Details

analyze388.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	93.7%	3.2%	6
4.7%	89%	6.3%	7
19.5%	68.7%	11.8%	8
22.6%	61.3%	16.1%	9
26.5%	54%	19.4%	10
28.3%	49.9%	21.9%	11
30.4%	45.9%	23.7%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample3.4s (35.1%)

Results

1.2s	1770×	body	1024	valid
1.1s	5261×	body	256	valid
400.0ms	1039×	body	512	valid
267.0ms	186×	body	2048	valid
176.0ms	902×	body	256	invalid
150.0ms	207×	body	1024	invalid
98.0ms	219×	body	512	invalid

preprocess61.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

501×	`associate-l_binary64`
493×	`fma-def_binary64`
436×	`associate-r_binary64`
400×	`times-frac_binary64`
393×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	29	26
2	45	26
3	96	26
4	242	26
5	602	26
6	1637	26
7	6306	26
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
(/.f64 (exp.f64 (*.f64 y (log.f64 (/.f64 y (+.f64 y x))))) y)

Outputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
(/.f64 (exp.f64 (*.f64 y (log.f64 (/.f64 y (+.f64 y x))))) y)
(/.f64 (pow.f64 (exp.f64 y) (log.f64 (/.f64 y (+.f64 x y)))) y)
(/.f64 (pow.f64 (/.f64 y (+.f64 x y)) y) y)

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

522×	`unswap-sqr_binary64`
443×	`fma-neg_binary64`
342×	`exp-sum_binary64`
258×	`associate-l_binary64`
255×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	13
2	25	13
3	54	13
4	133	13
5	327	13
6	878	13
7	3321	13
8	6606	13

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Outputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
(/.f64 (pow.f64 (exp.f64 x) (log.f64 (/.f64 x (+.f64 x y)))) x)
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

eval1.0ms (0%)

Compiler: Compiled 22 to 10 computations (54.5% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

11.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	11.1b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 11 to 6 computations (45.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	0.0b	(/.f64 x (+.f64 x y))
✓	6.4b	(pow.f64 (/.f64 x (+.f64 x y)) x)

Compiler

Compiled 28 to 6 computations (78.6% saved)

series84.0ms (0.9%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
63.0ms	y	@	-inf	(pow.f64 (/.f64 x (+.f64 x y)) x)
3.0ms	x	@	inf	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
3.0ms	x	@	inf	(pow.f64 (/.f64 x (+.f64 x y)) x)
2.0ms	y	@	inf	(pow.f64 (/.f64 x (+.f64 x y)) x)
2.0ms	x	@	-inf	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`prod-diff_binary64`
457×	`log-prod_binary64`
285×	`pow-prod-down_binary64`
235×	`pow2_binary64`
203×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	165	30
2	2529	30

Stop Event

1×	node limit

Counts

3 → 121

Calls

Call 1

Inputs
(pow.f64 (/.f64 x (+.f64 x y)) x)
(/.f64 x (+.f64 x y))
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 x (+.f64 x y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (/.f64 x (+.f64 x y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)) (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) (+.f64 x x))) (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x x) (pow.f64 (+.f64 x y) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 x) (pow.f64 (/.f64 x (+.f64 x y)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x y))) (.f64 2 x)) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x y))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (/.f64 x (+.f64 x y)) (exp.f64 (log1p.f64 x))) (/.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 x y) x) -3) x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (/.f64 x (+.f64 x y)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 x (+.f64 x y))) (.f64 2 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 x y) x) -3) x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (/.f64 x (+.f64 x y)))) (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 x (+.f64 x y)) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (/.f64 x (+.f64 x y)) (sqrt.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (/.f64 x (+.f64 x y))) 1) (.f64 2 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 x (log.f64 (/.f64 x (+.f64 x y)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (/.f64 x (+.f64 x y))) (*.f64 x 1/2)) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 x y)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 x y))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 x y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (/.f64 1 (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 x (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 x (+.f64 x y))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 x y))) 2) (cbrt.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 x (+.f64 x y))) (sqrt.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 x y)) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 x y)) -2) (/.f64 x (cbrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (cbrt.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 x y)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x y) -1/2) (/.f64 x (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 x y))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (fma.f64 y (-.f64 y x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (-.f64 (.f64 x x) (.f64 y y))) (-.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x y) x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x y) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 x y) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 x y) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 x y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (+.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 x (+.f64 x y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 x (+.f64 x y)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 x (+.f64 x y)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 x (+.f64 x y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (+.f64 x y) x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (/.f64 x (+.f64 x y))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 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Outputs

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

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

702×	`associate-/l*_binary64`
586×	`associate-/r*_binary64`
289×	`fma-def_binary64`
267×	`associate-*l/_binary64`
204×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	3273
1	953	2761
2	3930	2296

