Details

analyze1.4s (32.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	76.4%	0.2%	11
30.4%	69.4%	0.2%	12
30.8%	69%	0.2%	13
36.2%	63.6%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.5s (33.4%)

Results

1.3s	8012×	body	128	valid
78.0ms	580×	body	128	invalid
71.0ms	101×	body	1024	valid
31.0ms	85×	body	512	valid
18.0ms	58×	body	256	valid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess32.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

525×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
409×	`fma-def_binary64`
258×	`sub-neg_binary64`
130×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	161
1	243	147
2	722	147
3	2150	147
0	4	4

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2
3

Outputs
0
1
2
3

Call 2

Inputs
(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
(+.f64 y (.f64 (.f64 x z) (-.f64 (tanh.f64 (/.f64 t x)) (tanh.f64 (/.f64 y x)))))
(+.f64 z (.f64 (.f64 y x) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 z y)))))
(+.f64 t (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))))
(+.f64 x (.f64 (.f64 z y) (-.f64 (tanh.f64 (/.f64 t z)) (tanh.f64 (/.f64 x z)))))
(+.f64 x (.f64 (.f64 t z) (-.f64 (tanh.f64 (/.f64 y t)) (tanh.f64 (/.f64 x t)))))
(+.f64 x (.f64 (.f64 y t) (-.f64 (tanh.f64 (/.f64 z y)) (tanh.f64 (/.f64 x y)))))

Outputs
(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
(+.f64 y (.f64 (.f64 x z) (-.f64 (tanh.f64 (/.f64 t x)) (tanh.f64 (/.f64 y x)))))
(fma.f64 x (*.f64 z (-.f64 (tanh.f64 (/.f64 t x)) (tanh.f64 (/.f64 y x)))) y)
(fma.f64 (*.f64 x z) (-.f64 (tanh.f64 (/.f64 t x)) (tanh.f64 (/.f64 y x))) y)
(fma.f64 z (*.f64 x (-.f64 (tanh.f64 (/.f64 t x)) (tanh.f64 (/.f64 y x)))) y)
(+.f64 z (.f64 (.f64 y x) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 z y)))))
(+.f64 z (.f64 y (.f64 x (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 z y))))))
(fma.f64 y (*.f64 x (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 z y)))) z)
(fma.f64 x (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 z y)))) z)
(+.f64 t (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))))
(+.f64 t (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y))))))
(fma.f64 y (*.f64 z (-.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))) t)
(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y))) t)
(+.f64 x (.f64 (.f64 z y) (-.f64 (tanh.f64 (/.f64 t z)) (tanh.f64 (/.f64 x z)))))
(+.f64 x (.f64 z (.f64 y (-.f64 (tanh.f64 (/.f64 t z)) (tanh.f64 (/.f64 x z))))))
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t z)) (tanh.f64 (/.f64 x z)))) x)
(fma.f64 y (*.f64 z (-.f64 (tanh.f64 (/.f64 t z)) (tanh.f64 (/.f64 x z)))) x)
(+.f64 x (.f64 (.f64 t z) (-.f64 (tanh.f64 (/.f64 y t)) (tanh.f64 (/.f64 x t)))))
(+.f64 x (.f64 (.f64 z t) (-.f64 (tanh.f64 (/.f64 y t)) (tanh.f64 (/.f64 x t)))))
(fma.f64 t (*.f64 z (-.f64 (tanh.f64 (/.f64 y t)) (tanh.f64 (/.f64 x t)))) x)
(fma.f64 z (*.f64 t (-.f64 (tanh.f64 (/.f64 y t)) (tanh.f64 (/.f64 x t)))) x)
(+.f64 x (.f64 (.f64 y t) (-.f64 (tanh.f64 (/.f64 z y)) (tanh.f64 (/.f64 x y)))))
(fma.f64 y (*.f64 t (-.f64 (tanh.f64 (/.f64 z y)) (tanh.f64 (/.f64 x y)))) x)
(fma.f64 t (*.f64 y (-.f64 (tanh.f64 (/.f64 z y)) (tanh.f64 (/.f64 x y)))) x)

