Details

analyze120.0ms (2.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.3s (26.1%)

Results

687.0ms	2661×	body	1024	valid
301.0ms	3822×	body	256	valid
240.0ms	1455×	body	512	valid
106.0ms	318×	body	2048	valid
0.0ms	3×	body	256	invalid

preprocess15.0ms (0.3%)

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 (0.1%)

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))

eval1.0ms (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

1.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

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))

rewrite43.0ms (0.8%)

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))))))))

simplify180.0ms (3.5%)

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 (0.1%)

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

prune10.0ms (0.2%)

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

0.8b

Counts

40 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
▶	21.5b	(/.f64 1 x)
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
	21.5b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	21.2b	(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
▶	21.2b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	21.2b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 122 to 92 computations (24.6% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 x))
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	1.0b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
✓	1.0b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 34 to 14 computations (58.8% saved)

series6.0ms (0.1%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
1.0ms	x	@	0	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
1.0ms	x	@	inf	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
0.0ms	x	@	0	(sqrt.f64 (exp.f64 x))
0.0ms	x	@	0	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))

rewrite240.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

773×	`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: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	176	29
2	2081	29

Stop Event

1×	node limit

Counts

4 → 82

Calls

Call 1

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

simplify208.0ms (4%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
637×	`distribute-rgt-neg-in_binary64`
537×	`fma-def_binary64`
487×	`distribute-lft-neg-in_binary64`
401×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	384
1	130	358
2	306	358
3	860	352
4	1996	352
5	2976	352
6	4908	352

Stop Event

1×	node limit

Counts

122 → 112

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

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)

localize11.0ms (0.2%)

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	@	inf	(*.f64 1/12 x)
0.0ms	x	@	0	(*.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))

rewrite92.0ms (1.8%)

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))))))

simplify12.0ms (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))

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 15 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`pow1_binary64`
790×	`add-log-exp_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
776×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	172	16
2	2131	16

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/12) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/12) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x 1/12 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 2) (cbrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 1/12) 3) 1/8) (+.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) (-.f64 1/4 (*.f64 (*.f64 x 1/12) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/12) (*.f64 x 1/12)) 1/4) (-.f64 (*.f64 x 1/12) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 1/2)))))))

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	171
1	23	149
2	28	149
3	30	149

Stop Event

1×

saturated

Counts

78 → 63

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

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

eval93.0ms (1.8%)

Compiler: Compiled 3587 to 2163 computations (39.7% saved)

prune35.0ms (0.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	0	1	1
Picked	1	0	1
Done	2	3	5
Total	253	8	261

Error

0.8b

Counts

261 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.2b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
▶	1.0b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (exp.f64 (*.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
▶	21.5b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	39.5b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	1.2b	(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
✓	21.2b	(+.f64 (/.f64 1 x) 1/2)
✓	21.5b	(/.f64 1 x)

Compiler

Compiled 160 to 124 computations (22.5% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (exp.f64 x))
	0.0b	(/.f64 1 (expm1.f64 x))
✓	1.0b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (exp.f64 (*.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
✓	1.0b	(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 44 to 26 computations (40.9% 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)) (/.f64 1 (expm1.f64 x)))
1.0ms	x	@	inf	(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x)))
1.0ms	x	@	0	(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x)))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (exp.f64 (*.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
1.0ms	x	@	inf	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (exp.f64 (*.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

914×	`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: 1 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	235	18
2	2461	18

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

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

simplify66.0ms (1.3%)

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

64 → 55

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))

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
✓	0.3b	(*.f64 x 1/12)

Compiler

Compiled 25 to 19 computations (24% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 x 1/12)
0.0ms	x	@	inf	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
0.0ms	x	@	-inf	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
0.0ms	x	@	0	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
0.0ms	x	@	inf	(*.f64 x 1/12)

rewrite149.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

875×	`prod-diff_binary64`
620×	`unpow-prod-down_binary64`
408×	`log-prod_binary64`
342×	`fma-def_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	204	15
2	2775	15