Stop Event

1×	node limit

Counts

193 → 214

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(+.f64 1 (+.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x) (.f64 (-.f64 (*.f64 1/2 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2)) (/.f64 1 y)) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x) (+.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 y 2))) (+.f64 (.f64 1/6 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 3)) (.f64 -1 (/.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) y)))) (pow.f64 x 3)) (.f64 (-.f64 (*.f64 1/2 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2)) (/.f64 1 y)) (pow.f64 x 2)))))
(exp.f64 (*.f64 -1 y))
(+.f64 (exp.f64 (.f64 -1 y)) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))) x)))
(+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 1/8 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 2)) (.f64 1/6 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 -2 (pow.f64 y 3))))))) (pow.f64 x 2)) (+.f64 (exp.f64 (.f64 -1 y)) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (*.f64 2 (pow.f64 y 2)))) x))))
(+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 1/8 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 2)) (.f64 1/6 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 -2 (pow.f64 y 3))))))) (pow.f64 x 2)) (+.f64 (exp.f64 (.f64 -1 y)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/12 (.f64 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 -2 (pow.f64 y 3)))) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))))) (+.f64 (.f64 1/48 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 3)) (.f64 1/24 (+.f64 (.f64 -12 (pow.f64 y 4)) (+.f64 (.f64 48 (pow.f64 y 4)) (+.f64 (.f64 -24 (pow.f64 y 4)) (.f64 -6 (pow.f64 y 4)))))))) (exp.f64 (.f64 -1 y))) (pow.f64 x 3)) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))) x)))))
(exp.f64 (*.f64 -1 y))
(+.f64 (exp.f64 (.f64 -1 y)) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))) x)))
(+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 1/8 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 2)) (.f64 -1/6 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 2 (pow.f64 y 3))))))) (pow.f64 x 2)) (+.f64 (exp.f64 (.f64 -1 y)) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (*.f64 2 (pow.f64 y 2)))) x))))
(+.f64 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 1/8 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 2)) (.f64 -1/6 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 2 (pow.f64 y 3))))))) (pow.f64 x 2)) (+.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1/24 (+.f64 (.f64 -12 (pow.f64 y 4)) (+.f64 (.f64 48 (pow.f64 y 4)) (+.f64 (.f64 -24 (pow.f64 y 4)) (.f64 -6 (pow.f64 y 4)))))) (+.f64 (.f64 -1/48 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2))) 3)) (.f64 1/12 (.f64 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 2 (pow.f64 y 3)))) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))))))) (pow.f64 x 3))) (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (*.f64 2 (pow.f64 y 2)))) x)))))
1
(+.f64 1 (*.f64 -1 y))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 1/2 (.f64 1/2 (/.f64 1 x)))) (+.f64 1 (*.f64 -1 y)))
(+.f64 (.f64 (pow.f64 y 2) (+.f64 1/2 (.f64 1/2 (/.f64 1 x)))) (+.f64 1 (+.f64 (.f64 -1 (.f64 (pow.f64 y 3) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 1/6 (.f64 1/3 (/.f64 1 (pow.f64 x 2))))))) (*.f64 -1 y))))
(exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) (pow.f64 x 2)) y)) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 4)) (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) (pow.f64 x 2)) y)) (exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 4)) (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) (pow.f64 x 2)) y)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 3))) (.f64 1/6 (.f64 (+.f64 (.f64 -2 (pow.f64 x 3)) (+.f64 (.f64 -6 (pow.f64 x 3)) (.f64 6 (pow.f64 x 3)))) x)))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (pow.f64 y 3)) (exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)))))
(exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))
(+.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (pow.f64 x 2)) y)))
(+.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 4)) (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))) (pow.f64 y 2)) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (pow.f64 x 2)) y))))
(+.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (pow.f64 x 4)) (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))) (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 3))) (+.f64 (.f64 1/6 (pow.f64 x 6)) (.f64 1/6 (.f64 (+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 6 (pow.f64 x 3)) (.f64 -6 (pow.f64 x 3)))) x))))) (pow.f64 y 3))) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (pow.f64 x 2)) y)))))
(/.f64 x y)
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 4) (pow.f64 y 4))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3)))))
1
(+.f64 1 (*.f64 -1 (/.f64 y x)))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (*.f64 -1 (/.f64 y x))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (.f64 -1 (/.f64 y x)))))
1
(+.f64 1 (*.f64 -1 (/.f64 y x)))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (*.f64 -1 (/.f64 y x))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (.f64 -1 (/.f64 y x)))))
1
(+.f64 1 (*.f64 -1 (/.f64 y x)))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (*.f64 -1 (/.f64 y x))))
(+.f64 1 (+.f64 (/.f64 (pow.f64 y 2) (pow.f64 x 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 3) (pow.f64 x 3))) (.f64 -1 (/.f64 y x)))))
(/.f64 x y)
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 4) (pow.f64 y 4))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3)))))
(/.f64 x y)
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 x 2) (pow.f64 y 2))) (+.f64 (.f64 -1 (/.f64 (pow.f64 x 4) (pow.f64 y 4))) (+.f64 (/.f64 x y) (/.f64 (pow.f64 x 3) (pow.f64 y 3)))))
(/.f64 1 x)
(+.f64 (log.f64 (/.f64 1 y)) (+.f64 (/.f64 1 x) (log.f64 x)))
(+.f64 (.f64 (-.f64 (.f64 1/2 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2)) (/.f64 1 y)) x) (+.f64 (log.f64 (/.f64 1 y)) (+.f64 (/.f64 1 x) (log.f64 x))))
(+.f64 (.f64 (-.f64 (.f64 1/2 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2)) (/.f64 1 y)) x) (+.f64 (log.f64 (/.f64 1 y)) (+.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 y 2))) (+.f64 (.f64 1/6 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 3)) (.f64 -1 (/.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) y)))) (pow.f64 x 2)) (+.f64 (/.f64 1 x) (log.f64 x)))))
(/.f64 (exp.f64 (*.f64 -1 y)) x)
(+.f64 (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))) (pow.f64 x 2))) (/.f64 (exp.f64 (.f64 -1 y)) x))
(+.f64 (.f64 1/2 (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 -1 (pow.f64 y 2)) (.f64 2 (pow.f64 y 2)))) (pow.f64 x 2))) (+.f64 (/.f64 (exp.f64 (.f64 -1 y)) x) (/.f64 (.f64 (exp.f64 (.f64 -1 y)) (+.f64 (.f64 1/6 (+.f64 (.f64 -6 (pow.f64 y 3)) (+.f64 (.f64 6 (pow.f64 y 3)) (.f64 -2 (pow.f64 y 3))))) (.f64 1/8 (pow.f64 (+.f64 (.f64 -1 (pow.f64 y 2)) (*.f64 2 (pow.f64 y 2))) 2)))) (pow.f64 x 3))))
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Outputs
1
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(/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x)
(/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x)
(/.f64 (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))) x)
(/.f64 (pow.f64 (*.f64 (/.f64 1 y) x) x) x)
(+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) y)))
(+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x) (neg.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) (/.f64 y x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))) x) (/.f64 x (/.f64 y (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))))))
(-.f64 (/.f64 (pow.f64 (.f64 (/.f64 1 y) x) x) x) (.f64 (/.f64 x y) (pow.f64 (*.f64 (/.f64 1 y) x) x)))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 1/2 (pow.f64 x 4))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (.f64 (pow.f64 y 2) x)) (+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) y))))
(+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x) (neg.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) (/.f64 y x)))) (.f64 (/.f64 (.f64 1/2 (+.f64 (.f64 x (.f64 (.f64 x x) 1)) (pow.f64 x 4))) (.f64 y y)) (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x)))
(-.f64 (.f64 (+.f64 (.f64 (/.f64 1/2 y) (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 4)) y)) 1) (/.f64 (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))) x)) (/.f64 x (/.f64 y (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))))))
(-.f64 (.f64 (+.f64 (.f64 (/.f64 1/2 (.f64 y y)) (+.f64 (pow.f64 x 3) (pow.f64 x 4))) 1) (/.f64 (pow.f64 (.f64 (/.f64 1 y) x) x) x)) (.f64 (/.f64 x y) (pow.f64 (.f64 (/.f64 1 y) x) x)))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 1/2 (pow.f64 x 4))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (.f64 (pow.f64 y 2) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/6 (pow.f64 x 6)) (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 3))) (.f64 1/6 (.f64 (+.f64 (.f64 -2 (pow.f64 x 3)) (+.f64 (.f64 -6 (pow.f64 x 3)) (.f64 6 (pow.f64 x 3)))) x)))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))) (.f64 (pow.f64 y 3) x)) (+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) (.f64 -1 (/.f64 (.f64 (exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x)) x) y)))))
(+.f64 (.f64 (/.f64 (.f64 1/2 (+.f64 (.f64 x (.f64 (.f64 x x) 1)) (pow.f64 x 4))) (.f64 y y)) (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x)) (+.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x) (neg.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) (/.f64 y x)))) (.f64 (/.f64 (fma.f64 -1/6 (pow.f64 x 6) (fma.f64 -1/2 (.f64 (pow.f64 x 3) (.f64 (.f64 x x) 1)) (.f64 1/6 (.f64 x (fma.f64 -2 (pow.f64 x 3) (*.f64 (pow.f64 x 3) 0)))))) (pow.f64 y 3)) (/.f64 (pow.f64 (exp.f64 (+.f64 (neg.f64 (log.f64 y)) (log.f64 x))) x) x))))
(+.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))) x) (/.f64 x (/.f64 y (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y)))))) (.f64 (/.f64 (pow.f64 (exp.f64 x) (-.f64 (log.f64 x) (log.f64 y))) x) (+.f64 (.f64 (/.f64 1/2 y) (/.f64 (+.f64 (pow.f64 x 3) (pow.f64 x 4)) y)) (/.f64 (fma.f64 -1/6 (pow.f64 x 6) (fma.f64 1/6 (.f64 x (.f64 (pow.f64 x 3) -2)) (.f64 -1/2 (.f64 x (pow.f64 x 4))))) (pow.f64 y 3)))))
(-.f64 (.f64 (/.f64 (pow.f64 (.f64 (/.f64 1 y) x) x) x) (+.f64 (.f64 (/.f64 1/2 (.f64 y y)) (+.f64 (pow.f64 x 3) (pow.f64 x 4))) (+.f64 (/.f64 (fma.f64 -1/6 (pow.f64 x 6) (fma.f64 1/6 (.f64 x (.f64 (pow.f64 x 3) -2)) (.f64 -1/2 (pow.f64 x 5)))) (pow.f64 y 3)) 1))) (.f64 (/.f64 x y) (pow.f64 (*.f64 (/.f64 1 y) x) x)))
(/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x)
(/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x)
(/.f64 (pow.f64 (*.f64 (/.f64 -1 y) (neg.f64 x)) x) x)
(+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) y)))
(+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (neg.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x)))
(-.f64 (/.f64 (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x) x) (.f64 (/.f64 x y) (pow.f64 (*.f64 (/.f64 -1 y) (neg.f64 x)) x)))
(+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) y)) (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 1/2 (pow.f64 x 4)))) (*.f64 (pow.f64 y 2) x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (fma.f64 -1 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 (.f64 x (.f64 y y)) (.f64 1/2 (+.f64 (.f64 x (.f64 (.f64 x x) 1)) (pow.f64 x 4)))))))
(+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (.f64 y y)) (/.f64 1/2 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 x 4))))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x))))
(-.f64 (.f64 (+.f64 (.f64 (/.f64 1/2 (.f64 y y)) (+.f64 (pow.f64 x 3) (pow.f64 x 4))) 1) (/.f64 (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x) x)) (.f64 (/.f64 x y) (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x)))
(+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) (pow.f64 x 3))) (+.f64 (.f64 1/6 (pow.f64 x 6)) (.f64 1/6 (.f64 (+.f64 (.f64 2 (pow.f64 x 3)) (+.f64 (.f64 6 (pow.f64 x 3)) (.f64 -6 (pow.f64 x 3)))) x)))) (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))) (.f64 (pow.f64 y 3) x))) (+.f64 (/.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) (+.f64 (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) x) y)) (/.f64 (.f64 (exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x)) (+.f64 (.f64 1/2 (.f64 (+.f64 (.f64 2 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 2))) x)) (.f64 1/2 (pow.f64 x 4)))) (.f64 (pow.f64 y 2) x)))))
(fma.f64 -1 (.f64 (/.f64 (fma.f64 1/2 (.f64 (pow.f64 x 3) (.f64 (.f64 x x) 1)) (.f64 1/6 (+.f64 (pow.f64 x 6) (.f64 x (fma.f64 2 (pow.f64 x 3) (.f64 (pow.f64 x 3) 0)))))) (pow.f64 y 3)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x)) (+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (fma.f64 -1 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x)) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 (.f64 x (.f64 y y)) (.f64 1/2 (+.f64 (.f64 x (.f64 (*.f64 x x) 1)) (pow.f64 x 4))))))))
(-.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (.f64 y y)) (/.f64 1/2 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 x 4))))) (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) (/.f64 y x)))) (.f64 (/.f64 (pow.f64 (exp.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (neg.f64 x)))) x) x) (/.f64 (fma.f64 1/2 (.f64 x (pow.f64 x 4)) (.f64 1/6 (+.f64 (pow.f64 x 6) (.f64 x (*.f64 2 (pow.f64 x 3)))))) (pow.f64 y 3))))
(+.f64 (-.f64 (/.f64 (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x) x) (.f64 (/.f64 x y) (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x))) (.f64 (/.f64 (pow.f64 (.f64 (/.f64 -1 y) (neg.f64 x)) x) x) (+.f64 (.f64 (/.f64 1/2 (.f64 y y)) (+.f64 (pow.f64 x 3) (pow.f64 x 4))) (/.f64 (neg.f64 (fma.f64 1/6 (.f64 x (+.f64 (pow.f64 x 5) (.f64 2 (pow.f64 x 3)))) (.f64 1/2 (pow.f64 x 5)))) (pow.f64 y 3)))))

