Metrics for Hyperbolic tangent

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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 8 computations (46.7% saved)

sample2.6s (63.8%)

Results

1.3s	4037×	body	1024	valid
517.0ms	7621×	body	256	unsamplable
380.0ms	2016×	body	512	valid
191.0ms	1781×	body	256	valid
144.0ms	422×	body	2048	valid

Bogosity

preprocess142.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1572×	`div-sub`
1010×	`fma-neg`
638×	`cancel-sign-sub-inv`
606×	`sub-neg`
578×	`neg-mul-1`

Problems

249×	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
5×	No Errors
2×	`(/.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)

Iter	Nodes	Cost
0	18	220
1	49	220
2	94	220
3	193	220
4	542	220
5	2338	220
6	6399	220

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.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 x) (exp.f64 (neg.f64 x))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 (-.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))) (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(negabs x)

Compiler

Compiled 49 to 15 computations (69.4% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 28 to 14 computations (50% saved)

localize87.0ms (2.2%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.2%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	10.2%	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 35 to 8 computations (77.1% saved)

series2.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	-inf	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0ms	x	@	0	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	-inf	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite63.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

110×	`associate-r`
108×	`times-frac`
81×	`add-exp-log`
81×	`add-log-exp`
81×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	174	28
2	3418	28

Stop Event

1×

unsound

Counts

2 → 20

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1352×	`unswap-sqr`
1148×	`fma-def`
1084×	`associate-r`
1000×	`fma-neg`
704×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	612
1	104	608
2	235	604
3	630	600
4	1269	600
5	2831	600
6	3991	600
7	6911	600

Stop Event

1×	node limit

Counts

36 → 44

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5

Outputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x)))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
(fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5))))
(+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))))
(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 2 x (fma.f64 1/3 (pow.f64 x 3) (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/3 (pow.f64 x 3) (fma.f64 2 x (*.f64 1/2520 (pow.f64 x 7)))))
(fma.f64 1/3 (pow.f64 x 3) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 1/60 (pow.f64 x 5) (*.f64 2 x))))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
(-.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x)))
(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 2/15)))
(+.f64 x (fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 5) 2/15)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 x))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -17/315 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 2/15))))
(+.f64 x (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 (*.f64 (pow.f64 x 7) -17/315))))
(+.f64 x (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 7) -17/315 (*.f64 (pow.f64 x 3) -1/3))))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 7) -17/315 x)))
(fma.f64 (pow.f64 x 5) 2/15 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 7) -17/315 x)))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.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 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.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 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.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 (.f64 -1 x))) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
-2
-1
0
1/2
1
3/2
2
3
4
5
-2
-1
0
1/2
1
3/2
2
3
4
5

eval12.0ms (0.3%)

Compiler: Compiled 634 to 356 computations (43.8% saved)

prune21.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	7	45

Accuracy

99.3%

Counts

45 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.3%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
▶	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
▶	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.3%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
▶	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
▶	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x

Compiler

Compiled 384 to 292 computations (24% saved)

localize340.0ms (8.4%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	100.0%	(+.f64 (.f64 -17/315 (pow.f64 x 7)) (.f64 2/15 (pow.f64 x 5)))
✓	99.9%	(*.f64 -17/315 (pow.f64 x 7))
✓	99.9%	(*.f64 2/15 (pow.f64 x 5))
✓	99.8%	(*.f64 -1/3 (pow.f64 x 3))
✓	100.0%	(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
✓	100.0%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	99.8%	(*.f64 1/3 (pow.f64 x 3))
✓	100.0%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	100.0%	(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
✓	99.9%	(*.f64 2/15 (pow.f64 x 5))
✓	99.8%	(*.f64 -1/3 (pow.f64 x 3))
✓	100.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
✓	99.8%	(*.f64 (pow.f64 x 3) -1/3)
✓	100.0%	(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
✓	99.9%	(*.f64 1/2520 (pow.f64 x 7))
✓	99.9%	(*.f64 1/60 (pow.f64 x 5))
✓	99.8%	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 317 to 223 computations (29.7% saved)

series15.0ms (0.4%)

