Details

analyze500.0ms (8.9%)

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
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
43.7%	51.5%	4.8%	7
48.4%	46.8%	4.8%	8
55.4%	37.5%	7.1%	9
58.1%	34.7%	7.1%	10
61.9%	29.9%	8.3%	11
63.3%	28.4%	8.3%	12
65.2%	25.9%	8.9%	13
66%	25.1%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.1s (72.7%)

Results

2.7s	2662×	body	8192	exit
1.1s	7639×	body	128	valid
141.0ms	194×	body	1024	valid
111.0ms	248×	body	512	valid
46.0ms	174×	body	256	valid
12.0ms	93×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 24 to 18 computations (25% saved)

preprocess38.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

732×	`times-frac_binary64`
438×	`associate-/r/_binary64`
300×	`fma-def_binary64`
232×	`unswap-sqr_binary64`
157×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	32	22
2	45	22
3	71	22
4	101	22
5	150	22
6	231	22
7	320	22
8	425	22
9	543	22
10	635	22
11	675	22
12	823	22
13	1264	22
14	2823	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
(-.f64 (log.f64 (+.f64 1 (exp.f64 y))) (*.f64 y x))

Outputs
(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(-.f64 (log.f64 (+.f64 1 (exp.f64 y))) (*.f64 y x))
(-.f64 (log1p.f64 (exp.f64 y)) (*.f64 x y))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify32.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

369×	`times-frac_binary64`
363×	`associate-l_binary64`
285×	`associate-/l/_binary64`
280×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	30	11
3	47	11
4	66	11
5	100	11
6	154	11
7	205	11
8	273	11
9	352	11
10	414	11
11	440	11
12	519	11
13	747	11
14	1549	11
15	4642	11

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Outputs
(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

prune2.0ms (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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.7b	(log1p.f64 (exp.f64 x))

series60.0ms (1.1%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	x	@	inf	(log1p.f64 (exp.f64 x))
26.0ms	x	@	-inf	(log1p.f64 (exp.f64 x))
4.0ms	y	@	0	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
1.0ms	x	@	0	(log1p.f64 (exp.f64 x))
0.0ms	y	@	-inf	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite42.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

792×	`pow1_binary64`
733×	`expm1-log1p-u_binary64`
732×	`log1p-expm1-u_binary64`
78×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	16
2	2012	16

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

Inputs
(log1p.f64 (exp.f64 x))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

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

Outputs

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

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

simplify38.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-neg_binary64`
566×	`associate-l_binary64`
366×	`fma-def_binary64`
342×	`unswap-sqr_binary64`
313×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	363
1	86	333
2	182	333
3	431	321
4	1390	321
5	3741	321

Stop Event

1×	node limit

Counts

91 → 74

Calls

Call 1

Inputs
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (log.f64 2)))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log.f64 2)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(+.f64 (.f64 (-.f64 1/2 y) x) (+.f64 (.f64 1/8 (pow.f64 x 2)) (log.f64 2)))
(+.f64 (.f64 (-.f64 1/2 y) x) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(.f64 -1 (.f64 y x))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(log.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(.f64 -1 (.f64 y x))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))

Outputs
(log.f64 2)
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (log.f64 2)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (log.f64 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) (log.f64 2)))
(fma.f64 x (fma.f64 x 1/8 1/2) (log.f64 2))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (fma.f64 x 1/8 1/2) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2)))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(log.f64 2)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(fma.f64 x (-.f64 1/2 y) (log.f64 2))
(+.f64 (.f64 (-.f64 1/2 y) x) (+.f64 (.f64 1/8 (pow.f64 x 2)) (log.f64 2)))
(fma.f64 (-.f64 1/2 y) x (fma.f64 1/8 (*.f64 x x) (log.f64 2)))
(fma.f64 x (-.f64 1/2 y) (fma.f64 1/8 (*.f64 x x) (log.f64 2)))
(fma.f64 x (-.f64 1/2 y) (fma.f64 x (*.f64 x 1/8) (log.f64 2)))
(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
(+.f64 (.f64 (-.f64 1/2 y) x) (+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/192 (pow.f64 x 4)) (log.f64 2))))
(fma.f64 (-.f64 1/2 y) x (fma.f64 1/8 (*.f64 x x) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (-.f64 1/2 y) (fma.f64 1/8 (*.f64 x x) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (-.f64 1/2 y) (fma.f64 x (*.f64 x 1/8) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2))))
(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (fma.f64 -1/192 (pow.f64 x 4) (log.f64 2)))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 x (neg.f64 y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 x (neg.f64 y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(log.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 x (neg.f64 y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 x y))
(*.f64 x (neg.f64 y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+.f64 (log.f64 (+.f64 1 (exp.f64 x))) (.f64 -1 (.f64 y x)))
(+.f64 (log1p.f64 (exp.f64 x)) (neg.f64 (*.f64 x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