eval165.0ms (1.7%)

Compiler: Compiled 5638 to 3191 computations (43.4% saved)

prune78.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	209	5	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	5	215

Error

0.0b

Counts

215 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.4b	(/.f64 (-.f64 1 y) x)
▶	21.4b	(-.f64 (/.f64 1 x) (/.f64 y x))
▶	10.1b	(/.f64 (exp.f64 (neg.f64 y)) x)
▶	38.4b	(/.f64 (pow.f64 (/.f64 x y) x) x)
▶	11.5b	(/.f64 1 x)

Compiler

Compiled 74 to 50 computations (32.4% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

Compiler

Compiled 14 to 5 computations (64.3% saved)

series7.0ms (0.1%)

Counts

1 → 8

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(/.f64 (exp.f64 (neg.f64 y)) x)
1.0ms	x	@	0	(/.f64 (exp.f64 (neg.f64 y)) x)
1.0ms	y	@	inf	(/.f64 (exp.f64 (neg.f64 y)) x)
1.0ms	y	@	0	(/.f64 (exp.f64 (neg.f64 y)) x)
1.0ms	x	@	-inf	(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`pow1_binary64`
514×	`add-log-exp_binary64`
513×	`log1p-expm1-u_binary64`
513×	`expm1-log1p-u_binary64`
502×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	6
2	1660	6

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 (exp.f64 (neg.f64 y)) x)

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

Outputs

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

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1034×	`fma-neg_binary64`
799×	`distribute-rgt-neg-in_binary64`
762×	`distribute-lft-neg-in_binary64`
556×	`unswap-sqr_binary64`
433×	`associate-r_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	103
1	64	98
2	143	96
3	354	96
4	963	93
5	4405	89

Stop Event

1×	node limit

Counts

38 → 39

Calls

Call 1

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

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

localize8.0ms (0.1%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 y) x)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series6.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(/.f64 (-.f64 1 y) x)
1.0ms	x	@	0	(/.f64 (-.f64 1 y) x)
1.0ms	x	@	-inf	(/.f64 (-.f64 1 y) x)
1.0ms	y	@	0	(/.f64 (-.f64 1 y) x)
1.0ms	y	@	-inf	(/.f64 (-.f64 1 y) x)

rewrite80.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

756×	`pow1_binary64`
706×	`add-log-exp_binary64`
706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
692×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1797	7

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

Inputs
(/.f64 (-.f64 1 y) x)

Outputs

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

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

202×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`cancel-sign-sub-inv_binary64`
31×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	124
1	16	106
2	25	106
3	35	106
4	48	106
5	74	106
6	130	106
7	253	106
8	494	79
9	732	79
10	829	79
11	895	79

Stop Event

1×

saturated

Counts

45 → 38

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))

Outputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(/.f64 (-.f64 1 y) x)

localize20.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 x) (/.f64 y x))

Compiler

Compiled 18 to 9 computations (50% saved)

series6.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 (/.f64 1 x) (/.f64 y x))
1.0ms	x	@	-inf	(-.f64 (/.f64 1 x) (/.f64 y x))
1.0ms	y	@	inf	(-.f64 (/.f64 1 x) (/.f64 y x))
1.0ms	y	@	0	(-.f64 (/.f64 1 x) (/.f64 y x))
1.0ms	x	@	inf	(-.f64 (/.f64 1 x) (/.f64 y x))

rewrite91.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`pow1_binary64`
889×	`add-log-exp_binary64`
889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
82×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	158	7
2	2402	7

Stop Event

1×	node limit

Counts

1 → 56

Calls

Call 1

Inputs
(-.f64 (/.f64 1 x) (/.f64 y x))

Outputs

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

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

135×	`fma-def_binary64`
118×	`fma-neg_binary64`
27×	`div-sub_binary64`
25×	`cancel-sign-sub-inv_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Stop Event

1×

saturated

Counts

80 → 61

Calls

Call 1

Inputs
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))

Outputs
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)

localize16.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.4b	(pow.f64 (/.f64 x y) x)

Compiler

Compiled 19 to 5 computations (73.7% saved)

series130.0ms (1.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
79.0ms	y	@	0	(pow.f64 (/.f64 x y) x)
27.0ms	y	@	-inf	(pow.f64 (/.f64 x y) x)
14.0ms	y	@	inf	(pow.f64 (/.f64 x y) x)
5.0ms	x	@	inf	(pow.f64 (/.f64 x y) x)
2.0ms	x	@	-inf	(pow.f64 (/.f64 x y) x)

rewrite110.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`pow1_binary64`
550×	`add-log-exp_binary64`
550×	`log1p-expm1-u_binary64`
550×	`expm1-log1p-u_binary64`
536×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	109	7
2	1466	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

Inputs
(pow.f64 (/.f64 x y) x)

Outputs

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

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
844×	`distribute-rgt-in_binary64`
825×	`distribute-lft-in_binary64`
295×	`*-commutative_binary64`
221×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	249
1	107	229
2	290	225
3	1582	219
4	7650	219