Counts

17 → 57

Calls

51 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(*.f64 (pow.f64 x 3) -1/3)
2.0ms	x	@	-inf	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	inf	(*.f64 1/60 (pow.f64 x 5))
1.0ms	x	@	inf	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
1.0ms	x	@	0	(*.f64 1/2520 (pow.f64 x 7))

rewrite48.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

430×	`associate-r`
274×	`prod-diff`
274×	`associate-l`
257×	`log1p-expm1-u`
257×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	272
1	580	272

Stop Event

1×	node limit

Counts

17 → 663

Calls

Call 1

Inputs
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/60 (pow.f64 x 5))
(*.f64 1/2520 (pow.f64 x 7))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (*.f64 2 x)))
(*.f64 (pow.f64 x 3) -1/3)
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(*.f64 1/3 (pow.f64 x 3))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 -17/315 (pow.f64 x 7))
(+.f64 (.f64 -17/315 (pow.f64 x 7)) (.f64 2/15 (pow.f64 x 5)))

Outputs
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14

simplify132.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2516×	`fma-def`
1320×	`associate-r`
880×	`times-frac`
822×	`associate-*l/`
798×	`associate-l`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	84	2260
1	147	2216
2	267	2212
3	595	2208
4	1183	2046
5	2961	2028
6	4687	2028
7	6872	2028

Stop Event

1×	node limit

Counts

720 → 81

Calls

Call 1

Inputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (.f64 1/3 (pow.f64 x 3)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (.f64 1/3 (pow.f64 x 3)))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 -1/3 (pow.f64 x 3))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(*.f64 -1/3 (pow.f64 x 3))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(*.f64 -1/3 (pow.f64 x 3))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 2/15 (pow.f64 x 5))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 1/8 (pow.f64 x 5))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -1/20 (pow.f64 x 7)) (*.f64 1/8 (pow.f64 x 5)))))
(*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x)))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(*.f64 2 x)
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 -17/315 (pow.f64 x 7))
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14

Outputs
(*.f64 2 x)
(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 2 x))
(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))
(*.f64 1/60 (pow.f64 x 5))
(+.f64 (.f64 1/60 (pow.f64 x 5)) (.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/60 (pow.f64 x 5) (*.f64 1/3 (pow.f64 x 3)))
(fma.f64 1/3 (pow.f64 x 3) (*.f64 1/60 (pow.f64 x 5)))
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(*.f64 -1/3 (pow.f64 x 3))
(*.f64 (pow.f64 x 3) -1/3)
(*.f64 2/15 (pow.f64 x 5))
(*.f64 (pow.f64 x 5) 2/15)
(*.f64 2/15 (pow.f64 x 5))
(*.f64 (pow.f64 x 5) 2/15)
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(*.f64 2/15 (pow.f64 x 5))
(*.f64 (pow.f64 x 5) 2/15)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 2/15))
(fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 5) 2/15))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 (pow.f64 x 5) 2/15)
(+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))
(fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 2/15))
(fma.f64 (pow.f64 x 3) -1/3 (*.f64 (pow.f64 x 5) 2/15))
x
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 1/8 (pow.f64 x 5))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (*.f64 (pow.f64 x 5) 1/8)))
(+.f64 x (fma.f64 (pow.f64 x 5) 1/8 (*.f64 (pow.f64 x 3) -1/3)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 1/8 x))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -1/20 (pow.f64 x 7)) (*.f64 1/8 (pow.f64 x 5)))))
(+.f64 x (fma.f64 -1/3 (pow.f64 x 3) (fma.f64 -1/20 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 1/8))))
(+.f64 (fma.f64 (pow.f64 x 3) -1/3 x) (fma.f64 -1/20 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 1/8)))
(fma.f64 -1/20 (pow.f64 x 7) (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 1/8 x)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 1/8 (fma.f64 -1/20 (pow.f64 x 7) x)))
(*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
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(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x)))))
(*.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 (pow.f64 x 3) (/.f64 1/3 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 1/3 (pow.f64 x 3)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 1/3 (/.f64 (pow.f64 x 3) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 (*.f64 2 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (fma.f64 x (.f64 x 1/3) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.f64 2 x)
(*.f64 1/3 (pow.f64 x 3))
(*.f64 1/3 (pow.f64 x 3))
(*.f64 2/15 (pow.f64 x 5))
(*.f64 (pow.f64 x 5) 2/15)
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 (pow.f64 x 7) -17/315)
(*.f64 -17/315 (pow.f64 x 7))
(*.f64 (pow.f64 x 7) -17/315)
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
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-1
-1/2
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-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
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-1
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-4913/31255875
0
1/6350400
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289/99225
1/60
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1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
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-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
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-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
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-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14
-4
-2
-1
-1/2
-1/3
-2/15
-17/315
-1/27
-4913/31255875
0
1/6350400
1/216000
1/3600
1/2520
8/3375
289/99225
1/60
4/225
1/27
1/9
2/15
1/3
1/2
3/4
1
5/4
3/2
7/4
2
5/2
3
7/2
4
5
6
7
8
10
14