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
289×	`fma-def_binary64`
256×	`associate-l_binary64`
255×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	21
2	154	21
3	391	21
4	1460	21

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Outputs
(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
(fma.f64 y (*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
	4.8b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 107 to 60 computations (43.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	2.2b	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series62.0ms (1.4%)

Counts

4 → 132

Calls

33 calls:

Time	Variable		Point	Expression
7.0ms	y	@	-inf	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
6.0ms	y	@	inf	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
4.0ms	t	@	-inf	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
4.0ms	z	@	inf	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
3.0ms	t	@	0	(tanh.f64 (/.f64 t y))

rewrite70.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
160×	`*-un-lft-identity_binary64`
160×	`pow1_binary64`
152×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	289	50
2	4494	50

Stop Event

1×	node limit

Counts

4 → 110

Calls

Call 1

Inputs
(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
(tanh.f64 (/.f64 t y))
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
(tanh.f64 (/.f64 x y))

Outputs
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simplify116.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
310×	`times-frac_binary64`
206×	`associate-/l*_binary64`
193×	`associate-/r*_binary64`
166×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	429	10353
1	1498	7882

Stop Event

1×	node limit

Counts

242 → 221

Calls

Call 1

Inputs
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(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 (-.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))
(/.f64 x y)
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (/.f64 x y))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (/.f64 x y) (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/2 (pow.f64 x 3)) (.f64 1/3 (pow.f64 x 3)))) (pow.f64 y 3))))) (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (/.f64 x y) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 -1/2 (pow.f64 x 3)))) x)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 2))) (+.f64 (.f64 -1/6 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4))))) (pow.f64 y 4))) (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/2 (pow.f64 x 3)) (.f64 1/3 (pow.f64 x 3)))) (pow.f64 y 3)))))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 -1/2 (pow.f64 x 3))) x) (pow.f64 y 4))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 1/4 (/.f64 (.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 4))))))
(/.f64 x y)
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (/.f64 x y))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)))) (.f64 -1/2 (pow.f64 x 3))) (pow.f64 y 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) x) (+.f64 (.f64 -1/6 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4))))) (pow.f64 y 4))) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)))) (.f64 -1/2 (pow.f64 x 3))) (pow.f64 y 3)))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 4))) (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) x) (pow.f64 y 4)))))