Stop Event

1×	node limit

Counts

2 → 101

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/12)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/12))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x 1/12))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/12) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 1/144) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/12) 3) 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 x) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/12) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x 1/12)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 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 1/2))) (/.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 2) (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (/.f64 1 (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 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 1/2) 3)) (pow.f64 (/.f64 1 (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) (pow.f64 x -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (/.f64 1 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (pow.f64 (/.f64 1 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 2) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 2) (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))) 1/3) (cbrt.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))) 2) 3) (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) (pow.f64 x -2)) (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3)) (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 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 1/2) 3)) (+.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (-.f64 (pow.f64 x -2) (/.f64 (fma.f64 x 1/12 1/2) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2)) (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))) (neg.f64 (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 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 1/2) 2))) (neg.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) (*.f64 x (fma.f64 (pow.f64 x 3) 1/1728 1/8))) (*.f64 x (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) (*.f64 (neg.f64 x) (fma.f64 (pow.f64 x 3) 1/1728 1/8))) (*.f64 (neg.f64 x) (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (fma.f64 x 1/12 -1/2) (*.f64 x (fma.f64 (*.f64 x x) 1/144 -1/4))) (*.f64 x (fma.f64 x 1/12 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 (fma.f64 x 1/12 -1/2) (*.f64 (neg.f64 x) (fma.f64 (*.f64 x x) 1/144 -1/4))) (*.f64 (neg.f64 x) (fma.f64 x 1/12 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 1/8) x (*.f64 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) 1)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (fma.f64 (*.f64 x x) 1/144 -1/4) x (*.f64 (fma.f64 x 1/12 -1/2) 1)) (*.f64 (fma.f64 x 1/12 -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 1/8) (neg.f64 x) (*.f64 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) -1)) (*.f64 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (fma.f64 (*.f64 x x) 1/144 -1/4) (neg.f64 x) (*.f64 (fma.f64 x 1/12 -1/2) -1)) (*.f64 (fma.f64 x 1/12 -1/2) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3) 1/8) (+.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2) (-.f64 1/4 (*.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x 1/12 1/2) 2) (pow.f64 x -2)) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2) 1/4) (-.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (fma.f64 x 1/12 1/2) (-.f64 (fma.f64 x 1/12 1/2) (/.f64 1 x)) (pow.f64 x -2)) (+.f64 (pow.f64 x -3) (pow.f64 (fma.f64 x 1/12 1/2) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/12 1/2) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (exp.f64 (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 x 1/12 1/2)) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 1/2))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/12) 1 (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 1/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 (/.f64 1 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/12 1/2) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 1/12 1/2)) (pow.f64 (cbrt.f64 (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 x 1/12 1/2)) 2) (cbrt.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 (cbrt.f64 x) 1/12) (+.f64 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 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 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/12)) (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (cbrt.f64 (*.f64 x 1/12)) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 1/2)) (sqrt.f64 (fma.f64 x 1/12 1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (+.f64 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 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (sqrt.f64 (*.f64 x 1/12)) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 x 1/12 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 1/8) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 1/144 1/4) (*.f64 x 1/24))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (*.f64 x x) 1/144 -1/4) (/.f64 1 (fma.f64 x 1/12 -1/2)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 1/2 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 1/2 (/.f64 1 x)))))))

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	147
1	22	143
2	27	143
3	29	143

Stop Event

1×

saturated

Counts

125 → 110

Calls

Call 1

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

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

localize23.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	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)

series2.0ms (0%)

Counts

1 → 0

Calls

3 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))

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`pow1_binary64`
499×	`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	6	7
1	129	7
2	1325	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

Calls

Call 1

Inputs

Outputs

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 x) (*.f64 1/12 x))
✓	0.2b	(.f64 (.f64 x x) 1/144)
	0.3b	(*.f64 1/12 x)
✓	26.6b	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))

Compiler

Compiled 76 to 49 computations (35.5% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
1.0ms	x	@	inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
1.0ms	x	@	-inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
0.0ms	x	@	inf	(.f64 (.f64 x x) 1/144)
0.0ms	x	@	0	(.f64 (.f64 x x) 1/144)

rewrite217.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`log-prod_binary64`
532×	`fma-def_binary64`
258×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	325	27
2	4574	23

