) (cosh.f64 x))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Outputs
(tanh.f64 x)
Calls

2 calls:

2.0ms
x
2.0ms
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Results
AccuracySegmentsBranch
100.0%1(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
100.0%1x
Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes26.0ms (0.3%)

Memory
-39.0MiB live, 6.2MiB allocated
Accuracy

Total -0.1b remaining (-7.5%)

Threshold costs -0.1b (-7.5%)

Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x))
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x))
Outputs
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
Calls

2 calls:

24.0ms
x
1.0ms
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Results
AccuracySegmentsBranch
97.5%1(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
97.5%1x
Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify40.0ms (0.5%)

Memory
11.5MiB live, 55.5MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01627
13527
28527
331827
4175523
Stop Event
node limit
Calls
Call 1
Inputs
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
Outputs
(tanh.f64 x)
#s(approx (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))

derivations652.0ms (7.6%)

Memory
-1.8MiB live, 436.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
02326
19426
268626
0853426
01236
01625
17523
261223
0845921
079210
1292210
2958200
33882200
08155179
046127
1130121
2324121
31203121
43795121
08028116
0727
01312
15012
239512
3619612
0920112
Stop Event
fuel
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
Compiler

Compiled 27 to 17 computations (37% saved)

preprocess18.0ms (0.2%)

Memory
27.4MiB live, 27.4MiB allocated
Remove

(negabs x)

Compiler

Compiled 84 to 52 computations (38.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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