Outputs
(.f64 (-.f64 (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (*.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) y)
(*.f64 y (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (neg.f64 (/.f64 x y))) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y)))))))))
(*.f64 y (+.f64 (/.f64 1 (fma.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 x y)) 1)) (-.f64 (/.f64 (-.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y)))) (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))))))
(.f64 (-.f64 (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (*.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) y)
(*.f64 y (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (neg.f64 (/.f64 x y))) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y)))))))))
(*.f64 y (+.f64 (/.f64 1 (fma.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 x y)) 1)) (-.f64 (/.f64 (-.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y)))) (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))))))
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(*.f64 y (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (neg.f64 (/.f64 x y))) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y)))))))))
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(*.f64 y (+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (neg.f64 (/.f64 x y))) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (neg.f64 (/.f64 x y))))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y)))))))))
(*.f64 y (+.f64 (/.f64 1 (fma.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 x y)) 1)) (-.f64 (/.f64 (-.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (/.f64 (neg.f64 t) y)))) (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))))))
(-.f64 t x)
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(.f64 -1 (-.f64 (.f64 -1 t) (*.f64 -1 x)))
(neg.f64 (*.f64 -1 (-.f64 t x)))
(*.f64 1 (-.f64 t x))
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(+.f64 (/.f64 0 (.f64 y y)) (+.f64 (fma.f64 1/2 (/.f64 (.f64 1/3 (pow.f64 x 3)) (pow.f64 y 3)) (/.f64 x y)) (*.f64 -1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (/.f64 x y) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 -1/2 (pow.f64 x 3)))) x)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 2))) (+.f64 (.f64 -1/6 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4))))) (pow.f64 y 4))) (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/2 (pow.f64 x 3)) (.f64 1/3 (pow.f64 x 3)))) (pow.f64 y 3)))))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 -1/2 (pow.f64 x 3))) x) (pow.f64 y 4))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 1/4 (/.f64 (.f64 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 4))))))
(-.f64 (+.f64 (fma.f64 1/2 (/.f64 (.f64 0 (.f64 x x)) (.f64 y y)) (/.f64 x y)) (.f64 1/2 (+.f64 (/.f64 (fma.f64 -1 (.f64 x (fma.f64 -1 (.f64 x (.f64 (.f64 x x) -1/2)) (.f64 (pow.f64 x 3) -1/3))) (fma.f64 -1/2 (.f64 (.f64 x x) (.f64 (.f64 x x) -1/2)) (.f64 (pow.f64 x 4) -1/12))) (pow.f64 y 4)) (/.f64 (fma.f64 -1 (.f64 x (.f64 (.f64 x x) -1/2)) (.f64 (pow.f64 x 3) -1/6)) (pow.f64 y 3))))) (fma.f64 -1/2 (/.f64 (fma.f64 -1 (.f64 x (.f64 (.f64 x x) -1/2)) (.f64 -1/2 (pow.f64 x 3))) (/.f64 (pow.f64 y 4) x)) (fma.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3)) (.f64 1/4 (/.f64 (.f64 0 (.f64 x x)) (/.f64 (pow.f64 y 4) (.f64 x x)))))))
(+.f64 (/.f64 0 (.f64 y y)) (-.f64 (fma.f64 1/2 (+.f64 (/.f64 (fma.f64 (neg.f64 (.f64 (pow.f64 x 3) 1/6)) x (fma.f64 -1/2 (.f64 (pow.f64 x 4) -1/2) (.f64 (pow.f64 x 4) -1/12))) (pow.f64 y 4)) (/.f64 (.f64 1/3 (pow.f64 x 3)) (pow.f64 y 3))) (/.f64 x y)) (fma.f64 -1/2 (/.f64 (fma.f64 1/2 (pow.f64 x 3) (.f64 -1/2 (pow.f64 x 3))) (/.f64 (pow.f64 y 4) x)) (fma.f64 1/2 (/.f64 (pow.f64 x 3) (pow.f64 y 3)) (/.f64 0 (pow.f64 y 4))))))
(/.f64 x y)
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (/.f64 x y))
(fma.f64 1/2 (/.f64 (.f64 0 (.f64 x x)) (*.f64 y y)) (/.f64 x y))
(+.f64 (/.f64 x y) (/.f64 0 (*.f64 y y)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)))) (.f64 -1/2 (pow.f64 x 3))) (pow.f64 y 3)))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 0 (.f64 x x)) (.f64 y y)) (/.f64 x y)) (neg.f64 (/.f64 (fma.f64 1/2 (fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/3 (pow.f64 x 3) (.f64 x (.f64 (.f64 x x) -1/2)))) (neg.f64 (*.f64 -1/2 (pow.f64 x 3)))) (pow.f64 y 3))))
(+.f64 (/.f64 0 (.f64 y y)) (-.f64 (/.f64 x y) (/.f64 (.f64 1/2 (+.f64 (*.f64 (pow.f64 x 3) -1/3) (pow.f64 x 3))) (pow.f64 y 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 2))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 2))) (+.f64 (.f64 (+.f64 (.f64 -1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) x) (+.f64 (.f64 -1/6 (pow.f64 x 4)) (.f64 1/12 (pow.f64 x 4))))) (pow.f64 y 4))) (+.f64 (/.f64 x y) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (+.f64 (.f64 1/2 (pow.f64 x 3)) (+.f64 (.f64 -1/3 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)))) (.f64 -1/2 (pow.f64 x 3))) (pow.f64 y 3)))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 x 2)) (pow.f64 y 4))) (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 3)) (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) x) (pow.f64 y 4)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 0 (.f64 x x)) (.f64 y y)) (fma.f64 1/2 (/.f64 (fma.f64 -1/2 (.f64 (.f64 x x) (.f64 (.f64 x x) -1/2)) (fma.f64 (fma.f64 -1/6 (pow.f64 x 3) (fma.f64 1/2 (pow.f64 x 3) (.f64 x (.f64 (.f64 x x) -1/2)))) x (.f64 (pow.f64 x 4) -1/12))) (pow.f64 y 4)) (+.f64 (/.f64 x y) (neg.f64 (/.f64 (fma.f64 1/2 (fma.f64 1/2 (pow.f64 x 3) (fma.f64 -1/3 (pow.f64 x 3) (.f64 x (.f64 (.f64 x x) -1/2)))) (neg.f64 (.f64 -1/2 (pow.f64 x 3)))) (pow.f64 y 3)))))) (fma.f64 1/4 (/.f64 (.f64 0 (.f64 x x)) (/.f64 (pow.f64 y 4) (.f64 x x))) (.f64 1/2 (/.f64 (fma.f64 1/2 (pow.f64 x 3) (.f64 x (.f64 (.f64 x x) -1/2))) (/.f64 (pow.f64 y 4) x)))))
(+.f64 (/.f64 0 (.f64 y y)) (-.f64 (-.f64 (fma.f64 1/2 (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 x 4) -1/2) (fma.f64 x (.f64 (pow.f64 x 3) -1/6) (.f64 (pow.f64 x 4) -1/12))) (pow.f64 y 4)) (/.f64 x y)) (/.f64 (.f64 1/2 (+.f64 (.f64 (pow.f64 x 3) -1/3) (pow.f64 x 3))) (pow.f64 y 3))) (fma.f64 1/2 (/.f64 (fma.f64 1/2 (pow.f64 x 3) (*.f64 -1/2 (pow.f64 x 3))) (/.f64 (pow.f64 y 4) x)) (/.f64 0 (pow.f64 y 4)))))