Stop Event

1×	node limit

Counts

3 → 205

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x)))
(.f64 (.f64 x x) 1/144)
(-.f64 (/.f64 1 x) (*.f64 1/12 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 x -2) (fma.f64 x -1/12 (/.f64 1 x))) (neg.f64 (*.f64 1/144 (/.f64 (*.f64 x x) (fma.f64 x -1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x)))) (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (fma.f64 x -1/12 (/.f64 1 x))) (*.f64 1/144 (/.f64 (*.f64 x x) (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 1/12 (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2) (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) (*.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (/.f64 1 (neg.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) 1) (/.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 1) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (fma.f64 x -1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) 2)) (/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) (pow.f64 (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) 2)) (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (pow.f64 (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) 2)) (/.f64 (sqrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))) (/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) 2) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))) (/.f64 (cbrt.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (-.f64 (pow.f64 x -3) (pow.f64 (*.f64 x 1/12) 3))) (fma.f64 (*.f64 x 1/12) (fma.f64 x 1/12 (/.f64 1 x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2))) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x 1/12 (/.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) (neg.f64 (fma.f64 x -1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (pow.f64 (exp.f64 1/12) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (*.f64 x 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (*.f64 x 1/12)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/12))) (exp.f64 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (pow.f64 (exp.f64 1/12) x) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/12))) (+.f64 1 (expm1.f64 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 (*.f64 x x) -1/144 (pow.f64 x -2)) 3) (pow.f64 (fma.f64 x -1/12 (/.f64 1 x)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/12 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/12 (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -2) (/.f64 1 (fma.f64 x -1/12 (/.f64 1 x))) (neg.f64 (*.f64 1/144 (/.f64 (*.f64 x x) (fma.f64 x -1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (pow.f64 x -2) (fma.f64 x -1/12 (/.f64 1 x))) (neg.f64 (*.f64 1/144 (/.f64 (*.f64 x x) (fma.f64 x -1/12 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/12) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/12)) (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (cbrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x 1/144)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (sqrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 x 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x 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(fma.f64 (*.f64 x -1/12) 1 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (sqrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x 1/12) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) 1/12 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3) (pow.f64 (*.f64 x 1/12) 3)) (/.f64 1 (fma.f64 (*.f64 x 1/12) (fma.f64 x 1/12 (/.f64 1 x)) (pow.f64 x -2))) (fma.f64 (*.f64 x -1/12) 1 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3) (pow.f64 (*.f64 x 1/12) 3)) (/.f64 1 (fma.f64 (*.f64 x 1/12) (fma.f64 x 1/12 (/.f64 1 x)) (pow.f64 x -2))) (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x -3) (pow.f64 (*.f64 x 1/12) 3)) (/.f64 1 (fma.f64 (*.f64 x 1/12) (fma.f64 x 1/12 (/.f64 1 x)) (pow.f64 x -2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/12 x (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 x -1/12)) (cbrt.f64 (*.f64 x -1/12))) (cbrt.f64 (*.f64 x -1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -1/12)) (sqrt.f64 (*.f64 x -1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -4))) (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -4))) (sqrt.f64 (cbrt.f64 (pow.f64 x -2))) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2)) (cbrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (sqrt.f64 (*.f64 x 1/12))) (sqrt.f64 (*.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1) (pow.f64 (cbrt.f64 x) -1) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 (sqrt.f64 x) -1) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) -1) (pow.f64 (sqrt.f64 x) -1) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (fma.f64 (*.f64 x -1/12) 1 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (fma.f64 -1/12 x (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (-.f64 (pow.f64 x -1/2) (sqrt.f64 (*.f64 x 1/12))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (pow.f64 (cbrt.f64 (*.f64 x 1/12)) 2) (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/12 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/12 (sqrt.f64 x)) (sqrt.f64 x) (/.f64 1 x))))))

simplify137.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

778×	`sqr-pow_binary64`
574×	`associate-l_binary64`
542×	`associate-/l/_binary64`
439×	`cube-prod_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	252
1	27	252
2	38	252
3	69	252
4	161	252
5	477	252
6	1695	252
7	2808	252
8	3727	252
9	3941	252
10	4166	252
11	4472	252
12	4897	252
13	5476	252
14	6042	252
15	6724	252
16	7565	252
17	7959	252

Stop Event

1×	node limit

Counts

241 → 215

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.f64 1 x))
(+.f64 (*.f64 1/12 x) (/.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))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(*.f64 1/144 (pow.f64 x 2))
(/.f64 1 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(*.f64 -1/12 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(*.f64 -1/12 x)
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))
(+.f64 (*.f64 -1/12 x) (/.f64 1 x))

