Details

analyze116.0ms (3.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
28.6%	25%	62.5%	0%	0%	0%	12.5%	4
30.8%	25%	56.2%	0%	0%	0%	18.7%	5
36%	28.1%	50%	0%	0%	0%	21.9%	6
38.8%	29.7%	46.9%	0%	0%	0%	23.4%	7
40.2%	30.5%	45.3%	0%	0%	0%	24.2%	8
40.7%	30.8%	44.9%	0%	0%	0%	24.2%	9
41.2%	31.2%	44.5%	0%	0%	0%	24.2%	10
41.4%	31.3%	44.4%	0%	0%	0%	24.2%	11
41.5%	31.4%	44.3%	0%	0%	0%	24.3%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.6s (41.5%)

Results

895.0ms	2794×	body	1024	valid
333.0ms	3806×	body	256	valid
235.0ms	1369×	body	512	valid
87.0ms	287×	body	2048	valid
0.0ms	3×	body	256	unsamplable

Bogosity

preprocess14.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% 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

0.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (exp.f64 x) (expm1.f64 x))
1.0ms	x	@	0	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

516×	`pow1_binary64`
493×	`add-sqr-sqrt_binary64`
477×	`add-log-exp_binary64`
477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1287	8

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 (exp.f64 x) (expm1.f64 x))

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

Outputs

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

simplify175.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
470×	`fabs-mul_binary64`
446×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	104
1	48	104
2	94	104
3	213	104
4	327	104
5	572	104
6	1504	104
7	2330	104
8	2416	104
9	2549	104
10	2707	104
11	2961	104
12	3283	104
13	3707	104
14	4207	104
15	4809	104
16	5533	104
17	5856	104
18	6138	104
19	6358	104
20	6534	104
21	6616	104
22	7556	104

Stop Event

1×	node limit

Counts

42 → 39

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))

eval7.0ms (0.2%)

Compiler: Compiled 379 to 160 computations (57.8% saved)

prune10.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

0.4b

Counts

40 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	19.5b	(/.f64 1 x)
	19.8b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
▶	19.6b	(+.f64 (/.f64 1 x) 1/2)
▶	19.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	19.8b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	0.5b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

Compiler

Compiled 132 to 100 computations (24.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (exp.f64 x))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓	0.5b	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

Compiler

Compiled 33 to 11 computations (66.7% saved)

series5.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
1.0ms	x	@	inf	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
1.0ms	x	@	0	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
0.0ms	x	@	0	(sqrt.f64 (exp.f64 x))
0.0ms	x	@	0	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

rewrite65.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`pow1_binary64`
713×	`add-log-exp_binary64`
713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
695×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	184	23
2	2037	23

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
(sqrt.f64 (exp.f64 x))

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

Outputs

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

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

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

simplify75.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-def_binary64`
554×	`associate-*l/_binary64`
435×	`associate-*r/_binary64`
401×	`unswap-sqr_binary64`
298×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	296
1	120	270
2	278	270
3	772	264
4	1764	263
5	2885	263
6	3906	263
7	4973	263
8	7509	263

Stop Event

1×	node limit

Counts

133 → 128

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 x))))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))

Outputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(fma.f64 -1/24 x (/.f64 1 x))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (/.f64 1 x)))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 -31/967680 (pow.f64 x 5) (fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x (fma.f64 x (*.f64 x 7/5760) -1/24) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (-.f64 (exp.f64 x) 1)))
(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 x) (expm1.f64 x))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) 1))
(fma.f64 x (fma.f64 x 1/8 1/2) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/8 (.f64 x x) (fma.f64 1/2 x (+.f64 1 (.f64 (pow.f64 x 3) 1/48))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 3) 1/48 1)))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) (fma.f64 x 1/48 1/8) 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/48 1/8))) 1)

localize3.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.3b	(*.f64 1/12 x)

Compiler

Compiled 27 to 20 computations (25.9% saved)

series3.0ms (0.1%)

Counts

2 → 9

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 1/12 x)
0.0ms	x	@	inf	(*.f64 1/12 x)
0.0ms	x	@	-inf	(*.f64 1/12 x)
0.0ms	x	@	0	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
0.0ms	x	@	inf	(+.f64 (*.f64 1/12 x) (/.f64 1 x))

rewrite57.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

748×	`pow1_binary64`
701×	`add-log-exp_binary64`
701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
687×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	151	12
2	1947	12