prune193.0ms (4.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	221	2	223

Error

0.0b

Counts

223 → 2

Alt Table

Status	Error	Program
▶	4.8b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
	27.6b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 9549 to 5084 computations (46.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
	0.0b	(tanh.f64 (/.f64 x y))
	0.0b	(tanh.f64 (/.f64 t y))
✓	5.2b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series28.0ms (0.6%)

Counts

2 → 84

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	t	@	-inf	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
3.0ms	z	@	0	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
2.0ms	z	@	inf	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
2.0ms	y	@	-inf	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
2.0ms	y	@	0	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite97.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
160×	`*-un-lft-identity_binary64`
160×	`pow1_binary64`
152×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	290	34
2	4540	34

Stop Event

1×	node limit

Counts

2 → 118

Calls

Call 1

Inputs
(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (tanh.f64 (/.f64 t y)) (neg.f64 (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (tanh.f64 (/.f64 t y)) (.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (fma.f64 (neg.f64 (tanh.f64 (/.f64 x y))) 1 (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (fma.f64 (neg.f64 (cbrt.f64 (tanh.f64 (/.f64 x y)))) (pow.f64 (cbrt.f64 (tanh.f64 (/.f64 x y))) 2) (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (fma.f64 (neg.f64 (sqrt.f64 (tanh.f64 (/.f64 x y)))) (sqrt.f64 (tanh.f64 (/.f64 x y))) (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (fma.f64 -1 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))))) 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Outputs

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y)) (tanh.f64 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (tanh.f64 (/.f64 t y)) (neg.f64 (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) 2) (cbrt.f64 (tanh.f64 (/.f64 t y))) (neg.f64 (tanh.f64 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (tanh.f64 (/.f64 t y))) (sqrt.f64 (tanh.f64 (/.f64 t y))) (neg.f64 (tanh.f64 (/.f64 x y))))))))

simplify132.0ms (3%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-def_binary64`
309×	`fma-neg_binary64`
279×	`+-commutative_binary64`
252×	`associate-+r+_binary64`
240×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	323	8825
1	1151	7198
2	4973	7198

