Hyperbolic tangent

Time bar (total: 8.7s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
0.4MiB live, 0.4MiB 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)

sample4.8s (55.6%)

Memory
-151.7MiB live, 3 987.2MiB allocated
Samples
1.4s4 741×1valid
1.4s2 954×2valid
1.3s7 898×0exit
40.0ms561×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.0s
ival-exp: 1.8s (59.2% of total)
ival-add: 322.0ms (10.9% of total)
ival-div: 281.0ms (9.5% of total)
adjust: 227.0ms (7.7% of total)
ival-sub: 221.0ms (7.5% of total)
ival-neg: 138.0ms (4.7% of total)
ival-true: 13.0ms (0.4% of total)
ival-assert: 7.0ms (0.2% of total)
Bogosity

explain293.0ms (3.4%)

Memory
23.8MiB live, 384.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2500-0-(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
50-0-(/.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)))cancellation2500
/.f64(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))o/o50
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))overflow5
(exp.f64 (neg.f64 x))overflow5
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))overflow5
(exp.f64 (neg.f64 x))overflow5
Confusion
Predicted +Predicted -
+2550
-01
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+25500
-001
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
01
1255
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
112.0ms172×2valid
98.0ms314×1valid
2.0ms26×0valid
Compiler

Compiled 116 to 32 computations (72.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 150.0ms
ival-exp: 108.0ms (71.8% of total)
ival-add: 12.0ms (8% of total)
adjust: 11.0ms (7.3% of total)
ival-sub: 9.0ms (6% of total)
ival-div: 7.0ms (4.7% of total)
ival-neg: 3.0ms (2% of total)
ival-true: 1.0ms (0.7% of total)
ival-assert: 0.0ms (0% of total)

preprocess88.0ms (1%)

Memory
-3.9MiB live, 69.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0927
13227
28026
320126
447326
5113926
6155526
7159326
8161226
9163126
10166526
11167926
0713
01313
12513
24213
36713
412213
527713
646713
771213
895613
9112313
10125113
11129813
0129813
Stop Event
iter limit
saturated
iter limit
saturated
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 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.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
7.7%
(/.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)

simplify37.0ms (0.4%)

Memory
-4.5MiB live, 32.8MiB allocated
Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0733
01333
12533
24233
36733
412233
527733
646733
771233
895633
9112333
10125133
11129833
0129833
Stop Event
iter limit
saturated
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 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 (neg.f64 x)) (exp.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)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

localize99.0ms (1.1%)

Memory
-16.2MiB live, 136.1MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(exp.f64 x)
accuracy0.00390625
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy1.218763755254126
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
accuracy57.8174168275959
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Samples
59.0ms86×2valid
30.0ms157×1valid
1.0ms13×0valid
Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 78.0ms
ival-exp: 51.0ms (65.2% of total)
adjust: 12.0ms (15.3% of total)
ival-div: 9.0ms (11.5% of total)
ival-add: 3.0ms (3.8% 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)

series5.0ms (0.1%)

Memory
-27.4MiB live, 11.9MiB allocated
Counts
5 → 28
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)
(exp.f64 (neg.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.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))))
(* 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))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
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)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg x))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(- (exp x) (exp (* -1 x)))
(exp (* -1 x))
(+ (exp x) (exp (* -1 x)))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (+ (exp x) (exp (neg x))))
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) (exp (neg 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) (exp (neg x))))

simplify197.0ms (2.3%)

Memory
18.0MiB live, 175.1MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
090242
1259241
2604231
31672231
42637231
54162231
64866231
76482231
08180203
Stop Event
iter limit
node limit
Counts
28 → 27
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))))
(* 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))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
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)))))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg x))
(+ (exp x) (exp (neg x)))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(- (exp x) (exp (* -1 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)) (fma.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 (fma.f64 #s(literal -17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/3 (pow x 2))))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #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)
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 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))
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(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))
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 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/360 binary64) (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/12 binary64) x) x #s(literal 2 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)))
(- (exp x) (exp (neg x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp x)
(exp.f64 x)
(exp (neg x))
(exp.f64 (neg.f64 x))
(+ (exp x) (exp (neg 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)))
(- (exp x) (exp (* -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(+ (exp x) (exp (* -1 x)))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))

rewrite169.0ms (1.9%)