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 1 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.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 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/12 x)
(*.f64 x 1/12)
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/12 x))
(fma.f64 1/12 x (/.f64 1 x))
(fma.f64 x 1/12 (/.f64 1 x))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(*.f64 1/144 (pow.f64 x 2))
(.f64 1/144 (.f64 x x))
(.f64 x (.f64 x 1/144))
(/.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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 -1/12 x)
(*.f64 x -1/12)
(+.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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 -1/12 x)
(*.f64 x -1/12)
(+.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 1 x))
(fma.f64 -1/12 x (/.f64 1 x))
(fma.f64 x -1/12 (/.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))

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
✓	0.0b	(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
	0.0b	(sqrt.f64 (exp.f64 x))
✓	0.3b	(*.f64 -1/24 x)

Compiler

Compiled 33 to 20 computations (39.4% saved)

series4.0ms (0.1%)

Counts

3 → 21

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
0.0ms	x	@	-inf	(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
0.0ms	x	@	0	(*.f64 -1/24 x)
0.0ms	x	@	inf	(*.f64 -1/24 x)
0.0ms	x	@	-inf	(*.f64 -1/24 x)

rewrite210.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

486×	`log-prod_binary64`
370×	`pow-prod-down_binary64`
356×	`exp-prod_binary64`
299×	`fma-def_binary64`
259×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	213	27
2	2843	27

Stop Event

1×	node limit

Counts

3 → 152

Calls

Call 1

Inputs
(*.f64 -1/24 x)
(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/24 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -1/24)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) -1/24))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) -1/24))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/24 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/24 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/576 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 -1/24 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 -1/24 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 -1/24 x))) 2)) (cbrt.f64 (log.f64 (*.f64 -1/24 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 -1/24 x)))) (sqrt.f64 (log.f64 (*.f64 -1/24 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/576 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/24 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 -1/24 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/24 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1/24 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 -1/24 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 -1/24 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 -1/24 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 -1/24 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 -1/24 x)) 3) 1/3))))))

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(#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 -1/24 x (/.f64 1 x)) (sqrt.f64 (exp.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 -1/24 x (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 -1/24 x (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 1/2 x (log.f64 (fma.f64 -1/24 x (/.f64 1 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (exp.f64 x)) x) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (*.f64 -1/24 x) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 x)) (*.f64 (pow.f64 (exp.f64 x) 1/6) (*.f64 -1/24 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 x)) (*.f64 (pow.f64 (exp.f64 x) 1/6) (/.f64 1 x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 (exp.f64 x))) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 2) (*.f64 (cbrt.f64 (*.f64 -1/24 x)) (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 -1/24 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 1 x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (sqrt.f64 (exp.f64 x))) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 -1/24 x)) (pow.f64 (*.f64 (*.f64 -1/24 x) (exp.f64 x)) 1/2) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))) 1 (*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) 2) (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x)))) 2) (cbrt.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x)))) (sqrt.f64 (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) -1/24) x (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) x) -1/24 (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (*.f64 -1/24 x)) 2)) (cbrt.f64 (*.f64 -1/24 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (exp.f64 x) (*.f64 -1/24 x)) 1/2) (sqrt.f64 (*.f64 -1/24 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/24 x) (cbrt.f64 (exp.f64 x))) (pow.f64 (exp.f64 x) 1/6) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/24 x) (pow.f64 (exp.f64 x) 1/4)) (pow.f64 (exp.f64 x) 1/4) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 x -1/2)) (pow.f64 x -1/2) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (exp.f64 x))) (pow.f64 (exp.f64 x) 1/6) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (exp.f64 x) 1/4)) (pow.f64 (exp.f64 x) 1/4) (*.f64 (*.f64 -1/24 x) (sqrt.f64 (exp.f64 x))))))))

simplify119.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
633×	`sqr-pow_binary64`
498×	`*-commutative_binary64`
493×	`associate-l_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	266
1	61	236
2	122	212
3	268	212
4	405	212
5	788	212
6	2455	212
7	4913	212
8	5152	212
9	5342	212
10	5575	212
11	5972	212
12	6466	212
13	7423	212

Stop Event

1×	node limit

Counts

173 → 166

Calls

Call 1

Inputs
(/.f64 1 x)
(*.f64 -1/24 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(*.f64 -1/24 x)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(/.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 -1/384 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(.f64 -1/24 (.f64 (sqrt.f64 (exp.f64 x)) x))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(.f64 -1/24 (.f64 (sqrt.f64 (exp.f64 x)) x))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))