Stop Event

1×	node limit

Counts

202 → 187

Calls

Call 1

Inputs
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(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(*.f64 z (-.f64 t x))
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(+.f64 (/.f64 (.f64 (-.f64 (+.f64 (.f64 1/2 (+.f64 (.f64 -1 (.f64 t (+.f64 (.f64 -1 (pow.f64 t 2)) (.f64 1/2 (pow.f64 t 2))))) (+.f64 (.f64 -1/2 (pow.f64 t 3)) (.f64 1/3 (pow.f64 t 3))))) (.f64 1/2 (pow.f64 x 3))) (+.f64 (.f64 1/2 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (+.f64 (.f64 -1/2 (pow.f64 x 3)) (.f64 1/3 (pow.f64 x 3))))) (.f64 1/2 (pow.f64 t 3)))) z) (pow.f64 y 2)) (+.f64 (/.f64 (.f64 z (-.f64 (.f64 1/2 (+.f64 (.f64 -1 (pow.f64 t 2)) (pow.f64 t 2))) (.f64 1/2 (+.f64 (.f64 -1 (pow.f64 x 2)) (pow.f64 x 2))))) y) (*.f64 z (-.f64 t x))))
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(.f64 -1 (.f64 (-.f64 (.f64 -1 t) (.f64 -1 x)) z))
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(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
(.f64 y (.f64 (-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))))) z))
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Outputs
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(-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y))))))))
(+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (/.f64 (neg.f64 x) y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))))))
(+.f64 (/.f64 1 (+.f64 1 (exp.f64 (+.f64 (/.f64 x y) (/.f64 x y))))) (-.f64 (-.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y))))) (/.f64 1 (+.f64 1 (exp.f64 (+.f64 (/.f64 t y) (/.f64 t y)))))))
(-.f64 (+.f64 (/.f64 1 (.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y)))))) (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y)))))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (/.f64 1 (exp.f64 (/.f64 x y))))) (/.f64 1 (.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (/.f64 1 (exp.f64 (/.f64 t y))))))))
(+.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (-.f64 (/.f64 (exp.f64 (/.f64 (neg.f64 x) y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))) (+.f64 (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y)))) (/.f64 (exp.f64 (neg.f64 (/.f64 t y))) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))))))
(+.f64 (/.f64 1 (+.f64 1 (exp.f64 (+.f64 (/.f64 x y) (/.f64 x y))))) (-.f64 (-.f64 (/.f64 (exp.f64 (/.f64 t y)) (+.f64 (exp.f64 (/.f64 t y)) (exp.f64 (neg.f64 (/.f64 t y))))) (/.f64 (exp.f64 (/.f64 x y)) (+.f64 (exp.f64 (/.f64 x y)) (exp.f64 (/.f64 (neg.f64 x) y))))) (/.f64 1 (+.f64 1 (exp.f64 (+.f64 (/.f64 t y) (/.f64 t y)))))))

prune255.0ms (5.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	291	2	293

Error

0.0b

Counts

293 → 2

Alt Table

Status	Error	Program
✓	4.8b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
▶	27.6b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 13595 to 6989 computations (48.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 t x) x)

series4.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(fma.f64 z (-.f64 t x) x)
0.0ms	t	@	inf	(fma.f64 z (-.f64 t x) x)
0.0ms	t	@	0	(fma.f64 z (-.f64 t x) x)
0.0ms	x	@	-inf	(fma.f64 z (-.f64 t x) x)
0.0ms	t	@	-inf	(fma.f64 z (-.f64 t x) x)

rewrite35.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`pow1_binary64`
686×	`add-log-exp_binary64`
686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1793	8

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 z (-.f64 t x) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 z (-.f64 t x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 z (-.f64 t x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 z (-.f64 t x)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 z (-.f64 t x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 z (-.f64 t x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 z (-.f64 t x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 z (-.f64 t x) x)) (cbrt.f64 (pow.f64 (fma.f64 z (-.f64 t x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 z (-.f64 t x) x) 2)) (cbrt.f64 (fma.f64 z (-.f64 t x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 z (-.f64 t x) x)) (sqrt.f64 (fma.f64 z (-.f64 t x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 z (-.f64 t x)) 3) (pow.f64 x 3)) (+.f64 (*.f64 (*.f64 z (-.f64 t x)) (*.f64 z (-.f64 t x))) (-.f64 (*.f64 x x) (*.f64 (*.f64 z (-.f64 t x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 z (-.f64 t x)) (*.f64 z (-.f64 t x))) (*.f64 x x)) (-.f64 (*.f64 z (-.f64 t x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 z (-.f64 t x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 z (-.f64 t x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 z (-.f64 t x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 z (-.f64 t x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 z (-.f64 t x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 z (-.f64 t x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 z (-.f64 t x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 z (-.f64 t x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 z (-.f64 t x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 z (-.f64 t x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 z (-.f64 t x) x)))))))