Memory
23.9MiB live, 181.6MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0730
01315
15515
242415
3712015
0810215
Stop Event
iter limit
node limit
iter limit
Counts
5 → 644
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)
(exp.f64 (neg.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
Outputs
(tanh.f64 x)
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (tanh.f64 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)))) (-.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (tanh.f64 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 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))) (pow.f64 (exp.f64 x) #s(literal 4 binary64))))
(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (*.f64 (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (sinh.f64 x))) (sinh.f64 x))
(*.f64 (/.f64 (*.f64 (sinh.f64 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 (sinh.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 x)) (*.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 1/2 binary64) (cosh.f64 x)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.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 #s(literal 1/2 binary64) (cosh.f64 x)) #s(literal 2 binary64)) (sinh.f64 x))
(*.f64 (pow.f64 (pow.f64 (tanh.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (tanh.f64 x) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (neg.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(*.f64 (/.f64 (*.f64 #s(literal -2 binary64) (sinh.f64 x)) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(*.f64 (/.f64 (*.f64 (sinh.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (pow.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (*.f64 (cosh.f64 x) #s(literal 2 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 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x)))) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.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)) (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))))
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 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 (cosh.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))))
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(fma.f64 (/.f64 (exp.f64 x) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (/.f64 (exp.f64 x) (pow.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (/.f64 (exp.f64 x) (sinh.f64 x)) (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 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)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) #s(literal 1 binary64)))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(fma.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64))))
(fma.f64 (/.f64 (exp.f64 x) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x)))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (*.f64 (exp.f64 x) #s(literal 1/2 binary64)) (/.f64 (exp.f64 x) (sinh.f64 x)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x))) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)) (neg.f64 (neg.f64 (exp.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)) (exp.f64 x))
(fma.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)) (neg.f64 (neg.f64 (exp.f64 x))))
(fma.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)) (exp.f64 x))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (exp.f64 (neg.f64 x)))
(fma.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(fma.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64) (exp.f64 x))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (*.f64 (sinh.f64 x) #s(literal 2 binary64))) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(-.f64 (/.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) #s(literal 1 binary64)) (/.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal -2 binary64) (sinh.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal -2 binary64) (sinh.f64 x))))
(-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) (cosh.f64 x)))
(-.f64 (exp.f64 x) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(+.f64 (-.f64 (exp.f64 x) #s(literal 0 binary64)) (exp.f64 (neg.f64 x)))
(+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x))) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(+.f64 (*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(+.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))) (*.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x))))))
(+.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (*.f64 #s(literal 2 binary64) (cosh.f64 (*.f64 #s(literal 2 binary64) x)))) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 2 binary64) x))) (*.f64 #s(literal 2 binary64) (sinh.f64 (*.f64 #s(literal 3 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) #s(literal -1 binary64))))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) (exp.f64 (neg.f64 x)))
(+.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)))))
(+.f64 (exp.f64 (neg.f64 x)) (neg.f64 (neg.f64 (exp.f64 x))))
(+.f64 (exp.f64 (neg.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

eval106.0ms (1.2%)

Memory
-4.4MiB live, 148.0MiB allocated
Compiler

Compiled 16 689 to 1 766 computations (89.4% saved)

prune14.0ms (0.2%)

Memory
-23.7MiB live, 29.5MiB allocated
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New6933696
Fresh000
Picked101
Done000
Total6943697
Accuracy
100.0%
Counts
697 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
100.0%
(tanh.f64 x)
97.8%
#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 33 to 23 computations (30.3% saved)

simplify114.0ms (1.3%)

Memory
17.1MiB live, 127.9MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff0
(exp.f64 (neg.f64 x))
cost-diff0
(exp.f64 x)
cost-diff0
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
cost-diff14144
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
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
02167
03447
16947
213147
324747
457047
5175747
6400847
7657847
0837147
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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(cosh.f64 x)
#s(literal 2 binary64)
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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(tanh.f64 x)
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (cosh.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (cosh.f64 x))
(cosh.f64 x)
#s(literal 2 binary64)

localize135.0ms (1.5%)

Memory
-10.2MiB live, 148.1MiB allocated
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(exp.f64 x)
accuracy0.00390625
(cosh.f64 x)
accuracy1.218763755254126
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
accuracy57.8174168275959
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
accuracy0.0078125
(tanh.f64 x)
accuracy0.0
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
accuracy0.0
(pow.f64 x #s(literal 3 binary64))
accuracy1.4172957828230301
#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
58.0ms157×1valid
49.0ms86×2valid
2.0ms13×0valid
Compiler

