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)

sample2.7s (63.9%)

Results

1.3s	4040×	body	1024	valid
542.0ms	7824×	body	256	unsamplable
498.0ms	1988×	body	512	valid
184.0ms	1793×	body	256	valid
151.0ms	435×	body	2048	valid

Bogosity

preprocess168.0ms (4%)

Algorithm

1×	egg-herbie

Rules

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

Problems

242×	`(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
10×	`(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
4×	No Errors

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
▶	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	8.3%	(/.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)

localize80.0ms (1.9%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	96.2%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	12.2%	(-.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)))

rewrite67.0ms (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

simplify77.0ms (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

eval11.0ms (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

96.6%

Counts

45 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	95.2%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	95.5%	(/.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))))
▶	95.2%	(+.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)))))
▶	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
▶	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	95.2%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	95.5%	(/.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))))
▶	95.2%	(+.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)))))
▶	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
▶	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x

Compiler

Compiled 384 to 292 computations (24% saved)

localize308.0ms (7.3%)

Localize:

Found 19 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%	(pow.f64 x 3)
✓	100.0%	(/.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	100.0%	(+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 2 x))
✓	99.8%	(*.f64 1/3 (pow.f64 x 3))
✓	100.0%	(pow.f64 x 3)
✓	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%	(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

19 → 51

Calls

57 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 x 3)
1.0ms	x	@	0	(/.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	@	-inf	(pow.f64 x 3)

rewrite55.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

412×	`associate-r`
264×	`associate-l`
252×	`prod-diff`
241×	`log1p-expm1-u`
241×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	304
1	549	304

Stop Event

1×	node limit

Counts

19 → 741

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

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2392×	`fma-def`
1314×	`associate-r`
880×	`times-frac`
822×	`associate-*l/`
784×	`associate-l`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	83	2211
1	144	2171
2	261	2167
3	585	2163
4	1162	2001
5	2928	1983
6	4616	1983
7	6798	1983

Stop Event

1×	node limit

Counts

792 → 78

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))
(*.f64 2 x)
(*.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 (.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 2/15 (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
-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)
(*.f64 2 x)
(*.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 (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 3) -1/3 (*.f64 (pow.f64 x 5) 1/8)))
(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 x (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 -1/20 (pow.f64 x 7) (*.f64 (pow.f64 x 5) 1/8))))
(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)))
(fma.f64 (pow.f64 x 5) 1/8 (fma.f64 -1/20 (pow.f64 x 7) (fma.f64 (pow.f64 x 3) -1/3 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 (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 1/3 (.f64 x x) 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 1/3 (.f64 x x) 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 1/3 (.f64 x x) 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 1/3 (.f64 x x) 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 1/3 (.f64 x x) 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 1/3 (.f64 x x) 2))
(/.f64 (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(*.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
-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

eval42.0ms (1%)

Compiler: Compiled 2010 to 1142 computations (43.2% saved)

prune21.0ms (0.5%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	1	1
Picked	1	4	5
Done	0	1	1
Total	118	7	125

Accuracy

96.6%

Counts

125 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.5%	(/.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))))
▶	5.2%	(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.2%	(+.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)))))
✓	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.5%	(/.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))))
▶	5.2%	(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.2%	(+.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)))))
✓	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x

Compiler

Compiled 200 to 148 computations (26% saved)

localize40.0ms (0.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 14 (*.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 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	-inf	(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	x	@	0	(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Time

Variable

Point

Expression

0.0ms

inf

(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

0.0ms

-inf

(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

0.0ms

(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite25.0ms (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	3538	35

Stop Event

1×

unsound

Counts

1 → 38

Calls

Call 1

Inputs
(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-2744
-196
-98
-14
-7
-4
-2
-1
-1/2
-2/7
-1/7
0
1/1372
1/196
1/98
1/14
1/7
2/7
1/2
1
3/2
2
3
4
7
8
14
15
28
98
196
392
2744
5488
38416
537824
7529536
20661046784

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1108×	`unswap-sqr`
984×	`associate-r`
972×	`distribute-lft-in`
906×	`fma-def`
770×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	640
1	119	636
2	186	632
3	409	622
4	927	622
5	2806	622
6	5234	622

Stop Event

1×	node limit

Counts

50 → 56

Calls

Call 1

Inputs
7
(+.f64 7 x)
(+.f64 7 (+.f64 x (*.f64 -7/2 (pow.f64 x 2))))
(+.f64 7 (+.f64 x (+.f64 (.f64 -7/2 (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 14 (/.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 14 (/.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 14 (/.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 14 (/.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 14 (/.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 14 (/.f64 1 (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))))
-2744
-196
-98
-14
-7
-4
-2
-1
-1/2
-2/7
-1/7
0
1/1372
1/196
1/98
1/14
1/7
2/7
1/2
1
3/2
2
3
4
7
8
14
15
28
98
196
392
2744
5488
38416
537824
7529536
20661046784