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
300×	`fma-neg_binary64`
64×	`cancel-sign-sub-inv_binary64`
60×	`distribute-rgt-in_binary64`
42×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	267
1	56	264
2	108	264
3	213	264
4	373	264
5	674	264
6	1055	264
7	1294	264
8	1413	264
9	1415	264

Stop Event

1×

saturated

Counts

58 → 34

Calls

Call 1

Inputs
x
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(*.f64 (-.f64 t x) z)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(*.f64 (-.f64 t x) z)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(*.f64 t z)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(*.f64 t z)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(*.f64 t z)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(.f64 -1 (.f64 (-.f64 z 1) x))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))

Outputs
x
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(*.f64 (-.f64 t x) z)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(*.f64 (-.f64 t x) z)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (*.f64 (-.f64 t x) z) x)
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 -1 (.f64 z x)) x)
(fma.f64 -1 (*.f64 x z) x)
(-.f64 x (*.f64 x z))
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(*.f64 t z)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(*.f64 t z)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(fma.f64 (-.f64 t x) z x)
(*.f64 t z)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 x z) x)
(-.f64 x (*.f64 x z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (-.f64 t x) z x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 x z) x)
(-.f64 x (*.f64 x z))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (-.f64 t x) z x)
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (-.f64 t x) z x)

prune16.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Status	Error	Program
▶	27.6b	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
✓	4.8b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
✓	27.6b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 396 to 145 computations (63.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1 (.f64 z x)) x)
✓	1.1b	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))

series15.0ms (0.3%)

Counts

2 → 42

Calls

15 calls:

Time	Variable		Point	Expression
8.0ms	t	@	-inf	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
1.0ms	t	@	0	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
1.0ms	z	@	0	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
1.0ms	z	@	inf	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
1.0ms	x	@	0	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))

rewrite55.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`fma-def_binary64`
349×	`fma-neg_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
115×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	220	18
2	3234	14

Stop Event

1×	node limit

Counts

2 → 173

Calls

Call 1

Inputs
(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
(+.f64 (.f64 -1 (.f64 z x)) x)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 t z (fma.f64 z x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 t z) 2) (-.f64 (*.f64 t z) (fma.f64 z x x))) (/.f64 (pow.f64 (fma.f64 z x x) 2) (-.f64 (*.f64 t z) (fma.f64 z x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 t z (fma.f64 z x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 t z (fma.f64 z x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 t z (fma.f64 z x x))) (pow.f64 (cbrt.f64 (fma.f64 t z (fma.f64 z x x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 t z (fma.f64 z x x))) 2) (cbrt.f64 (fma.f64 t z (fma.f64 z x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 t z (fma.f64 z x x))) (sqrt.f64 (fma.f64 t z (fma.f64 z x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 t z) 3) (pow.f64 (fma.f64 z x x) 3)) (/.f64 1 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-1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 z x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x z x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (neg.f64 z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z x) -1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z x) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 z x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 z x)) (cbrt.f64 (pow.f64 (*.f64 z x) 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 z x) 2)) (cbrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (*.f64 z x) 2)) (neg.f64 (cbrt.f64 (*.f64 z x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 z x)) (sqrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 z x)) (neg.f64 (sqrt.f64 (*.f64 z x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 z x)) (*.f64 (sqrt.f64 (*.f64 z x)) -1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 z) x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) z x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 x) z x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (*.f64 z x))) (sqrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (*.f64 z x) 2))) (cbrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (cbrt.f64 (pow.f64 (*.f64 z x) 2))) (cbrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1 (sqrt.f64 (*.f64 z x))) (sqrt.f64 (*.f64 z x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) 1) x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 x)) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (sqrt.f64 x)) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 z)) (sqrt.f64 z) x)))))

simplify33.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

306×	`fma-neg_binary64`
289×	`fma-def_binary64`
56×	`distribute-rgt-in_binary64`
56×	`cancel-sign-sub-inv_binary64`
45×	`associate--r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	344
1	69	289
2	135	289
3	275	289
4	598	289
5	1032	289
6	1241	289
7	1268	289
8	1269	289