eval37.0ms (0.9%)

Compiler: Compiled 2041 to 1167 computations (42.8% saved)

prune25.0ms (0.6%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	1	4	5
Done	0	1	1
Total	121	7	128

Accuracy

99.3%

Counts

128 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	5.3%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	5.3%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x

Compiler

Compiled 200 to 148 computations (26% saved)

localize40.0ms (1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 38 to 19 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	-inf	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Time

Variable

Point

Expression

0.0ms

inf

(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

0.0ms

-inf

(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

0.0ms

(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite24.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

138×	`associate-r`
89×	`log1p-expm1-u`
89×	`expm1-log1p-u`
88×	`add-exp-log`
88×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	197	35
2	3575	35

Stop Event

1×

unsound

Counts

1 → 22

Calls

Call 1

Inputs
(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-50
-5
-4
-2
-1/2
-2/5
-1/5
0
1/500
1/50
1/5
2/5
1/2
3/2
2
4
5
8
20
50
200
2000

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`unswap-sqr`
980×	`associate-r`
930×	`distribute-lft-in`
906×	`fma-def`
776×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	624
1	107	620
2	174	616
3	399	606
4	919	606
5	2807	606
6	5234	606

Stop Event

1×	node limit

Counts

34 → 41

Calls

Call 1

Inputs
5
(+.f64 5 x)
(+.f64 5 (+.f64 x (*.f64 -5/2 (pow.f64 x 2))))
(+.f64 5 (+.f64 x (+.f64 (.f64 -5/2 (pow.f64 x 2)) (.f64 -1/2 (pow.f64 x 3)))))
(*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
-50
-5
-4
-2
-1/2
-2/5
-1/5
0
1/500
1/50
1/5
2/5
1/2
3/2
2
4
5
8
20
50
200
2000

Outputs
5
(+.f64 5 x)
(+.f64 5 (+.f64 x (*.f64 -5/2 (pow.f64 x 2))))
(+.f64 5 (fma.f64 -5/2 (pow.f64 x 2) x))
(fma.f64 (fma.f64 x -5/2 1) x 5)
(fma.f64 x (fma.f64 x -5/2 1) 5)
(+.f64 5 (+.f64 x (+.f64 (.f64 -5/2 (pow.f64 x 2)) (.f64 -1/2 (pow.f64 x 3)))))
(+.f64 5 (+.f64 x (fma.f64 -5/2 (pow.f64 x 2) (*.f64 -1/2 (pow.f64 x 3)))))
(+.f64 (fma.f64 -5/2 (pow.f64 x 2) x) (fma.f64 -1/2 (pow.f64 x 3) 5))
(+.f64 5 (fma.f64 (pow.f64 x 2) (fma.f64 x -1/2 -5/2) x))
(+.f64 x (fma.f64 (pow.f64 x 2) (fma.f64 x -1/2 -5/2) 5))
(fma.f64 (pow.f64 x 2) (fma.f64 x -1/2 -5/2) (+.f64 5 x))
(*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 2 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) x))
(/.f64 (*.f64 x 2) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x)))))
(*.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 2 (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) x))
(/.f64 (*.f64 x 2) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 10 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
(fma.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 10 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
-50
-5
-4
-2
-1/2
-2/5
-1/5
0
1/500
1/50
1/5
2/5
1/2
3/2
2
4
5
8
20
50
200
2000

eval7.0ms (0.2%)

Compiler: Compiled 253 to 157 computations (37.9% saved)

prune17.0ms (0.4%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	1	1
Picked	0	1	1
Done	0	5	5
Total	40	8	48