prune36.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Error

0.4b

Counts

75 → 2

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	12.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 1037 to 380 computations (63.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series9.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
3.0ms	x	@	0	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
1.0ms	y	@	inf	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
1.0ms	x	@	-inf	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
0.0ms	y	@	-inf	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

rewrite36.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`pow1_binary64`
775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	170	10
2	2028	10

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(fma.f64 x (-.f64 1/2 y) (log.f64 2))

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

Outputs

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

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

267×	`fma-neg_binary64`
251×	`fma-def_binary64`
87×	`cancel-sign-sub-inv_binary64`
43×	`sub-neg_binary64`
40×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	216
1	33	216
2	60	216
3	106	216
4	157	216
5	252	216
6	454	216
7	665	216
8	877	216
9	1096	216
10	1116	216

Stop Event

1×

saturated

Counts

47 → 32

Calls

Call 1

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

Outputs
(log.f64 2)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(*.f64 (-.f64 1/2 y) x)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(*.f64 (-.f64 1/2 y) x)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 x (neg.f64 y))
(*.f64 y (neg.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))

prune25.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	30	4	34

Error

0.4b

Counts

34 → 4

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	24.9b	(exp.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
	24.9b	(expm1.f64 (log1p.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	12.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 409 to 318 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.0b	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	0.7b	(exp.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

series7.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
1.0ms	y	@	0	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
1.0ms	y	@	inf	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
1.0ms	x	@	inf	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
1.0ms	x	@	-inf	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

837×	`log1p-expm1-u_binary64`
837×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
91×	`add-log-exp_binary64`
90×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	194	22
2	2214	22

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

Inputs
(exp.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

Outputs

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

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

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

620×	`associate-/l*_binary64`
525×	`associate-/r*_binary64`
471×	`fma-def_binary64`
178×	`associate-*l/_binary64`
166×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1231
1	412	1178
2	1480	1148

Stop Event

1×	node limit

Counts

92 → 100

Calls

Call 1

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

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

prune87.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	132	4	136

Error

0.4b

Counts

136 → 4

Alt Table

Status	Error	Program
	25.1b	(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) 2)) (cbrt.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))))
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	12.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
▶	25.1b	(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))))

Compiler

Compiled 2561 to 2019 computations (21.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
✓	0.5b	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	0.6b	(expm1.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))))
✓	0.7b	(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))))

series18.0ms (0.3%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
2.0ms	x	@	-inf	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
2.0ms	x	@	inf	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
2.0ms	y	@	-inf	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
2.0ms	y	@	0	(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

rewrite52.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

912×	`expm1-log1p-u_binary64`
911×	`log1p-expm1-u_binary64`
102×	`add-sqr-sqrt_binary64`
99×	`add-log-exp_binary64`
99×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	215	36
2	2420	36

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

Inputs

(exp.f64 (expm1.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))))

(expm1.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))))

(log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

Outputs

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

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

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

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
304×	`associate-/r*_binary64`
298×	`fma-def_binary64`
230×	`associate-r_binary64`
211×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	352	4014
1	1178	3770