Stop Event

1×	node limit

Counts

2 → 46

Calls

Call 1

Inputs
(*.f64 1/12 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/12 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 1/12 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 1/1728) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/144))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 1/1728))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 x)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/12 x (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 x x) 1/144) (-.f64 (*.f64 1/12 x) (/.f64 1 x))) (/.f64 (pow.f64 x -2) (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/12 x (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/144) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (/.f64 1 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 1/144) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))) (+.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x)) (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3)) (+.f64 (*.f64 (*.f64 x x) 1/144) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3)) (+.f64 (pow.f64 x -2) (-.f64 (*.f64 (*.f64 x x) 1/144) (/.f64 (*.f64 1/12 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2)) (-.f64 (*.f64 1/12 x) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/1728) (pow.f64 x -3))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 1/144) (-.f64 (pow.f64 x -2) (/.f64 (*.f64 1/12 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 1/144) (pow.f64 x -2))) (neg.f64 (-.f64 (*.f64 1/12 x) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (*.f64 (*.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/12 x (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/12 x (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/12 x (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/12 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/12 x)) 2) (cbrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 1/12 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/12 x)) (sqrt.f64 (*.f64 1/12 x)) (/.f64 1 x))))))

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	72
1	11	60
2	13	60

Stop Event

1×

saturated

Counts

55 → 50

Calls

Call 1

Inputs
(/.f64 1 x)
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))

Outputs
(/.f64 1 x)
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(+.f64 (/.f64 1 x) (*.f64 x 1/12))
(fma.f64 x 1/12 (/.f64 1 x))

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))
	0.0b	(+.f64 (*.f64 1/12 x) (/.f64 1 x))
✓	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.3b	(*.f64 1/12 x)

Compiler

Compiled 56 to 43 computations (23.2% saved)

series3.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	inf	(*.f64 -1/720 (pow.f64 x 3))
1.0ms	x	@	-inf	(*.f64 -1/720 (pow.f64 x 3))
0.0ms	x	@	inf	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))
0.0ms	x	@	0	(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))

rewrite67.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`fma-def_binary64`
549×	`log-prod_binary64`
320×	`pow2_binary64`
303×	`fma-neg_binary64`
220×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	273	22
2	3506	22

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

Inputs
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/720 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 6) 1/518400) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (cbrt.f64 -1/720)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 9) -1/373248000) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 6) 1/518400))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/720) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 9) -1/373248000))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 3 (log.f64 x) (log.f64 -1/720)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 6) 1/518400) (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))) (/.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2) (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 2) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 9) -1/373248000 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3)) (/.f64 1 (fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (*.f64 -1/720 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/518400))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 6) 1/518400) (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2)) (/.f64 1 (-.f64 (*.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (*.f64 -1/720 (pow.f64 x 3))) (*.f64 (pow.f64 x 6) 1/518400)) (fma.f64 (pow.f64 x 9) -1/373248000 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3))))))) (#(struct:change 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simplify171.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
472×	`fabs-mul_binary64`
445×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	138
1	39	138
2	64	138
3	126	138
4	199	138
5	424	138
6	1345	138
7	2090	138
8	2177	138
9	2310	138
10	2468	138
11	2713	138
12	3035	138
13	3458	138
14	3959	138
15	4558	138
16	5278	138
17	5599	138
18	5885	138
19	6109	138
20	6289	138
21	6371	138
22	7311	138

Stop Event

1×	node limit

Counts

118 → 115

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (.f64 1/12 x) (+.f64 (.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(+.f64 (.f64 1/12 x) (+.f64 (.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))

Outputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (.f64 1/12 x) (+.f64 (.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 1/12 x) (+.f64 (.f64 -1/720 (pow.f64 x 3)) (/.f64 1 x)))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)))

eval130.0ms (3.4%)

Compiler: Compiled 6425 to 4188 computations (34.8% saved)

prune47.0ms (1.3%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	378	2	380
Fresh	1	0	1
Picked	0	1	1
Done	1	4	5
Total	380	7	387

Error

0.4b

Counts

387 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.5b	(/.f64 1 x)
▶	19.8b	(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))
✓	19.6b	(+.f64 (/.f64 1 x) 1/2)
✓	19.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	19.8b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	0.5b	(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))

Compiler

Compiled 70 to 55 computations (21.4% saved)

localize19.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(sqrt.f64 (exp.f64 x))
✓	0.5b	(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))
✓	0.5b	(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))