Outputs
(/.f64 1 x)
(*.f64 -1/24 x)
(*.f64 x -1/24)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(*.f64 -1/24 x)
(*.f64 x -1/24)
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 -1/24 x))
(+.f64 (/.f64 1 x) (*.f64 x -1/24))
(fma.f64 x -1/24 (/.f64 1 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 -1/384 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/384 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/384 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/384 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 -1/384 (*.f64 x x) 1/12) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x (fma.f64 x (*.f64 x -1/384) 1/12) 1/2))
(.f64 -1/24 (.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x))))
(.f64 x (.f64 -1/24 (sqrt.f64 (exp.f64 x))))
(.f64 (.f64 x -1/24) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))
(.f64 -1/24 (.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x))))
(.f64 x (.f64 -1/24 (sqrt.f64 (exp.f64 x))))
(.f64 (.f64 x -1/24) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))
(+.f64 (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x)) (.f64 -1/24 (*.f64 (sqrt.f64 (exp.f64 x)) x)))
(fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x)))))
(fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(*.f64 (fma.f64 x -1/24 (/.f64 1 x)) (sqrt.f64 (exp.f64 x)))

eval855.0ms (16.6%)

Compiler: Compiled 12977 to 8851 computations (31.8% saved)

prune95.0ms (1.8%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	702	2	704
Fresh	0	0	0
Picked	1	0	1
Done	2	5	7
Total	705	7	712

Error

0.8b

Counts

712 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.2b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
✓	21.5b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	1.2b	(.f64 (exp.f64 (.f64 x 1/2)) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	21.2b	(+.f64 (/.f64 1 x) 1/2)
▶	1.0b	(.f64 (exp.f64 (.f64 x 1/2)) (.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
✓	21.5b	(/.f64 1 x)

Compiler

Compiled 70 to 55 computations (21.4% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (expm1.f64 x))
✓	1.0b	(.f64 (exp.f64 (.f64 x 1/2)) (.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
	1.0b	(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x)))

Compiler

Compiled 40 to 27 computations (32.5% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

857×	`pow1_binary64`
790×	`add-log-exp_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
773×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	198	8
2	2292	8

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

Inputs
(.f64 (exp.f64 (.f64 x 1/2)) (.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (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) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (exp.f64 x) -1) (neg.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 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 (log.f64 (/.f64 (exp.f64 x) (expm1.f64 x))))))))

simplify36.0ms (0.7%)

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

28 → 24

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))

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (exp.f64 (.f64 x 1/2)) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
	0.0b	(+.f64 (*.f64 -1/24 x) (/.f64 1 x))
	0.3b	(*.f64 -1/24 x)

Compiler

Compiled 37 to 27 computations (27% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

rewrite64.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
385×	`pow-prod-down_binary64`
326×	`fma-def_binary64`
283×	`pow2_binary64`
198×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	235	15
2	3055	15

Stop Event

1×	node limit

Counts

1 → 61

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) 1) (*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) 3) (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 3)) (+.f64 (pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) 2) (-.f64 (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 2) (*.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) 2) (pow.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 2)) (-.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 (pow.f64 x 3) -1/13824 (pow.f64 x -3)) (sqrt.f64 (exp.f64 x))) (-.f64 (fma.f64 (*.f64 x x) 1/576 (pow.f64 x -2)) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 (*.f64 x x) 1/576) (pow.f64 x -2)) (sqrt.f64 (exp.f64 x))) (-.f64 (*.f64 x -1/24) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 (pow.f64 x 3) -1/13824 (pow.f64 x -3))) (-.f64 (fma.f64 (*.f64 x x) 1/576 (pow.f64 x -2)) -1/24))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (-.f64 (*.f64 (*.f64 x x) 1/576) (pow.f64 x -2))) (-.f64 (*.f64 x -1/24) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (exp.f64 x) (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (exp.f64 x) (pow.f64 (fma.f64 x -1/24 (/.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (exp.f64 x))) (fma.f64 x -1/24 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 x 1/2 (log.f64 (fma.f64 x -1/24 (/.f64 1 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 x) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/24 (*.f64 x (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/24) (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (exp.f64 x)) x) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 x)) (*.f64 (pow.f64 (exp.f64 x) 1/6) (/.f64 1 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 x)) (*.f64 (pow.f64 (exp.f64 x) 1/6) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) (sqrt.f64 (exp.f64 x))) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x -1/24)) 2) (*.f64 (cbrt.f64 (*.f64 x -1/24)) (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) (/.f64 1 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 (pow.f64 (exp.f64 x) 1/4) (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) (sqrt.f64 (exp.f64 x))) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x -1/24)) (pow.f64 (*.f64 (*.f64 x -1/24) (exp.f64 x)) 1/2) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)) 1 (*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24))) 2) (cbrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) 2) (cbrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24))) (sqrt.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24))) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (sqrt.f64 (/.f64 (sqrt.f64 (exp.f64 x)) x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 x -1/2)) (pow.f64 x -1/2) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (exp.f64 x))) (pow.f64 (exp.f64 x) 1/6) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 1 x) (pow.f64 (exp.f64 x) 1/4)) (pow.f64 (exp.f64 x) 1/4) (*.f64 (sqrt.f64 (exp.f64 x)) (*.f64 x -1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/24) (cbrt.f64 (exp.f64 x))) (pow.f64 (exp.f64 x) 1/6) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x -1/24) (pow.f64 (exp.f64 x) 1/4)) (pow.f64 (exp.f64 x) 1/4) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) x) -1/24 (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) -1/24) x (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (*.f64 x -1/24)) 2)) (cbrt.f64 (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (*.f64 (exp.f64 x) (*.f64 x -1/24)) 1/2) (sqrt.f64 (*.f64 x -1/24)) (/.f64 (sqrt.f64 (exp.f64 x)) x))))))