Stop Event

1×

saturated

Counts

215 → 189

Calls

Call 1

Inputs
(+.f64 (.f64 -1 (.f64 z x)) x)
(*.f64 t z)
(*.f64 t z)
x
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(.f64 (+.f64 t (.f64 -1 x)) z)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z))
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(*.f64 t z)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(.f64 -1 (.f64 (-.f64 z 1) x))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
x
(.f64 -1 (.f64 z x))
(.f64 -1 (.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(.f64 -1 (.f64 (-.f64 z 1) x))

Outputs
(+.f64 (.f64 -1 (.f64 z x)) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(*.f64 t z)
(*.f64 z t)
(*.f64 t z)
(*.f64 z t)
x
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(.f64 (+.f64 t (.f64 -1 x)) z)
(*.f64 z (+.f64 t (neg.f64 x)))
(*.f64 z (-.f64 t x))
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 t (.f64 -1 x)) z) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z))
(*.f64 z (+.f64 t (neg.f64 x)))
(*.f64 z (-.f64 t x))
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 -1 (.f64 (+.f64 (*.f64 -1 t) x) z)) x)
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(*.f64 t z)
(*.f64 z t)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 (+.f64 (.f64 -1 z) 1) x) (*.f64 t z))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
(+.f64 (.f64 t z) (.f64 -1 (*.f64 (-.f64 z 1) x)))
(fma.f64 (+.f64 t (neg.f64 x)) z x)
(fma.f64 z (-.f64 t x) x)
x
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 x (neg.f64 z))
(neg.f64 (*.f64 z x))
(.f64 -1 (.f64 z x))
(*.f64 (neg.f64 z) x)
(*.f64 x (neg.f64 z))
(neg.f64 (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 (+.f64 (.f64 -1 z) 1) x)
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))
(.f64 -1 (.f64 (-.f64 z 1) x))
(fma.f64 -1 (*.f64 z x) x)
(-.f64 x (*.f64 z x))

prune94.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	189	3	192

Error

Counts

192 → 3

Alt Table

Status	Error	Program
✓	27.6b	(+.f64 (.f64 t z) (+.f64 (.f64 -1 (*.f64 z x)) x))
✓	4.8b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
✓	27.6b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 2604 to 771 computations (70.4% saved)

regimes126.0ms (2.9%)

Accuracy

Total 1.1b remaining (85.5%)

Threshold costs 0b (0%)

Counts

42 → 1

Compiler

Compiled 417 to 148 computations (64.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	15	21
2	20	21
3	22	21
4	23	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)

Outputs
(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)

end55.0ms (1.3%)

Stop Event

1×

done

Compiler

Compiled 80 to 50 computations (37.5% saved)

Details

analyze1.4s (32.1%)

sample1.5s (33.4%)

preprocess32.0ms (0.7%)

simplify18.0ms (0.4%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

series62.0ms (1.4%)

rewrite70.0ms (1.6%)

simplify116.0ms (2.6%)

prune193.0ms (4.4%)

localize12.0ms (0.3%)

series28.0ms (0.6%)

rewrite97.0ms (2.2%)

simplify132.0ms (3%)

prune255.0ms (5.8%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite35.0ms (0.8%)

simplify35.0ms (0.8%)

prune16.0ms (0.4%)

localize7.0ms (0.2%)

series15.0ms (0.3%)

rewrite55.0ms (1.2%)

simplify33.0ms (0.7%)

prune94.0ms (2.1%)

regimes126.0ms (2.9%)

simplify2.0ms (0.1%)

end55.0ms (1.3%)

Profiling