Compiled 130 to 40 computations (69.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 91.0ms
ival-exp: 39.0ms (42.9% of total)
ival-sub: 15.0ms (16.5% of total)
adjust: 11.0ms (12.1% of total)
ival-div: 7.0ms (7.7% of total)
const: 4.0ms (4.4% of total)
ival-add: 4.0ms (4.4% of total)
ival-pow: 3.0ms (3.3% of total)
ival-mult: 3.0ms (3.3% of total)
ival-cosh: 2.0ms (2.2% of total)
ival-tanh: 1.0ms (1.1% of total)
ival-neg: 1.0ms (1.1% 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
17.8MiB live, 17.8MiB allocated
Counts
9 → 33
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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
(exp.f64 (neg.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)
(* 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))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 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))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (/ 1 (exp x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg 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)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (/ 1 (exp x))))
(- (exp x) (exp (* -1 x)))
(exp (* -1 x))
Calls

3 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (cosh x))
3.0ms
x
@inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (pow x 3) -1/3) x) (pow x 3) (tanh x) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg 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) (/ (- (exp x) (exp (neg x))) (* (cosh x) 2)) (- (exp x) (exp (neg x))) (exp x) (exp (neg x)) (cosh x))

simplify137.0ms (1.6%)

Memory
-18.2MiB live, 134.0MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107304
1301293
2710293
31915293
43546293
56203293
08109263
Stop Event
iter limit
node limit
Counts
33 → 32
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)
(* 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))))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 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))))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (/ 1 (exp x))))
(- (exp x) (exp (neg x)))
(exp x)
(exp (neg 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)))))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (/ 1 (exp x))))
(- (exp x) (exp (* -1 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)) (fma.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 (fma.f64 #s(literal -17/315 binary64) (*.f64 x x) #s(literal 2/15 binary64)) (*.f64 x x) #s(literal -1/3 binary64)) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/3 (pow x 2))))
(*.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #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)
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))
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(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))
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) 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))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(/ (- (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)))
(/ (- (exp x) (exp (neg 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)))
(- (exp x) (exp (neg x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp x)
(exp.f64 x)
(exp (neg x))
(exp.f64 (neg.f64 x))
(* 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)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(/ (- (exp x) (exp (* -1 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)))
(- (exp x) (exp (* -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp (* -1 x))
(exp.f64 (neg.f64 x))

rewrite253.0ms (2.9%)