simplify80.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
625×	`associate-/r/_binary64`
448×	`times-frac_binary64`
377×	`associate-/l*_binary64`
317×	`associate-/r*_binary64`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	23	190
1	57	190
2	116	176
3	264	176
4	467	176
5	1024	176
6	1511	176
7	2471	176
8	5653	176
9	6609	164
10	7324	152

Stop Event

1×	node limit

Counts

73 → 72

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 -1/384 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(.f64 -1/24 (.f64 (exp.f64 (*.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(.f64 -1/24 (.f64 (exp.f64 (*.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))

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)))
(fma.f64 x 1/12 (+.f64 (/.f64 1 x) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/384 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/384 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1/384 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 x 1/12 (fma.f64 -1/384 (pow.f64 x 3) (/.f64 1 x))))
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 -1/384 (pow.f64 x 3) 1/2))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 (fma.f64 -1/384 (pow.f64 x 3) 1/2)))
(.f64 -1/24 (.f64 (exp.f64 (*.f64 1/2 x)) x))
(.f64 -1/24 (.f64 x (pow.f64 (exp.f64 1/2) x)))
(.f64 x (.f64 -1/24 (exp.f64 (*.f64 x 1/2))))
(.f64 x (.f64 -1/24 (sqrt.f64 (exp.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 x -1/24))
(.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x))))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(.f64 -1/24 (.f64 (exp.f64 (*.f64 1/2 x)) x))
(.f64 -1/24 (.f64 x (pow.f64 (exp.f64 1/2) x)))
(.f64 x (.f64 -1/24 (exp.f64 (*.f64 x 1/2))))
(.f64 x (.f64 -1/24 (sqrt.f64 (exp.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 x -1/24))
(.f64 -1/24 (.f64 x (sqrt.f64 (exp.f64 x))))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))
(+.f64 (.f64 -1/24 (.f64 (exp.f64 (.f64 1/2 x)) x)) (/.f64 (exp.f64 (.f64 1/2 x)) x))
(fma.f64 -1/24 (*.f64 x (pow.f64 (exp.f64 1/2) x)) (/.f64 (pow.f64 (exp.f64 1/2) x) x))
(fma.f64 -1/24 (.f64 x (exp.f64 (.f64 x 1/2))) (/.f64 (exp.f64 (*.f64 x 1/2)) x))
(fma.f64 x (*.f64 -1/24 (sqrt.f64 (exp.f64 x))) (/.f64 (sqrt.f64 (exp.f64 x)) x))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 x -1/24) (/.f64 1 x)))
(*.f64 (sqrt.f64 (exp.f64 x)) (fma.f64 x -1/24 (/.f64 1 x)))

eval80.0ms (1.5%)