Outputs
7
(+.f64 7 x)
(+.f64 7 (+.f64 x (*.f64 -7/2 (pow.f64 x 2))))
(+.f64 7 (fma.f64 -7/2 (pow.f64 x 2) x))
(fma.f64 (fma.f64 x -7/2 1) x 7)
(fma.f64 x (fma.f64 x -7/2 1) 7)
(+.f64 7 (+.f64 x (+.f64 (.f64 -7/2 (pow.f64 x 2)) (.f64 -1/2 (pow.f64 x 3)))))
(+.f64 7 (+.f64 x (fma.f64 -7/2 (pow.f64 x 2) (*.f64 -1/2 (pow.f64 x 3)))))
(+.f64 (fma.f64 -7/2 (pow.f64 x 2) x) (fma.f64 -1/2 (pow.f64 x 3) 7))
(+.f64 7 (fma.f64 (pow.f64 x 2) (fma.f64 x -1/2 -7/2) 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 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 x (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.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 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(/.f64 x (/.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(+.f64 (.f64 2 (/.f64 x (+.f64 (exp.f64 x) (exp.f64 (.f64 -1 x))))) (.f64 14 (/.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 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
(fma.f64 x (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 14 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
-2744
-196
-98
-14
-7
-4
-2
-1
-1/2
-2/7
-1/7
0
1/1372
1/196
1/98
1/14
1/7
2/7
1/2
1
3/2
2
3
4
7
8
14
15
28
98
196
392
2744
5488
38416
537824
7529536
20661046784

eval8.0ms (0.2%)

Compiler: Compiled 257 to 160 computations (37.7% saved)

prune14.0ms (0.3%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	1	1
Picked	1	0	1
Done	0	5	5
Total	56	7	63

Accuracy

100.0%

Counts

63 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.5%	(/.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))))
✓	95.2%	(+.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)))))
✓	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x
	9.4%	1
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.5%	(/.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))))
✓	95.2%	(+.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)))))
✓	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x
	9.4%	1

Compiler

Compiled 178 to 132 computations (25.8% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune6.0ms (0.1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	5	5
Total	7	7

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.3%	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	95.5%	(/.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))))
✓	95.2%	(+.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)))))
✓	95.5%	(+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5))))
✓	95.0%	(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
	95.1%	x
	9.4%	1

Compiler

Compiled 200 to 135 computations (32.5% saved)

regimes17.0ms (0.4%)

Counts

9 → 2

Calls

Call 1

Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 14 (*.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))))
1

Calls

2 calls:

9.0ms	x
5.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(/.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
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 14 (*.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)))))
1

Calls

2 calls:

11.0ms	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
99.5%	2	`x`
99.5%	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)

regimes9.0ms (0.2%)

Counts

6 → 2

Calls

Call 1

Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 14 (*.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))))

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 53 to 35 computations (34% saved)

regimes12.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
1
x
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(/.f64 (+.f64 14 (*.f64 2 x)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

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

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 24 to 17 computations (29.2% saved)

regimes6.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
1
x

Outputs
x
1

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.9%	2	`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
1

Outputs
1

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
9.4%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9933258082858624	1.0

Compiler

Compiled 18 to 10 computations (44.4% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.11841765472958785	0.9933258082858624

Compiler

Compiled 18 to 10 computations (44.4% saved)

bsearch15.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.11897587232072153	2.8496558388614157

Results

14.0ms

112×

body

256

valid

Compiler

Compiled 144 to 115 computations (20.1% saved)

bsearch13.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.11897587232072153	2.8496558388614157

Results

12.0ms

112×

body

256

valid

Compiler

Compiled 102 to 80 computations (21.6% saved)

bsearch15.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.11897587232072153	2.8496558388614157

Results

13.0ms

112×

body

256

valid

Compiler

Compiled 60 to 45 computations (25% 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	60	413
1	85	413
2	90	413
3	93	413
4	94	413

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1) (/.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)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/18014398509481984) (+.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))))) 1)
(if (<=.f64 x 5/4) (+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))) 1)
(if (<=.f64 x 5224175567749775/4503599627370496) (+.f64 x (*.f64 (pow.f64 x 3) -1/3)) 1)
(if (<=.f64 x 1) x 1)
1

Outputs
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1) (/.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)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 1) (/.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)))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/18014398509481984) (+.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))))) 1)
(if (<=.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3602879701896397/18014398509481984) (+.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)))) 1)
(if (<=.f64 x 5/4) (+.f64 x (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 2/15 (pow.f64 x 5)))) 1)
(if (<=.f64 x 5/4) (+.f64 x (+.f64 (.f64 (pow.f64 x 3) -1/3) (.f64 (pow.f64 x 5) 2/15))) 1)
(if (<=.f64 x 5224175567749775/4503599627370496) (+.f64 x (*.f64 (pow.f64 x 3) -1/3)) 1)
(if (<=.f64 x 1) x 1)
1

Compiler

Compiled 124 to 87 computations (29.8% saved)

soundness178.0ms (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	37	304
1	549	304
0	15	35
1	197	35
2	3538	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%)

preprocess80.0ms (1.9%)

Compiler: Compiled 340 to 218 computations (35.9% saved)

analyze0.0ms (0%)

sample2.7s (63.9%)

preprocess168.0ms (4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize80.0ms (1.9%)

series2.0ms (0.1%)

rewrite67.0ms (1.6%)

simplify77.0ms (1.8%)

eval11.0ms (0.3%)

prune21.0ms (0.5%)

localize308.0ms (7.3%)

series15.0ms (0.4%)

rewrite55.0ms (1.3%)

simplify116.0ms (2.7%)

eval42.0ms (1%)

prune21.0ms (0.5%)

localize40.0ms (0.9%)

series1.0ms (0%)

rewrite25.0ms (0.6%)

simplify65.0ms (1.6%)

eval8.0ms (0.2%)

prune14.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune6.0ms (0.1%)

regimes17.0ms (0.4%)

regimes16.0ms (0.4%)

regimes9.0ms (0.2%)

regimes12.0ms (0.3%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch15.0ms (0.4%)

bsearch13.0ms (0.3%)

bsearch15.0ms (0.4%)

simplify8.0ms (0.2%)

soundness178.0ms (4.2%)

end0.0ms (0%)

preprocess80.0ms (1.9%)

Profiling