Stop Event

1×	node limit

Counts

137 → 169

Calls

Call 1

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

Outputs
(log.f64 2)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(*.f64 (-.f64 1/2 y) x)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(*.f64 (-.f64 1/2 y) x)
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 (-.f64 1/2 y) x) (log.f64 2))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (*.f64 1/2 x) (log.f64 2))
(fma.f64 1/2 x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(.f64 -1 (.f64 y x))
(neg.f64 (*.f64 y x))
(*.f64 y (neg.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (*.f64 y x))))
(fma.f64 (-.f64 1/2 y) x (log.f64 2))
(log.f64 (log.f64 2))
(+.f64 (log.f64 (log.f64 2)) (.f64 (-.f64 (.f64 1/2 (/.f64 1 (log.f64 2))) (/.f64 y (log.f64 2))) x))
(+.f64 (log.f64 (log.f64 2)) (*.f64 x (-.f64 (/.f64 1/2 (log.f64 2)) (/.f64 y (log.f64 2)))))
(fma.f64 x (-.f64 (/.f64 1/2 (log.f64 2)) (/.f64 y (log.f64 2))) (log.f64 (log.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 (-.f64 1/2 y) 2) (pow.f64 x 2)) (pow.f64 (log.f64 2) 2))) (+.f64 (log.f64 (log.f64 2)) (.f64 (-.f64 (.f64 1/2 (/.f64 1 (log.f64 2))) (/.f64 y (log.f64 2))) x)))
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(fma.f64 -1 (log.f64 (/.f64 -1 x)) (+.f64 (/.f64 (log.f64 2) (*.f64 (-.f64 1/2 y) x)) (log.f64 (neg.f64 (-.f64 1/2 y)))))
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(fma.f64 -1 (log.f64 (/.f64 -1 x)) (fma.f64 -1/2 (/.f64 (pow.f64 (log.f64 2) 2) (.f64 (pow.f64 (-.f64 1/2 y) 2) (.f64 x x))) (+.f64 (/.f64 (log.f64 2) (*.f64 (-.f64 1/2 y) x)) (log.f64 (neg.f64 (-.f64 1/2 y))))))
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(fma.f64 -1 (log.f64 (/.f64 -1 x)) (fma.f64 -1/2 (/.f64 (pow.f64 (log.f64 2) 2) (.f64 (pow.f64 (-.f64 1/2 y) 2) (.f64 x x))) (+.f64 (fma.f64 1/3 (/.f64 (pow.f64 (log.f64 2) 3) (.f64 (pow.f64 (-.f64 1/2 y) 3) (pow.f64 x 3))) (/.f64 (log.f64 2) (.f64 (-.f64 1/2 y) x))) (log.f64 (neg.f64 (-.f64 1/2 y))))))
(-.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (log.f64 2) 2) (.f64 x (.f64 x (pow.f64 (-.f64 1/2 y) 2)))) (+.f64 (fma.f64 1/3 (/.f64 (pow.f64 (log.f64 2) 3) (.f64 (pow.f64 (-.f64 1/2 y) 3) (pow.f64 x 3))) (/.f64 (log.f64 2) (.f64 (-.f64 1/2 y) x))) (log.f64 (neg.f64 (-.f64 1/2 y))))) (log.f64 (/.f64 -1 x)))
(log.f64 (+.f64 (*.f64 1/2 x) (log.f64 2)))
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(+.f64 (fma.f64 1/6 (/.f64 (fma.f64 -2 (+.f64 (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 3) (.f64 (pow.f64 x 3) (pow.f64 (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1)) 3))) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 3) (.f64 (pow.f64 x 3) (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1))))) (.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 3) (pow.f64 (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1)) 2)))) (pow.f64 y 3)) (/.f64 (.f64 -1/2 (+.f64 (/.f64 (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 x x)) (pow.f64 (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1)) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 (.f64 x x) (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1)))))) (.f64 y y))) (-.f64 (log1p.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 y))) (/.f64 (/.f64 (fma.f64 1/2 x (log.f64 2)) (*.f64 y x)) (+.f64 (log.f64 (neg.f64 x)) (+.f64 (log.f64 y) 1)))))
(log.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))))
(log.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))
(log.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))
(+.f64 (log.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))) (.f64 -1 (/.f64 (+.f64 (/.f64 (log.f64 2) (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) x)) (.f64 1/2 (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))))) y)))
(+.f64 (log.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x)))) (neg.f64 (/.f64 (+.f64 (/.f64 (log.f64 2) (*.f64 x (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) (/.f64 1/2 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) y)))
(-.f64 (log.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y))))) (/.f64 (+.f64 (/.f64 (log.f64 2) (*.f64 x (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) (/.f64 1/2 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) y))
(+.f64 (log.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) 2))) (.f64 -1 (/.f64 (pow.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 2) (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) (pow.f64 x 2))))) (pow.f64 y 2))) (.f64 -1 (/.f64 (+.f64 (/.f64 (log.f64 2) (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) x)) (.f64 1/2 (/.f64 1 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))))) y))))
(+.f64 (log.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x)))) (fma.f64 1/2 (/.f64 (.f64 -1 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 (.f64 x x) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))))) (.f64 y y)) (neg.f64 (/.f64 (+.f64 (/.f64 (log.f64 2) (*.f64 x (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) (/.f64 1/2 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) y))))
(-.f64 (+.f64 (log.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y))))) (/.f64 (.f64 -1/2 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 (.f64 x x) (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))))) (.f64 y y))) (/.f64 (+.f64 (/.f64 (log.f64 2) (*.f64 x (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) (/.f64 1/2 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) y))
(+.f64 (log.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) 2))) (.f64 -1 (/.f64 (pow.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 2) (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) (pow.f64 x 2))))) (pow.f64 y 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 (log.f64 2) (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) x)) (.f64 1/2 (/.f64 1 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x)))))) y)) (.f64 -1/6 (/.f64 (+.f64 (.f64 3 (/.f64 (.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) (pow.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 2)) (.f64 (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 3) (pow.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) 3))) (.f64 2 (/.f64 (pow.f64 (+.f64 (.f64 1/2 x) (log.f64 2)) 3) (.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 y))) (+.f64 1 (log.f64 x))) (pow.f64 x 3)))))) (pow.f64 y 3))))))
(+.f64 (log.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x)))) (fma.f64 1/2 (/.f64 (.f64 -1 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 (.f64 x x) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))))) (.f64 y y)) (fma.f64 -1 (/.f64 (+.f64 (/.f64 (log.f64 2) (.f64 x (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) (/.f64 1/2 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))))) y) (.f64 -1/6 (/.f64 (fma.f64 3 (.f64 (/.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 x x))) (.f64 2 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 3) (pow.f64 (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x))) 3)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 3) (.f64 (pow.f64 x 3) (fma.f64 -1 (log.f64 (/.f64 -1 y)) (+.f64 1 (log.f64 x)))))))) (pow.f64 y 3))))))
(+.f64 (/.f64 (.f64 -1/2 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 2) (pow.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))) 2)) (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2) (.f64 (.f64 x x) (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))))) (.f64 y y)) (+.f64 (fma.f64 -1/6 (/.f64 (fma.f64 2 (+.f64 (/.f64 (pow.f64 (+.f64 1/2 (/.f64 (log.f64 2) x)) 3) (pow.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))) 3)) (/.f64 (/.f64 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 3) (pow.f64 x 3)) (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) (/.f64 (/.f64 (.f64 (.f64 3 (pow.f64 (fma.f64 1/2 x (log.f64 2)) 2)) (+.f64 1/2 (/.f64 (log.f64 2) x))) (.f64 x x)) (pow.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))) 2))) (pow.f64 y 3)) (/.f64 (neg.f64 (+.f64 (/.f64 (log.f64 2) (.f64 x (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))) (/.f64 1/2 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y))))))) y)) (log.f64 (+.f64 1 (-.f64 (log.f64 x) (log.f64 (/.f64 -1 y)))))))