Accuracy

99.4%

Counts

48 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.3%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x
	5.6%	3/2
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.3%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x
	5.6%	3/2

Compiler

Compiled 204 to 152 computations (25.5% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune6.0ms (0.2%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	6	6
Total	8	8

Accuracy

99.4%

Counts

8 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	9.4%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.8%	(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	5.3%	(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
✓	97.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	97.1%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	97.0%	x
	5.6%	3/2

Compiler

Compiled 213 to 145 computations (31.9% saved)

regimes10.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

Inputs
3/2
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

2 calls:

4.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 127 to 77 computations (39.4% saved)

regimes16.0ms (0.4%)

Counts

8 → 2

Calls

Call 1

Inputs
3/2
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))
(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

2 calls:

8.0ms	x
3.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
99.2%	2	`x`
99.2%	2	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`

Compiler

Compiled 99 to 59 computations (40.4% saved)

regimes6.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

Inputs
3/2
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5)))))

Outputs
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
97.5%	1	`x`

Compiler

Compiled 72 to 50 computations (30.6% saved)

regimes8.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
3/2
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 10 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
97.1%	1	`x`

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes3.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
3/2
x

Outputs
x

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.0%	1	`x`

Compiler

Compiled 5 to 3 computations (40% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
3/2

Outputs
3/2

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
5.6%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.011941925493275954	0.02792303669964786

Compiler

Compiled 18 to 10 computations (44.4% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`+-commutative`
18×	`*-commutative`
6×	`sub-neg`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	364
1	74	364
2	79	364
3	82	364
4	83	364

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 5764607523034235/288230376151711744) (+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5))))) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
x
3/2

Outputs
(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 (+.f64 (.f64 1/2520 (pow.f64 x 7)) (+.f64 (.f64 1/60 (pow.f64 x 5)) (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 x 2)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 5764607523034235/288230376151711744) (+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (+.f64 (.f64 -17/315 (pow.f64 x 7)) (*.f64 2/15 (pow.f64 x 5))))) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 5764607523034235/288230376151711744) (+.f64 x (+.f64 (.f64 (pow.f64 x 3) -1/3) (+.f64 (.f64 (pow.f64 x 7) -17/315) (*.f64 (pow.f64 x 5) 2/15)))) (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
(+.f64 x (+.f64 (.f64 (pow.f64 x 3) -1/3) (.f64 (pow.f64 x 5) 2/15)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
x
3/2

Compiler

Compiled 104 to 68 computations (34.6% saved)

soundness171.0ms (4.2%)

Rules

1352×	`unswap-sqr`
1148×	`fma-def`
1084×	`associate-r`
1000×	`fma-neg`
704×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	272
1	580	272
0	15	35
1	197	35
2	3575	35
0	48	612
1	104	608
2	235	604
3	630	600
4	1269	600
5	2831	600
6	3991	600
7	6911	600

Stop Event

1×	node limit
1×	unsound
1×	node limit

Compiler

Compiled 15 to 11 computations (26.7% saved)

end0.0ms (0%)

preprocess78.0ms (1.9%)

Compiler: Compiled 324 to 182 computations (43.8% saved)

analyze0.0ms (0%)

sample2.6s (63.8%)

preprocess142.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize87.0ms (2.2%)

series2.0ms (0.1%)

rewrite63.0ms (1.6%)

simplify74.0ms (1.8%)

eval12.0ms (0.3%)

prune21.0ms (0.5%)

localize340.0ms (8.4%)

series15.0ms (0.4%)

rewrite48.0ms (1.2%)

simplify132.0ms (3.3%)

eval37.0ms (0.9%)

prune25.0ms (0.6%)

localize40.0ms (1%)

series1.0ms (0%)

rewrite24.0ms (0.6%)

simplify62.0ms (1.5%)

eval7.0ms (0.2%)

prune17.0ms (0.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune6.0ms (0.2%)

regimes10.0ms (0.2%)

regimes16.0ms (0.4%)

regimes6.0ms (0.1%)

regimes8.0ms (0.2%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

soundness171.0ms (4.2%)

end0.0ms (0%)

preprocess78.0ms (1.9%)

Profiling