Memory
9.5MiB live, 265.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02155
03433
111933
271733
0866433
Stop Event
iter limit
node limit
iter limit
Counts
9 → 1 078
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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(exp.f64 x)
(exp.f64 (neg.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 (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)) (neg.f64 (pow.f64 x #s(literal 3 binary64))))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))))
(*.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 -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))) (-.f64 (*.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 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (*.f64 (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (fma.f64 x x (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 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 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
(*.f64 (fma.f64 x x (*.f64 #s(literal -1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))
(*.f64 (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)))
(*.f64 (pow.f64 (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))))) #s(literal -1 binary64)) (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (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 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64)))
(*.f64 (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 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (pow.f64 (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))))) #s(literal -1 binary64))))
(*.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal 1/3 binary64) (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (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))))) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x) (*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)) #s(literal -1 binary64))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) #s(literal -1 binary64))) (+.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 2 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (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))))) #s(literal -1 binary64))) (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (neg.f64 (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/19683 binary64) (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (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))))) #s(literal -1 binary64))) (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -1/27 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64))))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 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 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))) (*.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))) (+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (fma.f64 (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 #s(literal -1/9 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (-.f64 x (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/27 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (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 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))) (*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (*.f64 x x))) (*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))))
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 x x))))
(/.f64 (fma.f64 x x (*.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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(fma.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)) (exp.f64 x))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(fma.f64 (exp.f64 x) (*.f64 (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)) (exp.f64 x)) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(-.f64 (+.f64 (exp.f64 x) #s(literal 0 binary64)) (exp.f64 (neg.f64 x)))
(-.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)) (exp.f64 x))
(+.f64 (*.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))))) (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))))))
(+.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))))) (*.f64 (expm1.f64 (*.f64 #s(literal -2 binary64) x)) (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))))))
(+.f64 (*.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(+.f64 (*.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) (*.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))))
(+.f64 (*.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))
(+.f64 (neg.f64 (neg.f64 (exp.f64 x))) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(+.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x))) (neg.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))) (neg.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) (exp.f64 x))
(+.f64 (exp.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(/.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 x #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 x #s(literal 2 binary64))))
(*.f64 (pow.f64 (exp.f64 x) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 x) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 x)))
(*.f64 (exp.f64 (neg.f64 x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) x)
(pow.f64 (exp.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (exp.f64 x)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) x))
(exp.f64 (neg.f64 x))
(*.f64 (/.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)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))))
(*.f64 (/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64)))) (*.f64 (fma.f64 (*.f64 (exp.f64 x) #s(literal 2 binary64)) (cosh.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (cosh.f64 x)))
(*.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (sinh.f64 x))))
(*.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sinh.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))))
(*.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (cosh.f64 x))
(*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (cosh.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 2 binary64) (*.f64 (cosh.f64 x) #s(literal 1/2 binary64)))
(*.f64 (cosh.f64 x) #s(literal 1 binary64))
(*.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (cosh.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (*.f64 (*.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (sinh.f64 x))
(/.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (*.f64 (neg.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) (sinh.f64 x)))
(/.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))
(/.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))
(/.f64 (*.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) #s(literal 1/2 binary64)) (*.f64 (sinh.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) #s(literal 4 binary64))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 4 binary64))) (*.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x)) (fma.f64 (exp.f64 x) (exp.f64 x) (pow.f64 (exp.f64 x) #s(literal -2 binary64)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 6 binary64))) (*.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x)) (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 6 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) (-.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (pow.f64 (exp.f64 x) #s(literal -3 binary64)))))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/2 binary64) (cosh.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 9 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal 9 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) (+.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (expm1.f64 (*.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 3 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (*.f64 #s(literal -2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) 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 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (*.f64 #s(literal -2 binary64) (*.f64 (sinh.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (*.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x))))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))) (neg.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x))))
(/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) (sinh.f64 x))))
(/.f64 (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x)) (*.f64 #s(literal 4 binary64) (sinh.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (cosh.f64 x) #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal -2 binary64) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (*.f64 #s(literal -2 binary64) (cosh.f64 x)) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4 binary64) (sinh.f64 x)) (*.f64 (*.f64 #s(literal 4 binary64) (cosh.f64 x)) (sinh.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (expm1.f64 (*.f64 #s(literal -2 binary64) x)))) (+.f64 (pow.f64 (exp.f64 x) #s(literal -3 binary64)) (pow.f64 (exp.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (cosh.f64 x) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 2 binary64) (cosh.f64 x)) #s(literal 2 binary64))
(neg.f64 (neg.f64 (cosh.f64 x)))
(cosh.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (sinh.f64 x))) (/.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (*.f64 #s(literal 4 binary64) (sinh.f64 x))))
(-.f64 (/.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) #s(literal 2 binary64)) (/.f64 (*.f64 (pow.f64 (exp.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal 1/2 binary64) (sinh.f64 x))) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (cosh.f64 x)))

eval117.0ms (1.3%)

Memory
-15.1MiB live, 177.3MiB allocated
Compiler

Compiled 18 405 to 1 953 computations (89.4% saved)

prune11.0ms (0.1%)

Memory
34.6MiB live, 34.6MiB allocated
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New7142716
Fresh000
Picked123
Done000
Total7154719
Accuracy
100.0%
Counts
719 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
100.0%
(tanh.f64 x)
97.8%
#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))
97.8%
#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 57 to 36 computations (36.8% saved)

simplify169.0ms (1.9%)

Memory
-24.1MiB live, 168.2MiB allocated
Algorithm
egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
cost-diff-5824
(fma.f64 (*.f64 x x) (*.f64 x #s(literal -1/3 binary64)) x)
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-diff-5824
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) x)
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))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01780
02580
14980
27776
310476
418676
535276
657976
788076
8130976
9240276
10482776
11630776
0806272
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)
#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)))) (*.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)
#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)

localize145.0ms (1.7%)

Memory
15.0MiB live, 179.5MiB allocated
Localize:

Found 8 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))
accuracy1.4172957828230301
#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))
accuracy0.00390625
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
accuracy0.0078125
(*.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)
accuracy1.4172957828230301
#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
79.0ms157×1valid
52.0ms86×2valid
2.0ms13×0valid
Compiler