Stop Event

1×	node limit

Counts

40 → 28

Calls

Call 1

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

Outputs
1
(+.f64 1 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(+.f64 1 (*.f64 x (fma.f64 -1 (log.f64 y) (log.f64 x))))
(fma.f64 x (log.f64 (/.f64 x y)) 1)
(+.f64 1 (+.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x) (.f64 1/2 (*.f64 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2) (pow.f64 x 2)))))
(+.f64 1 (fma.f64 (fma.f64 -1 (log.f64 y) (log.f64 x)) x (.f64 1/2 (.f64 (pow.f64 (fma.f64 -1 (log.f64 y) (log.f64 x)) 2) (*.f64 x x)))))
(+.f64 1 (fma.f64 1/2 (.f64 (pow.f64 (log.f64 (/.f64 x y)) 2) (.f64 x x)) (*.f64 x (log.f64 (/.f64 x y)))))
(fma.f64 x (log.f64 (/.f64 x y)) (fma.f64 (pow.f64 (log.f64 (/.f64 x y)) 2) (.f64 x (.f64 x 1/2)) 1))
(fma.f64 x (fma.f64 x (*.f64 1/2 (pow.f64 (log.f64 (/.f64 x y)) 2)) (log.f64 (/.f64 x y))) 1)
(+.f64 (.f64 1/6 (.f64 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 3) (pow.f64 x 3))) (+.f64 1 (+.f64 (.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x) (.f64 1/2 (*.f64 (pow.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) 2) (pow.f64 x 2))))))
(fma.f64 1/6 (.f64 (pow.f64 (fma.f64 -1 (log.f64 y) (log.f64 x)) 3) (pow.f64 x 3)) (+.f64 1 (fma.f64 (fma.f64 -1 (log.f64 y) (log.f64 x)) x (.f64 1/2 (.f64 (pow.f64 (fma.f64 -1 (log.f64 y) (log.f64 x)) 2) (.f64 x x))))))
(+.f64 (fma.f64 1/2 (.f64 (pow.f64 (log.f64 (/.f64 x y)) 2) (.f64 x x)) (.f64 x (log.f64 (/.f64 x y)))) (fma.f64 1/6 (.f64 (pow.f64 (log.f64 (/.f64 x y)) 3) (pow.f64 x 3)) 1))
(fma.f64 1/6 (.f64 (pow.f64 (log.f64 (/.f64 x y)) 3) (pow.f64 x 3)) (fma.f64 x (log.f64 (/.f64 x y)) (fma.f64 (pow.f64 (log.f64 (/.f64 x y)) 2) (.f64 x (*.f64 x 1/2)) 1)))
(fma.f64 (.f64 x x) (fma.f64 1/2 (pow.f64 (log.f64 (/.f64 x y)) 2) (.f64 x (*.f64 1/6 (pow.f64 (log.f64 (/.f64 x y)) 3)))) (fma.f64 x (log.f64 (/.f64 x y)) 1))
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (log.f64 (/.f64 x y)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (*.f64 (+.f64 (log.f64 (/.f64 1 y)) (log.f64 x)) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))
(pow.f64 (/.f64 x y) x)
(exp.f64 (.f64 (+.f64 (log.f64 (/.f64 -1 y)) (log.f64 (.f64 -1 x))) x))
(pow.f64 (/.f64 x y) x)

eval103.0ms (1.1%)

Compiler: Compiled 1862 to 997 computations (46.5% saved)

prune56.0ms (0.6%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	162	9	171

Error

Counts

171 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	10.1b	(/.f64 (exp.f64 (neg.f64 y)) x)
▶	39.4b	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
✓	21.4b	(/.f64 (-.f64 1 y) x)
✓	21.4b	(-.f64 (/.f64 1 x) (/.f64 y x))
▶	10.1b	(pow.f64 (*.f64 x (exp.f64 y)) -1)
▶	35.8b	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
▶	21.4b	(/.f64 1 (/.f64 x (-.f64 1 y)))
✓	38.4b	(/.f64 (pow.f64 (/.f64 x y) x) x)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 76 to 54 computations (28.9% saved)

localize21.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	28.3b	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))

Compiler

Compiled 25 to 10 computations (60% saved)

series9.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
2.0ms	x	@	-inf	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
1.0ms	y	@	0	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
1.0ms	y	@	-inf	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
1.0ms	x	@	inf	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))

rewrite113.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`pow1_binary64`
874×	`add-log-exp_binary64`
873×	`log1p-expm1-u_binary64`
873×	`expm1-log1p-u_binary64`
855×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	180	13
2	2404	13

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (pow.f64 x -2)) (*.f64 (*.f64 x (neg.f64 y)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) x) (*.f64 (pow.f64 x -2) (*.f64 x (neg.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x 3) (pow.f64 (*.f64 x y) 3)) (pow.f64 x -2)) (fma.f64 x x (*.f64 (*.f64 x y) (+.f64 x (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 x x) (pow.f64 (*.f64 x y) 2)) (pow.f64 x -2)) (+.f64 x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (-.f64 (pow.f64 x 3) (pow.f64 (*.f64 x y) 3))) (fma.f64 x x (*.f64 (*.f64 x y) (+.f64 x (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 x -2) (-.f64 (*.f64 x x) (pow.f64 (*.f64 x y) 2))) (+.f64 x (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (-.f64 x (*.f64 x y))) (/.f64 1 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (-.f64 x (*.f64 x y)) 2) (pow.f64 x -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 x (*.f64 x y))) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (-.f64 x (*.f64 x y)) 3) (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (-.f64 x (*.f64 x y)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (-.f64 x (*.f64 x y)) (pow.f64 x -2))))))))

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

135×	`fma-def_binary64`
118×	`fma-neg_binary64`
27×	`div-sub_binary64`
25×	`cancel-sign-sub-inv_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Stop Event

1×

saturated

Counts

43 → 25

Calls

Call 1

Inputs
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))

Outputs
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (+.f64 1 (*.f64 -1 y)) x)
(/.f64 (-.f64 1 y) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)

localize29.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 1 y) x)
✓	4.5b	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)

Compiler

Compiled 29 to 20 computations (31% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
1.0ms	y	@	-inf	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
0.0ms	y	@	inf	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
0.0ms	x	@	inf	(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)

rewrite113.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

656×	`prod-diff_binary64`
440×	`fma-def_binary64`
412×	`log-prod_binary64`
246×	`pow-prod-down_binary64`
234×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	191	7
2	2951	7