prune205.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	235	4	239

Error

0.4b

Counts

239 → 4

Alt Table

Status	Error	Program
	58.0b	(exp.f64 (expm1.f64 (pow.f64 (sqrt.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))) 2)))
✓	0.8b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	25.4b	(exp.f64 (expm1.f64 (pow.f64 (cbrt.f64 (log1p.f64 (log.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))) 3)))
✓	12.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 8097 to 6565 computations (18.9% saved)

regimes71.0ms (1.3%)

Accuracy

Total 0.3b remaining (51.9%)

Threshold costs 0.3b (51.9%)

Counts

32 → 1

Compiler

Compiled 332 to 252 computations (24.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	25	11
3	31	11
4	35	11
5	36	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Outputs
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

end67.0ms (1.2%)

Stop Event

1×

fuel

Compiler

Compiled 68 to 53 computations (22.1% saved)

Details

analyze500.0ms (8.9%)

sample4.1s (72.7%)

preprocess38.0ms (0.7%)

simplify32.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series60.0ms (1.1%)

rewrite42.0ms (0.7%)

simplify38.0ms (0.7%)

prune36.0ms (0.6%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite36.0ms (0.6%)

simplify29.0ms (0.5%)

prune25.0ms (0.4%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite40.0ms (0.7%)

simplify33.0ms (0.6%)

prune87.0ms (1.6%)

localize15.0ms (0.3%)

series18.0ms (0.3%)

rewrite52.0ms (0.9%)

simplify62.0ms (1.1%)

prune205.0ms (3.7%)

regimes71.0ms (1.3%)

simplify2.0ms (0%)

end67.0ms (1.2%)

Profiling