Compiler: Compiled 3881 to 2538 computations (34.6% saved)

prune35.0ms (0.7%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	247	8	255

Error

0.8b

Counts

255 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.2b	(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
✓	21.5b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
	1.5b	(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 x))
✓	1.0b	(.f64 (exp.f64 (.f64 x 1/2)) (.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
✓	1.2b	(.f64 (exp.f64 (.f64 x 1/2)) (+.f64 (*.f64 -1/24 x) (/.f64 1 x)))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	21.2b	(+.f64 (/.f64 1 x) 1/2)
✓	21.5b	(/.f64 1 x)

Compiler

Compiled 79 to 62 computations (21.5% saved)

regimes18.0ms (0.3%)

Counts

15 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 x))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(.f64 (exp.f64 (.f64 x 1/2)) (+.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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (exp.f64 (*.f64 x 1/2)) (/.f64 1 (expm1.f64 x))))
(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))

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

Calls

3 calls:

8.0ms	x
3.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
1.0b	1	`(exp.f64 x)`

Compiler

Compiled 164 to 110 computations (32.9% saved)

regimes19.0ms (0.4%)

Counts

12 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 x))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(.f64 (exp.f64 (.f64 x 1/2)) (+.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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
(.f64 (sqrt.f64 (exp.f64 x)) (+.f64 (.f64 -1/24 x) (/.f64 1 x)))

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

Calls

3 calls:

7.0ms	x
6.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(exp.f64 x)

Results

Error	Segments	Branch
1.0b	1	`x`
1.0b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
1.0b	1	`(exp.f64 x)`

Compiler

Compiled 125 to 89 computations (28.8% saved)

regimes9.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/12) 1/2))
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(.f64 (exp.f64 (.f64 x 1/2)) (/.f64 1 x))
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 1/2))
(.f64 (exp.f64 (.f64 x 1/2)) (+.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 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 1/12 x))))

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

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
1.2b	1	`x`

Compiler

Compiled 91 to 69 computations (24.2% saved)

regimes10.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
1.5b	1	`x`

Compiler

Compiled 45 to 34 computations (24.4% saved)

regimes6.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
21.2b	1	`x`

Compiler

Compiled 29 to 22 computations (24.1% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.7b remaining (-3.5%)

Threshold costs -0.7b (-3.5%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
21.2b	1	`x`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	84
1	36	84

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 63 to 49 computations (22.2% saved)

soundness7.0ms (0.1%)

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)

end51.0ms (1%)

Compiler: Compiled 57 to 42 computations (26.3% saved)

Details

analyze120.0ms (2.3%)

sample1.3s (26.1%)

preprocess15.0ms (0.3%)

simplify6.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite43.0ms (0.8%)

simplify180.0ms (3.5%)

eval7.0ms (0.1%)

prune10.0ms (0.2%)

localize22.0ms (0.4%)

series6.0ms (0.1%)

rewrite240.0ms (4.7%)

simplify208.0ms (4%)

localize3.0ms (0.1%)

localize5.0ms (0.1%)

localize11.0ms (0.2%)

series3.0ms (0.1%)

rewrite92.0ms (1.8%)

simplify12.0ms (0.2%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite62.0ms (1.2%)

simplify10.0ms (0.2%)

eval93.0ms (1.8%)

prune35.0ms (0.7%)

localize19.0ms (0.4%)

series5.0ms (0.1%)

rewrite63.0ms (1.2%)

simplify66.0ms (1.3%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite149.0ms (2.9%)

simplify10.0ms (0.2%)

localize23.0ms (0.5%)

series2.0ms (0%)

rewrite44.0ms (0.9%)

simplify6.0ms (0.1%)

localize31.0ms (0.6%)

series4.0ms (0.1%)

rewrite217.0ms (4.2%)

simplify137.0ms (2.7%)

localize17.0ms (0.3%)

series4.0ms (0.1%)

rewrite210.0ms (4.1%)

simplify119.0ms (2.3%)

eval855.0ms (16.6%)

prune95.0ms (1.8%)

localize17.0ms (0.3%)

series3.0ms (0.1%)

rewrite55.0ms (1.1%)

simplify36.0ms (0.7%)

localize16.0ms (0.3%)

series2.0ms (0%)

rewrite64.0ms (1.2%)

simplify80.0ms (1.6%)

eval80.0ms (1.5%)

prune35.0ms (0.7%)

regimes18.0ms (0.3%)

regimes19.0ms (0.4%)

regimes9.0ms (0.2%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

simplify6.0ms (0.1%)

soundness7.0ms (0.1%)

end51.0ms (1%)

Profiling