Stop Event

1×	node limit

Counts

1 → 147

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 (-.f64 1 y) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 y) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 y) x) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x)) (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 1 y) x) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 x))) (/.f64 (sqrt.f64 y) (sqrt.f64 x)) (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 1 y) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (/.f64 (-.f64 1 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (/.f64 y x) 1))) (fma.f64 (neg.f64 (/.f64 y x)) 1 (*.f64 (/.f64 y x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1 x)) 2) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (/.f64 y x) 1))) (fma.f64 (neg.f64 (/.f64 y x)) 1 (*.f64 (/.f64 y x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (/.f64 y x) 1))) (fma.f64 (neg.f64 (/.f64 y x)) 1 (*.f64 (/.f64 y x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (/.f64 1 x) y))) (fma.f64 (neg.f64 (/.f64 1 x)) y (*.f64 (/.f64 1 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1 x)) 2) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (/.f64 1 x) y))) (fma.f64 (neg.f64 (/.f64 1 x)) y (*.f64 (/.f64 1 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (/.f64 1 x) y))) (fma.f64 (neg.f64 (/.f64 1 x)) y (*.f64 (/.f64 1 x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1 (/.f64 1 x) (neg.f64 (*.f64 (cbrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 (/.f64 y x)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y x))) (pow.f64 (cbrt.f64 (/.f64 y x)) 2) (*.f64 (cbrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 (/.f64 y x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (pow.f64 (cbrt.f64 (/.f64 1 x)) 2) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (cbrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 (/.f64 y x)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y x))) (pow.f64 (cbrt.f64 (/.f64 y x)) 2) (*.f64 (cbrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 (/.f64 y x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (cbrt.f64 (/.f64 y x)) (pow.f64 (cbrt.f64 (/.f64 y x)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 y x))) (pow.f64 (cbrt.f64 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((x hypot.f64 (sqrt.f64 (/.f64 (-.f64 1 y) x)) (sqrt.f64 (-.f64 (pow.f64 (/.f64 x (-.f64 1 y)) -2) (/.f64 (-.f64 1 y) x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 1 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (/.f64 (-.f64 1 y) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (-.f64 1 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 1 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 1 y) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (-.f64 1 y) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (/.f64 (-.f64 1 y) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (neg.f64 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 (-.f64 1 y) x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 y) (/.f64 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (-.f64 1 y) x) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (-.f64 1 y) x)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 y) x)) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 y) x)) 2) (cbrt.f64 (/.f64 (-.f64 1 y) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 y)) 2) (*.f64 (cbrt.f64 (-.f64 1 y)) (/.f64 1 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (-.f64 1 y) x)) (sqrt.f64 (/.f64 (-.f64 1 y) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) (*.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 y)) (*.f64 (sqrt.f64 (-.f64 1 y)) (/.f64 1 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (-.f64 1 y)) (/.f64 1 (neg.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (-.f64 1 y) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 (-.f64 1 y) x)))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 2) (+.f64 (/.f64 (-.f64 1 y) x) 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (/.f64 (-.f64 1 y) x) 3)) (/.f64 1 (fma.f64 (/.f64 (-.f64 1 y) x) (+.f64 (/.f64 (-.f64 1 y) x) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 1 y) x)))) (/.f64 1 (+.f64 (/.f64 (-.f64 1 y) x) 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (/.f64 x (-.f64 1 y)) -2)) (/.f64 1 (-.f64 1 (/.f64 (-.f64 1 y) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1)) 2) (cbrt.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 1 x)) 2) (cbrt.f64 (/.f64 1 x)) (neg.f64 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1)) (sqrt.f64 (+.f64 (/.f64 (-.f64 1 y) x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 x)) (neg.f64 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (-.f64 1 y) (cbrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (/.f64 (-.f64 1 y) (sqrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 y)) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 y)) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 1 y)) 1) (/.f64 (sqrt.f64 (-.f64 1 y)) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 y)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (-.f64 1 y) x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 1 y)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (-.f64 1 y)) (cbrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 y)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (-.f64 1 y)) (sqrt.f64 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 1 (/.f64 (-.f64 1 y) x))) 1) (expm1.f64 (*.f64 1/2 (log1p.f64 (/.f64 (-.f64 1 y) x)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (/.f64 (-.f64 1 y) x)) 1) (-.f64 (sqrt.f64 (/.f64 (-.f64 1 y) x)) 1) 1)))))

simplify46.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

135×	`fma-def_binary64`
118×	`fma-neg_binary64`
27×	`div-sub_binary64`
25×	`cancel-sign-sub-inv_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	268
1	21	163
2	31	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	525	163
9	670	163
10	716	163

Stop Event

1×

saturated

Counts

171 → 151

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(*.f64 -1 (/.f64 y x))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)

Outputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (neg.f64 (/.f64 y x)))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 1 y))
✓	0.1b	(/.f64 1 (/.f64 x (-.f64 1 y)))

Compiler

Compiled 20 to 13 computations (35% saved)

series14.0ms (0.1%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	(/.f64 x (-.f64 1 y))
1.0ms	x	@	-inf	(/.f64 x (-.f64 1 y))
1.0ms	x	@	inf	(/.f64 x (-.f64 1 y))
1.0ms	y	@	inf	(/.f64 x (-.f64 1 y))
1.0ms	y	@	0	(/.f64 x (-.f64 1 y))

rewrite101.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`pow1_binary64`
787×	`add-log-exp_binary64`
787×	`log1p-expm1-u_binary64`
787×	`expm1-log1p-u_binary64`
770×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	14
2	2141	14

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs
(/.f64 1 (/.f64 x (-.f64 1 y)))
(/.f64 x (-.f64 1 y))

Outputs

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

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

simplify295.0ms (3%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l*_binary64`
565×	`fma-def_binary64`
421×	`distribute-lft-out_binary64`
362×	`associate-*r/_binary64`
318×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	368
1	111	355
2	292	340
3	941	322
4	3864	316

Stop Event

1×	node limit

Counts

108 → 92

Calls

Call 1

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

Outputs
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 (-.f64 1 y) x)
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(*.f64 -1 (/.f64 y x))
(neg.f64 (/.f64 y x))
(/.f64 (neg.f64 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(/.f64 (-.f64 1 y) x)
x
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 y 2) x) x))
(fma.f64 y x (fma.f64 (*.f64 y y) x x))
(*.f64 x (+.f64 y (fma.f64 y y 1)))
(fma.f64 x (+.f64 y (*.f64 y y)) x)
(fma.f64 y (fma.f64 y x x) x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (*.f64 (pow.f64 y 3) x) x)))
(fma.f64 y x (fma.f64 (*.f64 y y) x (fma.f64 (pow.f64 y 3) x x)))
(fma.f64 y x (fma.f64 x (*.f64 y y) (fma.f64 x (pow.f64 y 3) x)))
(fma.f64 y x (fma.f64 x (fma.f64 y y (pow.f64 y 3)) x))
(*.f64 (fma.f64 y y 1) (fma.f64 y x x))
(*.f64 -1 (/.f64 x y))
(neg.f64 (/.f64 x y))
(/.f64 (neg.f64 x) y)
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (.f64 -1 (/.f64 x y)))
(.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y)))
(-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y))
(*.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (*.f64 -1 (/.f64 x y))))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y))))
(-.f64 (-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y)) (/.f64 x (pow.f64 y 3)))
(-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 -1 (/.f64 -1 y))) (/.f64 x y))
(fma.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y)) (/.f64 (neg.f64 x) (pow.f64 y 3)))
(-.f64 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y))) (/.f64 x (pow.f64 y 3)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 4))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (.f64 -1 (/.f64 x y)))))
(fma.f64 -1 (/.f64 x (pow.f64 y 4)) (fma.f64 -1 (/.f64 x (pow.f64 y 3)) (.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y)))))
(-.f64 (-.f64 (-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y)) (/.f64 x (pow.f64 y 3))) (/.f64 x (pow.f64 y 4)))
(-.f64 (-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 -1 (/.f64 -1 y))) (/.f64 x y)) (/.f64 x (pow.f64 y 4)))
(.f64 (+.f64 (/.f64 x y) (/.f64 x (.f64 y y))) (+.f64 -1 (/.f64 -1 (*.f64 y y))))
(*.f64 (+.f64 (/.f64 x y) (/.f64 x (pow.f64 y 3))) (+.f64 -1 (/.f64 -1 y)))
(*.f64 -1 (/.f64 x y))
(neg.f64 (/.f64 x y))
(/.f64 (neg.f64 x) y)
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (.f64 -1 (/.f64 x y)))
(.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y)))
(-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y))
(*.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (*.f64 -1 (/.f64 x y))))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y))))
(-.f64 (-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y)) (/.f64 x (pow.f64 y 3)))
(-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 -1 (/.f64 -1 y))) (/.f64 x y))
(fma.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y)) (/.f64 (neg.f64 x) (pow.f64 y 3)))
(-.f64 (*.f64 (/.f64 x y) (+.f64 -1 (/.f64 -1 y))) (/.f64 x (pow.f64 y 3)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 4))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (.f64 -1 (/.f64 x (pow.f64 y 2))) (.f64 -1 (/.f64 x y)))))
(fma.f64 -1 (/.f64 x (pow.f64 y 4)) (fma.f64 -1 (/.f64 x (pow.f64 y 3)) (.f64 -1 (+.f64 (/.f64 x (.f64 y y)) (/.f64 x y)))))
(-.f64 (-.f64 (-.f64 (neg.f64 (/.f64 x y)) (/.f64 (/.f64 x y) y)) (/.f64 x (pow.f64 y 3))) (/.f64 x (pow.f64 y 4)))
(-.f64 (-.f64 (.f64 (/.f64 x (.f64 y y)) (+.f64 -1 (/.f64 -1 y))) (/.f64 x y)) (/.f64 x (pow.f64 y 4)))
(.f64 (+.f64 (/.f64 x y) (/.f64 x (.f64 y y))) (+.f64 -1 (/.f64 -1 (*.f64 y y))))
(*.f64 (+.f64 (/.f64 x y) (/.f64 x (pow.f64 y 3))) (+.f64 -1 (/.f64 -1 y)))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (*.f64 x (exp.f64 y)) -1)
✓	0.0b	(*.f64 x (exp.f64 y))