Compiled 147 to 36 computations (75.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 117.0ms
adjust: 51.0ms (43.7% of total)
ival-exp: 37.0ms (31.7% of total)
ival-mult: 9.0ms (7.7% of total)
ival-add: 5.0ms (4.3% of total)
ival-neg: 5.0ms (4.3% of total)
ival-div: 4.0ms (3.4% of total)
const: 4.0ms (3.4% of total)
ival-sub: 3.0ms (2.6% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
10.4MiB live, 10.4MiB allocated
Counts
8 → 15
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))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) 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))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(fma.f64 (*.f64 x x) (*.f64 x #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)
(pow x 2)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
Calls

3 calls:

TimeVariablePointExpression
2.0ms
x
@inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x))
2.0ms
x
@-inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x))
1.0ms
x
@0
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (+ (* (* -1/3 x) x) 1) (* -1/3 x) (* (+ (* (* -1/3 x) x) 1) x) (/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* x x) (* x -1/3) (+ (* (* x x) (* x -1/3)) x))

simplify135.0ms (1.5%)

Memory
-36.4MiB live, 86.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046121
1117111
2264111
3777111
42601111
55872111
08159101
Stop Event
iter limit
node limit
Counts
15 → 14
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)
(pow x 2)
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(/ (- (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)) (fma.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 (fma.f64 #s(literal -17/315 binary64) (*.f64 x x) #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 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(pow x 2)
(*.f64 x 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)))
(* -1/3 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(* -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))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) 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)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)

rewrite165.0ms (1.9%)

Memory
28.3MiB live, 187.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01775
02553
110353
274649
0858845
Stop Event
iter limit
node limit
iter limit
Counts
8 → 231
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))
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))
(*.f64 #s(literal -1/3 binary64) 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))
(*.f64 x x)
(*.f64 x #s(literal -1/3 binary64))
(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)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64))))
(*.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))))
(*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.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 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))) (*.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (fma.f64 (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) #s(literal 4 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x)))))
(/.f64 (*.f64 (fma.f64 #s(literal -1/19683 binary64) (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 #s(literal 1/729 binary64) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x)))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64))) (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)) #s(literal 1 binary64))) (*.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 #s(literal 1/3 binary64) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x)))))
(/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64)))))
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(/.f64 (*.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 3 binary64)) #s(literal -1/19683 binary64) (pow.f64 x #s(literal 9 binary64))) #s(literal 1 binary64)) (*.f64 (fma.f64 (pow.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 3 binary64)) #s(literal 1/729 binary64) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (*.f64 x x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(/.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 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(/.f64 (*.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
(/.f64 (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))))
(/.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x))) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (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 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (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) (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (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 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) (*.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))) (*.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal -1 binary64)) (*.f64 x (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal -1/3 binary64) x) x))) (*.f64 x (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/27 binary64) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64))) (-.f64 (*.f64 x x) (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (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)))) (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) x #s(literal 1 binary64))))
(neg.f64 (/.f64 (neg.f64 (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) (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64))))))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 (neg.f64 x) x)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal -1/27 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/3 binary64)))))))
(fma.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(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 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) x x)
(fma.f64 (*.f64 #s(literal -1/3 binary64) x) (*.f64 x x) x)
(fma.f64 (*.f64 x x) (*.f64 #s(literal -1/3 binary64) x) x)
(fma.f64 #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(fma.f64 #s(literal -1/3 binary64) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 x (*.f64 (*.f64 #s(literal -1/3 binary64) x) x) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))) (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))))
(+.f64 (/.f64 (*.f64 #s(literal 1/9 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x))) (neg.f64 (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) (neg.f64 x)))))
(+.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)) x)
(+.f64 x (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64)))

eval19.0ms (0.2%)

Memory
9.0MiB live, 46.2MiB allocated
Compiler

Compiled 5 199 to 605 computations (88.4% saved)

prune8.0ms (0.1%)

Memory
-36.3MiB live, 10.3MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1541155
Fresh000
Picked112
Done022
Total1554159
Accuracy
100.0%
Counts
159 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
100.0%
(tanh.f64 x)
97.8%
#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))
97.8%
#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 60 to 40 computations (33.3% saved)

simplify157.0ms (1.8%)

Memory
34.3MiB live, 191.4MiB allocated
Algorithm
egg-herbie
Localize:

Found 3 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01547
01647
13447
25047
37547
413047
528747
650947
776947
8105647
9155847
10310247
11473047
12651747
0810244
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 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x))
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
#s(literal 1 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))
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x

localize171.0ms (2%)