Compiler

Compiled 43 to 24 computations (44.2% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))
1.0ms	x	@	0	(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))
1.0ms	x	@	inf	(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))
1.0ms	x	@	-inf	(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))

rewrite61.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`pow1_binary64`
842×	`add-log-exp_binary64`
842×	`log1p-expm1-u_binary64`
842×	`expm1-log1p-u_binary64`
823×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	247	18
2	2421	18

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

Inputs
(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))
(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))

Outputs

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

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

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
550×	`associate-/r*_binary64`
426×	`fma-neg_binary64`
390×	`fabs-div_binary64`
384×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	321
1	93	321
2	201	305
3	493	233
4	889	233
5	2316	233
6	5310	233
7	7356	233

Stop Event

1×	node limit

Counts

99 → 91

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 x))))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))

Outputs
(/.f64 1 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(fma.f64 -1/24 x (/.f64 1 x))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (/.f64 1 x)))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (/.f64 1 x)))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x)))
(fma.f64 x (fma.f64 7/5760 (*.f64 x x) -1/24) (/.f64 1 x))
(+.f64 (.f64 7/5760 (pow.f64 x 3)) (+.f64 (.f64 -1/24 x) (+.f64 (*.f64 -31/967680 (pow.f64 x 5)) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -1/24 x (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 7/5760 (pow.f64 x 3) (fma.f64 x -1/24 (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x (fma.f64 7/5760 (*.f64 x x) -1/24) (fma.f64 -31/967680 (pow.f64 x 5) (/.f64 1 x)))
(fma.f64 -31/967680 (pow.f64 x 5) (fma.f64 x -1/24 (fma.f64 7/5760 (pow.f64 x 3) (/.f64 1 x))))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (*.f64 1/2 x)) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1/2) (expm1.f64 x))
(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 (pow.f64 x 3) -1/720 1/2)))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (exp.f64 (.f64 1/2 x)) (-.f64 (exp.f64 x) 1)))
(*.f64 (/.f64 (pow.f64 (exp.f64 1/2) x) (expm1.f64 x)) (sqrt.f64 (exp.f64 x)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (pow.f64 (exp.f64 x) 1/2)))
(/.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 (exp.f64 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))

localize17.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))
✓	0.1b	(fma.f64 x 1/12 1/2)

Compiler

Compiled 39 to 30 computations (23.1% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(fma.f64 x 1/12 1/2)
0.0ms	x	@	0	(fma.f64 x 1/12 1/2)
0.0ms	x	@	-inf	(fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))
0.0ms	x	@	inf	(fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))
0.0ms	x	@	inf	(fma.f64 x 1/12 1/2)

rewrite68.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

603×	`prod-diff_binary64`
454×	`log-prod_binary64`
296×	`pow2_binary64`
285×	`pow-prod-down_binary64`
242×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	262	35
2	3001	35

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs
(fma.f64 x 1/12 1/2)
(fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))

Outputs

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x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x -1/720) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) 2) (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) (sqrt.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (*.f64 (pow.f64 x 3/2) -1/720) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 x 3) -1/720)) 2) (cbrt.f64 (*.f64 (pow.f64 x 3) -1/720)) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (pow.f64 x 3) -1/720)) (sqrt.f64 (*.f64 (pow.f64 x 3) -1/720)) (+.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 1 (cbrt.f64 x)) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))))))

simplify191.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
473×	`fabs-mul_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	340
1	55	320
2	105	304
3	215	304
4	313	304
5	567	304
6	1508	304
7	2338	304
8	2424	304
9	2557	304
10	2715	304
11	2968	304
12	3290	304
13	3712	304
14	4212	304
15	4811	304
16	5529	304
17	5850	304
18	6138	304
19	6362	304
20	6544	304
21	6626	304
22	7566	304

Stop Event

1×	node limit

Counts

152 → 132

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (*.f64 1/12 x))
1/2
(+.f64 1/2 (*.f64 1/12 x))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))

Outputs
1/2
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(*.f64 1/12 x)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
1/2
(+.f64 1/2 (*.f64 1/12 x))
(fma.f64 1/12 x 1/2)
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (+.f64 1/2 (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (+.f64 1/2 (/.f64 1 x)))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) 1/2)
(fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x 1/2))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 1/12 x (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x (fma.f64 x (*.f64 x -1/720) 1/12) (/.f64 1 x)))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) (+.f64 1/2 (/.f64 1 x)))

eval94.0ms (2.5%)