Compiler

Compiled 17 to 7 computations (58.8% saved)

series68.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
58.0ms	x	@	0	(*.f64 x (exp.f64 y))
1.0ms	y	@	inf	(pow.f64 (*.f64 x (exp.f64 y)) -1)
1.0ms	y	@	-inf	(pow.f64 (*.f64 x (exp.f64 y)) -1)
1.0ms	x	@	0	(pow.f64 (*.f64 x (exp.f64 y)) -1)
1.0ms	x	@	inf	(*.f64 x (exp.f64 y))

rewrite92.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`pow1_binary64`
580×	`add-log-exp_binary64`
580×	`log1p-expm1-u_binary64`
580×	`expm1-log1p-u_binary64`
564×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	139	15
2	1609	15

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs
(*.f64 x (exp.f64 y))
(pow.f64 (*.f64 x (exp.f64 y)) -1)

Outputs

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

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

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1022×	`fma-neg_binary64`
507×	`distribute-rgt-neg-in_binary64`
503×	`fma-def_binary64`
334×	`times-frac_binary64`
332×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	38	417
1	103	392
2	254	385
3	704	381
4	2260	378
5	5489	374

Stop Event

1×	node limit

Counts

82 → 51

Calls

Call 1

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

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

eval230.0ms (2.4%)

Compiler: Compiled 5289 to 3388 computations (35.9% saved)

prune156.0ms (1.6%)

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	354	3	357
Fresh	0	0	0
Picked	1	0	1
Done	2	6	8
Total	357	9	366

Error

Counts

366 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.4b	(/.f64 (-.f64 1 y) x)
▶	15.4b	(/.f64 1 (+.f64 (*.f64 y x) x))
✓	10.1b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	39.4b	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
✓	21.4b	(/.f64 1 (/.f64 x (-.f64 1 y)))
▶	10.1b	(/.f64 (/.f64 1 x) (exp.f64 y))
▶	21.9b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
✓	38.4b	(/.f64 (pow.f64 (/.f64 x y) x) x)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 74 to 53 computations (28.4% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
0.0ms	x	@	inf	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (/.f64 1 x)) 1)

rewrite89.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`pow1_binary64`
626×	`add-log-exp_binary64`
626×	`log1p-expm1-u_binary64`
626×	`expm1-log1p-u_binary64`
615×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	139	4
2	2008	4

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (/.f64 1 x)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 1 x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (/.f64 1 (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 (sqrt.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (pow.f64 x -1/2)) 1) (-.f64 (hypot.f64 1 (pow.f64 x -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (neg.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2)) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1 x) 2) (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x -1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 1 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (+.f64 (/.f64 1 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x)) (-.f64 (+.f64 1 (/.f64 1 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 x)) 2) (+.f64 (/.f64 1 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (+.f64 (/.f64 1 x) 2) (/.f64 1 x))) (neg.f64 (+.f64 (/.f64 1 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 1 x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1)) (+.f64 (/.f64 1 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 1 x) -1) (+.f64 (/.f64 1 x) -1))) (-.f64 1 (+.f64 (/.f64 1 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (/.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 x))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 x -1/2)) (hypot.f64 1 (pow.f64 x -1/2)) -1)))))

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	6	48

Stop Event

1×

saturated

Counts

58 → 46

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)

Outputs
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)
(/.f64 1 x)

localize48.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y x) x)
✓	0.2b	(/.f64 1 (+.f64 (*.f64 y x) x))

Compiler

Compiled 20 to 7 computations (65% saved)

series7.0ms (0.1%)

Counts

2 → 39

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 1 (+.f64 (*.f64 y x) x))
1.0ms	x	@	0	(/.f64 1 (+.f64 (*.f64 y x) x))
1.0ms	y	@	0	(/.f64 1 (+.f64 (*.f64 y x) x))
1.0ms	y	@	inf	(/.f64 1 (+.f64 (*.f64 y x) x))
1.0ms	y	@	-inf	(/.f64 1 (+.f64 (*.f64 y x) x))

rewrite113.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

787×	`pow1_binary64`
732×	`add-log-exp_binary64`
731×	`log1p-expm1-u_binary64`
731×	`expm1-log1p-u_binary64`
716×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	151	13
2	2045	13

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

Inputs
(/.f64 1 (+.f64 (*.f64 y x) x))
(+.f64 (*.f64 y x) x)

Outputs

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

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

simplify125.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-/l*_binary64`
698×	`fma-neg_binary64`
555×	`cancel-sign-sub-inv_binary64`
258×	`associate-*l/_binary64`
224×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	481
1	116	474
2	275	426
3	724	420
4	2503	397