Memory
-9.1MiB live, 105.2MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0078125
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
accuracy1.4172957828230301
#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))
accuracy1.541064333005853
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
Samples
97.0ms157×1valid
63.0ms86×2valid
1.0ms13×0valid
Compiler

Compiled 80 to 31 computations (61.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 150.0ms
ival-sub: 65.0ms (43.3% of total)
ival-exp: 60.0ms (40% of total)
adjust: 8.0ms (5.3% of total)
ival-mult: 5.0ms (3.3% of total)
ival-div: 4.0ms (2.7% of total)
const: 4.0ms (2.7% of total)
ival-add: 4.0ms (2.7% 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)

series2.0ms (0%)

Memory
2.7MiB live, 2.7MiB allocated
Counts
3 → 13
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))
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 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))))
1
(+ 1 (* -1/3 (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))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ (- (exp x) (exp (* -1 x))) (+ (exp x) (exp (* -1 x))))
(* -1 (* (pow x 3) (- 1/3 (/ 1 (pow x 2)))))
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1))
1.0ms
x
@inf
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1))
0.0ms
x
@0
((/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x)))) (* (+ (* (* -1/3 x) x) 1) x) (+ (* (* -1/3 x) x) 1))

simplify178.0ms (2%)

Memory
-12.8MiB live, 80.4MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045115
1115105
2266105
3791105
42535105
55798105
0809795
Stop Event
iter limit
node limit
Counts
13 → 12
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)))
(/ (- (exp x) (exp (neg x))) (+ (exp x) (exp (neg x))))
(* -1/3 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/3))
(* -1/3 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(/ (- (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)) (fma.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 (fma.f64 #s(literal -17/315 binary64) (*.f64 x x) #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))
(/ (- (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))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)
(* -1/3 (pow x 2))
(*.f64 (*.f64 x x) #s(literal -1/3 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/3))
(fma.f64 (*.f64 x x) #s(literal -1/3 binary64) #s(literal 1 binary64))
(/ (- (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)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/3 binary64) x)

rewrite126.0ms (1.4%)

Memory
14.2MiB live, 86.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01545
01634
17634
256734
0848631
Stop Event
iter limit
node limit
iter limit
Counts
3 → 4
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))
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))
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))
(*.f64 #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)) x)
(*.f64 x #s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64)))
#s(approx (+ (* (* -1/3 x) x) 1) #s(literal 1 binary64))

eval2.0ms (0%)

Memory
1.9MiB live, 1.9MiB allocated
Compiler

Compiled 320 to 54 computations (83.1% saved)

prune3.0ms (0%)

Memory
5.8MiB live, 5.8MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New12012
Fresh000
Picked011
Done033
Total12416
Accuracy
100.0%
Counts
16 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
7.7%
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
100.0%
(tanh.f64 x)
97.8%
#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))
97.8%
#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 175 to 80 computations (54.3% saved)

regimes31.0ms (0.4%)

Memory
-44.4MiB live, 4.5MiB 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 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (*.f64 (cosh.f64 x) #s(literal 2 binary64)))
(/.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:

3.0ms
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%1x
100.0%1(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 14 to 8 computations (42.9% saved)

regimes3.0ms (0%)

Memory
3.5MiB live, 3.5MiB allocated
Accuracy

Total -0.1b remaining (-9.5%)

Threshold costs -0.1b (-9.5%)

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:

2.0ms
x
1.0ms
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Results
AccuracySegmentsBranch
97.8%1x
97.8%1(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify89.0ms (1%)

Memory
21.7MiB live, 57.6MiB allocated
Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01627
13327
24927
37727
415327
540027
6123727
7287027
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))

soundness655.0ms (7.5%)

Memory
-20.4MiB live, 377.1MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02155
03433
111933
271733
0866433
090242
1259241
2604231
31672231
42637231
54162231
64866231
76482231
08180203
0730
01315
15515
242415
3712015
0810215
046121
1117111
2264111
3777111
42601111
55872111
08159101
Stop Event
done
iter limit
node limit
iter limit
node limit
iter limit
iter limit
node limit
iter limit
node limit
iter limit
Compiler

Compiled 85 to 52 computations (38.8% saved)

preprocess19.0ms (0.2%)

Memory
31.5MiB live, 31.5MiB 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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