Compiler: Compiled 4394 to 2943 computations (33% saved)

prune31.0ms (0.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	0	0	0
Picked	1	0	1
Done	2	4	6
Total	261	6	267

Error

0.4b

Counts

267 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.5b	(/.f64 1 x)
▶	19.8b	(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))
✓	19.6b	(+.f64 (/.f64 1 x) 1/2)
✓	19.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	0.5b	(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

Compiler

Compiled 57 to 45 computations (21.1% saved)

localize16.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
	0.5b	(/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x))

Compiler

Compiled 40 to 28 computations (30% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

(*.f64 (/.f64 (exp.f64 (*.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

1.0ms

-inf

(*.f64 (/.f64 (exp.f64 (*.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

0.0ms

(*.f64 (/.f64 (exp.f64 (*.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

rewrite50.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`pow1_binary64`
785×	`add-log-exp_binary64`
785×	`log1p-expm1-u_binary64`
785×	`expm1-log1p-u_binary64`
768×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	206	8
2	2241	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

Inputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

Outputs

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

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-/l/_binary64`
501×	`fma-def_binary64`
366×	`associate-/r/_binary64`
363×	`associate-*l/_binary64`
306×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	152
1	58	152
2	118	128
3	291	104
4	614	104
5	2846	104

Stop Event

1×	node limit

Counts

52 → 48

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2) (-.f64 (exp.f64 x) 1))
(/.f64 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2) (expm1.f64 x))
(/.f64 (pow.f64 (exp.f64 x) 1) (expm1.f64 x))
(/.f64 (exp.f64 x) (expm1.f64 x))

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))
	0.1b	(*.f64 -1/720 (pow.f64 x 3))
	0.3b	(*.f64 1/12 x)

Compiler

Compiled 56 to 44 computations (21.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))))

0.0ms

inf

(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))))

0.0ms

-inf

(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (*.f64 1/12 x) (*.f64 -1/720 (pow.f64 x 3)))))

rewrite71.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`fma-def_binary64`
643×	`log-prod_binary64`
341×	`fma-neg_binary64`
267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	325	20
2	4370	18

Stop Event

1×	node limit

Counts

1 → 77

Calls

Call 1

Inputs
(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))) (/.f64 (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))) 2) (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (sqrt.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))) (pow.f64 x -1/2)) (hypot.f64 (sqrt.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 3)) (/.f64 1 (fma.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (-.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (/.f64 1 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2)) (/.f64 1 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (-.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (/.f64 1 x)) (pow.f64 x -2)) (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))) (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 3)) (fma.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (-.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (/.f64 1 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 3)) (+.f64 (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2) (-.f64 (pow.f64 x -2) (/.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2)) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 3))) (neg.f64 (fma.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (-.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) (/.f64 1 x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)) 2))) (neg.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)) (-.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)) 1/2) 1/4) (*.f64 x (+.f64 1/8 (pow.f64 (fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12)) 3)))) 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simplify178.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1274×	`sqr-pow_binary64`
666×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
467×	`fabs-mul_binary64`
443×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	140
1	54	140
2	106	136
3	221	136
4	319	136
5	577	136
6	1490	136
7	2316	136
8	2402	136
9	2535	136
10	2693	136
11	2944	136
12	3266	136
13	3688	136
14	4190	136
15	4790	136
16	5510	136
17	5831	136
18	6115	136
19	6335	136
20	6511	136
21	6593	136
22	7533	136

Stop Event

1×	node limit

Counts

89 → 90

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))

Outputs
(/.f64 1 x)
(+.f64 1/2 (/.f64 1 x))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (fma.f64 1/12 x (/.f64 1 x)))
(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(fma.f64 x 1/12 (+.f64 (/.f64 1 x) 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x 1/12 (+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (+.f64 (/.f64 1 x) 1/2)))
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x 1/12 (+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (+.f64 (/.f64 1 x) 1/2)))
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))
(*.f64 -1/720 (pow.f64 x 3))
(+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))
(fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3)))
(fma.f64 -1/720 (pow.f64 x 3) (*.f64 x 1/12))
(.f64 x (fma.f64 x (.f64 x -1/720) 1/12))
(.f64 x (fma.f64 -1/720 (.f64 x x) 1/12))
(+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 1/12 x (*.f64 -1/720 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 x 1/12 (*.f64 -1/720 (pow.f64 x 3))))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2))
(fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2)
(+.f64 1/2 (+.f64 (.f64 1/12 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x))))
(fma.f64 x 1/12 (+.f64 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) (+.f64 (/.f64 1 x) 1/2)))
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (/.f64 1 x)) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/720 (*.f64 x x) 1/12) 1/2))

eval81.0ms (2.1%)