Stop Event

1×	node limit

Counts

108 → 91

Calls

Call 1

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

Outputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x)))
(+.f64 (/.f64 1 x) (/.f64 (neg.f64 y) x))
(-.f64 (/.f64 1 x) (/.f64 y x))
(+.f64 (/.f64 (pow.f64 y 2) x) (+.f64 (/.f64 1 x) (*.f64 -1 (/.f64 y x))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 (neg.f64 y) x)) (/.f64 (*.f64 y y) x))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 y x)) (/.f64 y (/.f64 x y)))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 y x)) (*.f64 (/.f64 y x) y))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 y x) (+.f64 -1 y)))
(+.f64 (/.f64 (pow.f64 y 2) x) (+.f64 (.f64 -1 (/.f64 (pow.f64 y 3) x)) (+.f64 (/.f64 1 x) (.f64 -1 (/.f64 y x)))))
(+.f64 (/.f64 (*.f64 y y) x) (fma.f64 -1 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1 x) (/.f64 (neg.f64 y) x))))
(+.f64 (/.f64 y (/.f64 x y)) (-.f64 (-.f64 (/.f64 1 x) (/.f64 y x)) (/.f64 (pow.f64 y 3) x)))
(+.f64 (-.f64 (/.f64 1 x) (/.f64 y x)) (-.f64 (*.f64 (/.f64 y x) y) (/.f64 (pow.f64 y 3) x)))
(+.f64 (/.f64 1 x) (-.f64 (.f64 (/.f64 y x) (-.f64 y (.f64 y y))) (/.f64 y x)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 y x) (-.f64 y (fma.f64 y y 1))))
(/.f64 1 (*.f64 y x))
(/.f64 1 (*.f64 x y))
(-.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 2) x)))
(-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 x (*.f64 y y))))
(-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 y (*.f64 x y))))
(+.f64 (/.f64 1 (.f64 x y)) (/.f64 -1 (.f64 x (*.f64 y y))))
(.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y)))
(-.f64 (+.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 3) x))) (/.f64 1 (*.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 x (pow.f64 y 3)))) (/.f64 1 (.f64 x (.f64 y y))))
(+.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 y (.f64 x y)))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (/.f64 -1 (.f64 x (*.f64 y y)))))
(+.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y))) (/.f64 (/.f64 1 x) (pow.f64 y 3)))
(-.f64 (+.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 3) x))) (+.f64 (/.f64 1 (.f64 (pow.f64 y 4) x)) (/.f64 1 (.f64 (pow.f64 y 2) x))))
(+.f64 (/.f64 1 (.f64 x y)) (-.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (+.f64 (/.f64 1 (.f64 x (.f64 y y))) (/.f64 1 (*.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (-.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (+.f64 (/.f64 1 (.f64 y (.f64 x y))) (/.f64 1 (*.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (-.f64 (/.f64 -1 (.f64 x (.f64 y y))) (/.f64 1 (.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (-.f64 (/.f64 -1 (.f64 x (*.f64 y y))) (/.f64 (/.f64 1 x) (pow.f64 y 4)))))
(+.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y))) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (/.f64 (/.f64 -1 x) (pow.f64 y 4))))
(/.f64 1 (*.f64 y x))
(/.f64 1 (*.f64 x y))
(-.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 2) x)))
(-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 x (*.f64 y y))))
(-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 y (*.f64 x y))))
(+.f64 (/.f64 1 (.f64 x y)) (/.f64 -1 (.f64 x (*.f64 y y))))
(.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y)))
(-.f64 (+.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 3) x))) (/.f64 1 (*.f64 (pow.f64 y 2) x)))
(-.f64 (+.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 x (pow.f64 y 3)))) (/.f64 1 (.f64 x (.f64 y y))))
(+.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (-.f64 (/.f64 1 (.f64 x y)) (/.f64 1 (.f64 y (.f64 x y)))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (/.f64 -1 (.f64 x (*.f64 y y)))))
(+.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y))) (/.f64 (/.f64 1 x) (pow.f64 y 3)))
(-.f64 (+.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (.f64 (pow.f64 y 3) x))) (+.f64 (/.f64 1 (.f64 (pow.f64 y 4) x)) (/.f64 1 (.f64 (pow.f64 y 2) x))))
(+.f64 (/.f64 1 (.f64 x y)) (-.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (+.f64 (/.f64 1 (.f64 x (.f64 y y))) (/.f64 1 (*.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (-.f64 (/.f64 1 (.f64 x (pow.f64 y 3))) (+.f64 (/.f64 1 (.f64 y (.f64 x y))) (/.f64 1 (*.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (-.f64 (/.f64 -1 (.f64 x (.f64 y y))) (/.f64 1 (.f64 x (pow.f64 y 4))))))
(+.f64 (/.f64 1 (.f64 x y)) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (-.f64 (/.f64 -1 (.f64 x (*.f64 y y))) (/.f64 (/.f64 1 x) (pow.f64 y 4)))))
(+.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y))) (+.f64 (/.f64 (/.f64 1 x) (pow.f64 y 3)) (/.f64 (/.f64 -1 x) (pow.f64 y 4))))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 1 (*.f64 (+.f64 1 y) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 -1 (.f64 (-.f64 (.f64 -1 y) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 -1 (.f64 (-.f64 (.f64 -1 y) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 -1 (.f64 (-.f64 (.f64 -1 y) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
(/.f64 -1 (.f64 (-.f64 (.f64 -1 y) 1) x))
(/.f64 1 (*.f64 x (+.f64 1 y)))
(/.f64 1 (fma.f64 x y x))
x
(*.f64 y x)
(*.f64 x y)
(*.f64 y x)
(*.f64 x y)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(*.f64 (+.f64 1 y) x)
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(*.f64 x (+.f64 1 y))
(fma.f64 x y x)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 1 x) (exp.f64 y))

Compiler

Compiled 16 to 9 computations (43.8% saved)

series4.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (/.f64 1 x) (exp.f64 y))
1.0ms	x	@	inf	(/.f64 (/.f64 1 x) (exp.f64 y))
1.0ms	x	@	-inf	(/.f64 (/.f64 1 x) (exp.f64 y))
1.0ms	y	@	-inf	(/.f64 (/.f64 1 x) (exp.f64 y))
1.0ms	y	@	inf	(/.f64 (/.f64 1 x) (exp.f64 y))

rewrite116.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`pow1_binary64`
631×	`add-log-exp_binary64`
631×	`log1p-expm1-u_binary64`
631×	`expm1-log1p-u_binary64`
615×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	141	8
2	1797	8

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (/.f64 1 x) (exp.f64 y))

Outputs

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

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

993×	`fma-neg_binary64`
799×	`distribute-rgt-neg-in_binary64`
762×	`distribute-lft-neg-in_binary64`
536×	`unswap-sqr_binary64`
422×	`associate-l_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	251
1	64	226
2	140	224
3	336	224
4	905	221
5	4197	217

Stop Event

1×	node limit

Counts

55 → 40

Calls

Call 1

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

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

eval95.0ms (1%)

Compiler: Compiled 2011 to 1159 computations (42.4% saved)

prune82.0ms (0.8%)

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	0	0	0
Picked	0	1	1
Done	0	8	8
Total	174	12	186

Error

Counts

186 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.4b	(/.f64 (-.f64 1 y) x)
✓	15.4b	(/.f64 1 (+.f64 (*.f64 y x) x))
✓	10.1b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	39.4b	(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
✓	38.4b	(/.f64 (pow.f64 (/.f64 x y) x) x)
	57.1b	(.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y)))
	56.3b	(/.f64 1 (*.f64 y x))
	21.4b	(+.f64 (/.f64 1 x) (*.f64 (/.f64 y x) (+.f64 -1 y)))
✓	21.4b	(/.f64 1 (/.f64 x (-.f64 1 y)))
✓	10.1b	(/.f64 (/.f64 1 x) (exp.f64 y))
✓	21.9b	(-.f64 (+.f64 1 (/.f64 1 x)) 1)
✓	11.5b	(/.f64 1 x)

Compiler

Compiled 107 to 77 computations (28% saved)

regimes224.0ms (2.3%)

Counts

17 → 3

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 1 (*.f64 y x))
(/.f64 (-.f64 1 y) x)
(/.f64 1 (+.f64 (*.f64 y x) x))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(/.f64 1 (/.f64 x (-.f64 1 y)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
(.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 y x) (+.f64 -1 y)))
(/.f64 (exp.f64 (neg.f64 y)) x)
(/.f64 (/.f64 1 x) (exp.f64 y))
(/.f64 (pow.f64 (/.f64 x y) x) x)
(.f64 (-.f64 x (.f64 x y)) (pow.f64 x -2))
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
(pow.f64 (*.f64 x (exp.f64 y)) -1)
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Outputs
(/.f64 (exp.f64 (neg.f64 y)) x)
(/.f64 1 x)
(/.f64 (exp.f64 (neg.f64 y)) x)

Calls

3 calls:

120.0ms	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
51.0ms	x
46.0ms	y

Results

Error	Segments	Branch
0.3b	3	`x`
1.9b	2	`y`
0.6b	5	`(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)`

Compiler

Compiled 146 to 86 computations (41.1% saved)

bsearch672.0ms (6.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
524.0ms	0.0017352382398583288	114184006.31879717
147.0ms	-6485.810278240133	-0.001254518944148846

Compiler

Compiled 284 to 221 computations (22.2% saved)

regimes86.0ms (0.9%)

Counts

10 → 2

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 1 (*.f64 y x))
(/.f64 (-.f64 1 y) x)
(/.f64 1 (+.f64 (*.f64 y x) x))
(-.f64 (+.f64 1 (/.f64 1 x)) 1)
(/.f64 1 (/.f64 x (-.f64 1 y)))
(-.f64 (/.f64 1 x) (/.f64 y x))
(-.f64 (+.f64 1 (/.f64 (-.f64 1 y) x)) 1)
(.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 1 (.f64 x y)))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 y x) (+.f64 -1 y)))

Outputs
(/.f64 1 x)
(-.f64 (+.f64 1 (/.f64 1 x)) 1)

Calls

2 calls:

61.0ms	x
21.0ms	y

Results

Error	Segments	Branch
5.9b	3	`x`
1.9b	2	`y`

Compiler

Compiled 80 to 53 computations (33.8% saved)

bsearch20.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
19.0ms	29.98734520874927	16758261590773.621

Compiler

Compiled 34 to 26 computations (23.5% saved)

regimes72.0ms (0.7%)

Counts

4 → 3

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 1 (*.f64 y x))
(/.f64 (-.f64 1 y) x)
(/.f64 1 (+.f64 (*.f64 y x) x))

Outputs
(/.f64 1 (+.f64 (*.f64 y x) x))
(/.f64 1 x)
(/.f64 1 (+.f64 (*.f64 y x) x))

Calls

2 calls:

49.0ms	y
20.0ms	x

Results

Error	Segments	Branch
5.9b	3	`x`
10.2b	2	`y`

Compiler

Compiled 28 to 17 computations (39.3% saved)

bsearch328.0ms (3.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
236.0ms	0.0017352382398583288	114184006.31879717
91.0ms	-6485.810278240133	-0.001254518944148846

Compiler

Compiled 322 to 240 computations (25.5% saved)

regimes22.0ms (0.2%)

Accuracy

Total -52.1b remaining (-510.5%)

Threshold costs -52.1b (-510.5%)

Counts

3 → 2

Calls

Call 1

Inputs
(/.f64 1 x)
(/.f64 1 (*.f64 y x))
(/.f64 (-.f64 1 y) x)

Outputs
(/.f64 1 x)
(/.f64 1 (*.f64 y x))

Calls

2 calls:

11.0ms	y
10.0ms	x

Results

Error	Segments	Branch
10.3b	3	`x`
10.2b	2	`y`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch98.0ms (1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
97.0ms	7.83975516043117e+76	3.886811527469595e+82

Compiler

Compiled 144 to 111 computations (22.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	29	109
1	39	109
2	42	109
3	43	109

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -5810724383218509/4611686018427387904) (/.f64 (exp.f64 (neg.f64 y)) x) (if (<=.f64 x 112000000) (/.f64 1 x) (/.f64 (exp.f64 (neg.f64 y)) x)))
(if (<=.f64 y 10000000000) (/.f64 1 x) (-.f64 (+.f64 1 (/.f64 1 x)) 1))
(if (<=.f64 x -5810724383218509/4611686018427387904) (/.f64 1 (+.f64 (.f64 y x) x)) (if (<=.f64 x 112000000) (/.f64 1 x) (/.f64 1 (+.f64 (.f64 y x) x))))
(if (<=.f64 y 80000000000000003764810759672437567132476811262933046114229676279185996251136) (/.f64 1 x) (/.f64 1 (*.f64 y x)))
(/.f64 1 x)

Outputs
(if (<=.f64 x -5810724383218509/4611686018427387904) (/.f64 (exp.f64 (neg.f64 y)) x) (if (<=.f64 x 112000000) (/.f64 1 x) (/.f64 (exp.f64 (neg.f64 y)) x)))
(if (<=.f64 y 10000000000) (/.f64 1 x) (-.f64 (+.f64 1 (/.f64 1 x)) 1))
(if (<=.f64 y 10000000000) (/.f64 1 x) (+.f64 (+.f64 1 (/.f64 1 x)) -1))
(if (<=.f64 x -5810724383218509/4611686018427387904) (/.f64 1 (+.f64 (.f64 y x) x)) (if (<=.f64 x 112000000) (/.f64 1 x) (/.f64 1 (+.f64 (.f64 y x) x))))
(if (<=.f64 x -5810724383218509/4611686018427387904) (/.f64 1 (+.f64 x (.f64 x y))) (if (<=.f64 x 112000000) (/.f64 1 x) (/.f64 1 (+.f64 x (.f64 x y)))))
(if (<=.f64 y 80000000000000003764810759672437567132476811262933046114229676279185996251136) (/.f64 1 x) (/.f64 1 (*.f64 y x)))
(if (<=.f64 y 80000000000000003764810759672437567132476811262933046114229676279185996251136) (/.f64 1 x) (/.f64 1 (*.f64 x y)))
(/.f64 1 x)

Compiler

Compiled 85 to 56 computations (34.1% saved)

soundness419.0ms (4.3%)

Algorithm

3×	egg-herbie

Rules

702×	`associate-/l*_binary64`
586×	`associate-/r*_binary64`
522×	`unswap-sqr_binary64`
522×	`unswap-sqr_binary64`
443×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	13
2	25	13
3	54	13
4	133	13
5	327	13
6	878	13
7	3321	13
8	6606	13
0	286	3273
1	953	2761
2	3930	2296
0	9	17
1	16	13
2	25	13
3	54	13
4	133	13
5	327	13
6	878	13
7	3321	13
8	6606	13

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 85 to 53 computations (37.6% saved)

end82.0ms (0.8%)

Compiler: Compiled 77 to 47 computations (39% saved)

Iter	Nodes	Cost
0	9	124
1	16	106
2	25	106
3	35	106
4	48	106
5	74	106
6	130	106
7	253	106
8	494	79
9	732	79
10	829	79
11	895	79

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	11	268
1	21	163
2	31	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	525	163
9	670	163
10	716	163

Iter	Nodes	Cost
0	9	124
1	16	106
2	25	106
3	35	106
4	48	106
5	74	106
6	130	106
7	253	106
8	494	79
9	732	79
10	829	79
11	895	79

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	11	268
1	21	163
2	31	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	525	163
9	670	163
10	716	163

Details

analyze388.0ms (4%)

sample3.4s (35.1%)

preprocess61.0ms (0.6%)

simplify73.0ms (0.8%)

eval1.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series84.0ms (0.9%)

rewrite80.0ms (0.8%)

simplify109.0ms (1.1%)

eval165.0ms (1.7%)

prune78.0ms (0.8%)

localize11.0ms (0.1%)

series7.0ms (0.1%)

rewrite68.0ms (0.7%)

simplify70.0ms (0.7%)

localize8.0ms (0.1%)

localize12.0ms (0.1%)

series6.0ms (0.1%)

rewrite80.0ms (0.8%)

simplify72.0ms (0.7%)

localize20.0ms (0.2%)

series6.0ms (0.1%)

rewrite91.0ms (0.9%)

simplify54.0ms (0.6%)

localize16.0ms (0.2%)

series130.0ms (1.3%)

rewrite110.0ms (1.1%)

simplify97.0ms (1%)

eval103.0ms (1.1%)

prune56.0ms (0.6%)

localize21.0ms (0.2%)

series9.0ms (0.1%)

rewrite113.0ms (1.2%)

simplify45.0ms (0.5%)

localize29.0ms (0.3%)

series3.0ms (0%)

rewrite113.0ms (1.2%)

simplify46.0ms (0.5%)

localize14.0ms (0.1%)

series14.0ms (0.1%)

rewrite101.0ms (1%)

simplify295.0ms (3%)

localize12.0ms (0.1%)

series68.0ms (0.7%)

rewrite92.0ms (0.9%)

simplify98.0ms (1%)

eval230.0ms (2.4%)

prune156.0ms (1.6%)

localize13.0ms (0.1%)

series1.0ms (0%)

rewrite89.0ms (0.9%)

simplify15.0ms (0.2%)

localize48.0ms (0.5%)

series7.0ms (0.1%)

rewrite113.0ms (1.2%)

simplify125.0ms (1.3%)

localize12.0ms (0.1%)

series4.0ms (0%)

rewrite116.0ms (1.2%)

simplify75.0ms (0.8%)

eval95.0ms (1%)

prune82.0ms (0.8%)

regimes224.0ms (2.3%)

bsearch672.0ms (6.9%)

regimes86.0ms (0.9%)

bsearch20.0ms (0.2%)

regimes72.0ms (0.7%)

bsearch328.0ms (3.4%)

regimes22.0ms (0.2%)

bsearch98.0ms (1%)

simplify7.0ms (0.1%)

soundness419.0ms (4.3%)

end82.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	9	124
1	16	106
2	25	106
3	35	106
4	48	106
5	74	106
6	130	106
7	253	106
8	494	79
9	732	79
10	829	79
11	895	79

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	14	163
1	25	163
2	35	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	526	163
9	671	163
10	717	163

Iter	Nodes	Cost
0	11	268
1	21	163
2	31	163
3	48	163
4	68	163
5	101	163
6	166	163
7	298	163
8	525	163
9	670	163
10	716	163