Compiler: Compiled 3884 to 2733 computations (29.6% saved)

prune28.0ms (0.7%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	206	8	214

Error

0.4b

Counts

214 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.5b	(/.f64 1 x)
✓	19.8b	(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))
✓	19.6b	(+.f64 (/.f64 1 x) 1/2)
✓	19.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	0.5b	(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
	1.4b	(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
	1.3b	(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))

Compiler

Compiled 83 to 66 computations (20.5% saved)

regimes17.0ms (0.5%)

Counts

14 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
(.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (exp.f64 (.f64 x 1/2)) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

Outputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))

Calls

3 calls:

7.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.5b	1	`(exp.f64 x)`

Compiler

Compiled 162 to 113 computations (30.2% saved)

regimes14.0ms (0.4%)

Counts

11 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/720 (pow.f64 x 3) 1/2)))
(+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 1/2)))

Outputs
(/.f64 (exp.f64 x) (expm1.f64 x))

Calls

3 calls:

6.0ms	x
2.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.5b	1	`(exp.f64 x)`

Compiler

Compiled 123 to 91 computations (26% saved)

regimes8.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 (/.f64 1 x) (+.f64 1/2 (+.f64 (.f64 1/12 x) (.f64 -1/720 (pow.f64 x 3)))))

Outputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
1.3b	1	`x`

Compiler

Compiled 74 to 58 computations (21.6% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))

Outputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
1.4b	1	`x`

Compiler

Compiled 30 to 23 computations (23.3% saved)

regimes5.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Outputs
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
19.5b	1	`x`

Compiler

Compiled 20 to 15 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.5b remaining (-2.3%)

Threshold costs -0.5b (-2.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)

Outputs
(/.f64 1 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
19.5b	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	35	74

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(/.f64 1 x)

Outputs
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 (exp.f64 (*.f64 x 1/2)) (expm1.f64 x)))
(/.f64 (exp.f64 x) (expm1.f64 x))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (+.f64 (*.f64 x -1/24) (/.f64 1 x)))
(.f64 (/.f64 (exp.f64 (.f64 x 1/2)) 1) (/.f64 1 x))
(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 x))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (+.f64 (/.f64 1 x) (*.f64 x 1/12)))
(/.f64 1 x)

Compiler

Compiled 55 to 42 computations (23.6% saved)

soundness9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

Compiler

Compiled 14 to 9 computations (35.7% saved)

end42.0ms (1.1%)

Compiler: Compiled 50 to 36 computations (28% saved)

Details

analyze116.0ms (3.1%)

sample1.6s (41.5%)

preprocess14.0ms (0.4%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite42.0ms (1.1%)

simplify175.0ms (4.6%)

eval7.0ms (0.2%)

prune10.0ms (0.3%)

localize12.0ms (0.3%)

series5.0ms (0.1%)

rewrite65.0ms (1.7%)

simplify75.0ms (2%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

localize10.0ms (0.3%)

series3.0ms (0.1%)

rewrite57.0ms (1.5%)

simplify8.0ms (0.2%)

localize22.0ms (0.6%)

series3.0ms (0.1%)

rewrite67.0ms (1.8%)

simplify171.0ms (4.5%)

eval130.0ms (3.4%)

prune47.0ms (1.3%)

localize19.0ms (0.5%)

series5.0ms (0.1%)

rewrite61.0ms (1.6%)

simplify61.0ms (1.6%)

localize17.0ms (0.5%)

series3.0ms (0.1%)

rewrite68.0ms (1.8%)

simplify191.0ms (5.1%)

eval94.0ms (2.5%)

prune31.0ms (0.8%)

localize16.0ms (0.4%)

series2.0ms (0.1%)

rewrite50.0ms (1.3%)

simplify34.0ms (0.9%)

localize23.0ms (0.6%)

series1.0ms (0%)

rewrite71.0ms (1.9%)

simplify178.0ms (4.7%)

eval81.0ms (2.1%)

prune28.0ms (0.7%)

regimes17.0ms (0.5%)

regimes14.0ms (0.4%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness9.0ms (0.2%)

end42.0ms (1.1%)

Profiling