Details

analyze302.0ms (8.3%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.8s (49.2%)

Results

827.0ms	2714×	body	1024	valid
600.0ms	3930×	body	256	valid
239.0ms	1347×	body	512	valid
104.0ms	265×	body	2048	valid
1.0ms	4×	body	2048	infinite
0.0ms	3×	body	256	unsamplable

Bogosity

preprocess19.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite44.0ms (1.2%)

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))))))))

simplify178.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

42 → 39

Calls

Call 1

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

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

eval7.0ms (0.2%)

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

prune7.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Error

0.6b

Counts

40 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	20.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
▶	20.5b	(+.f64 (/.f64 1 x) 1/2)
▶	20.5b	(/.f64 1 x)

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize24.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 56 to 43 computations (23.2% saved)

series6.0ms (0.2%)

Counts

4 → 21

Calls

12 calls:

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

rewrite85.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	273	34
2	3506	34

Stop Event

1×	node limit

Counts

4 → 179

Calls

Call 1

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

Outputs
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exp.f64 (log.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/720 (pow.f64 x 3) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/12 (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 (.f64 x x) -1/720) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/720 (pow.f64 x 3)) 1 (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/12 x (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x 1/12) 1 (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 -1/720 (pow.f64 x 3)) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x 1/12) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/12 (/.f64 1 x)) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/12 (/.f64 1 x)) 1 (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) (.f64 x -1/720) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (cbrt.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2)) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x 1/12 (/.f64 1 x)) 2)) (cbrt.f64 (fma.f64 x 1/12 (/.f64 1 x))) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x 1/12)) (cbrt.f64 (.f64 (.f64 x x) 1/144)) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (.f64 x x) 1/144)) (cbrt.f64 (.f64 x 1/12)) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 -1/720)) (pow.f64 (.f64 x (cbrt.f64 -1/720)) 2) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 x (cbrt.f64 -1/720)) 2) (.f64 x (cbrt.f64 -1/720)) (fma.f64 x 1/12 (/.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 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (.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))) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x 1/12)) (sqrt.f64 (.f64 x 1/12)) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (.f64 (sqrt.f64 -1/720) (pow.f64 x 3/2)) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 1/12) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (neg.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/1728 (pow.f64 x -3)) (/.f64 1 (-.f64 (fma.f64 (.f64 x x) 1/144 (pow.f64 x -2)) (/.f64 (.f64 x 1/12) x))) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (.f64 (.f64 x x) 1/144) (pow.f64 x -2)) (/.f64 1 (-.f64 (.f64 x 1/12) (/.f64 1 x))) (.f64 -1/720 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (.f64 (pow.f64 x 3/2) -1/720) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12)) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12))) 2) (cbrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12))) (sqrt.f64 (fma.f64 -1/720 (pow.f64 x 3) (.f64 x 1/12))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 1 (cbrt.f64 x)) (fma.f64 -1/720 (pow.f64 x 3) (.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 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/12 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 (/.f64 1 x) (.f64 -1/720 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/720 x) (.f64 x x) (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/720 (.f64 x x)) x (fma.f64 x 1/12 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/720 (pow.f64 x 3/2)) (pow.f64 x 3/2) (fma.f64 x 1/12 (/.f64 1 x)))))))

simplify175.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	198
1	39	198
2	64	198
3	125	198
4	200	198
5	429	198
6	1325	198
7	2068	198
8	2155	198
9	2288	198
10	2446	198
11	2690	198
12	3012	198
13	3436	198
14	3939	198
15	4538	198
16	5262	198
17	5583	198
18	5867	198
19	6093	198
20	6273	198
21	6355	198
22	7295	198

Stop Event

1×	node limit

Counts

200 → 190

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

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

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

localize5.0ms (0.1%)

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

localize3.0ms (0.1%)

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

eval119.0ms (3.3%)

Compiler: Compiled 4939 to 3852 computations (22% saved)

prune40.0ms (1.1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	265	2	267
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	265	7	272

Error

0.6b

Counts

272 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
▶	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	20.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	20.5b	(+.f64 (/.f64 1 x) 1/2)
▶	42.4b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 x 1/12))))
✓	20.5b	(/.f64 1 x)

Compiler

Compiled 68 to 53 computations (22.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite41.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

345×	`pow1_binary64`
338×	`add-sqr-sqrt_binary64`
329×	`*-un-lft-identity_binary64`
321×	`add-log-exp_binary64`
321×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	80	4
2	873	4

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 x 1/12)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 x 1/12)) -1)))) (#(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 (exp.f64 x) 1/24)) (log.f64 (pow.f64 (exp.f64 x) 1/24)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/6) x))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/12) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/12)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (*.f64 x 1/12)) 3) 1) (+.f64 (*.f64 (+.f64 1 (*.f64 x 1/12)) (+.f64 1 (*.f64 x 1/12))) (+.f64 1 (*.f64 (+.f64 1 (*.f64 x 1/12)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (*.f64 x 1/12)) (+.f64 1 (*.f64 x 1/12))) 1) (+.f64 (+.f64 1 (*.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 (pow.f64 (*.f64 x 1/12) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/1728 (pow.f64 x 3)) 1/3)))) (#(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 (E.f64) (log.f64 (*.f64 x 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x 1/12)))) (sqrt.f64 (log.f64 (*.f64 x 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x 1/12))) 2)) (cbrt.f64 (log.f64 (*.f64 x 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x 1/12) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x 1/12))))) (#(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 1/1728 (pow.f64 x 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 (*.f64 3 (log.f64 (*.f64 x 1/12))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x 1/12))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x 1/12))) 2))))))

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

37 → 26

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)

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)

localize28.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 x) (*.f64 x 1/12))
✓	0.2b	(.f64 (.f64 x x) 1/144)
	0.3b	(*.f64 x 1/12)
✓	31.2b	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 x 1/12)))

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

rewrite82.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

730×	`log-prod_binary64`
530×	`fma-def_binary64`
258×	`fma-neg_binary64`
253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	323	27
2	4550	23

Stop Event

1×	node limit

Counts

3 → 203

Calls

Call 1

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

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 x (/.f64 (*.f64 x 1/144) (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 x (/.f64 (*.f64 x 1/144) (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 x (/.f64 (*.f64 x 1/144) (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 x (/.f64 (*.f64 x 1/144) (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 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(cbrt.f64 (fma.f64 x -1/12 (/.f64 1 x))) 2) (cbrt.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 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 x -1/12))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -2)) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (neg.f64 (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 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (*.f64 (*.f64 x -1/12) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/12)) (neg.f64 (sqrt.f64 (*.f64 x 1/12))) (/.f64 1 x))))) (#(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 (*.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 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (*.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 (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 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (*.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 (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 (cbrt.f64 (*.f64 x (*.f64 x 1/144)))) (cbrt.f64 (*.f64 x 1/12)) (/.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 (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 (neg.f64 (cbrt.f64 (*.f64 x 1/12))) (cbrt.f64 (*.f64 x (*.f64 x 1/144))) (*.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)))))))

simplify139.0ms (3.8%)

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

239 → 213

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))

eval124.0ms (3.4%)

Compiler: Compiled 5936 to 4358 computations (26.6% saved)

prune39.0ms (1.1%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	264	1	265
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	264	8	272

Error

0.6b

Counts

272 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	20.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	20.5b	(+.f64 (/.f64 1 x) 1/2)
✓	42.4b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 x 1/12))))
✓	20.5b	(/.f64 1 x)
▶	63.4b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12)))

Compiler

Compiled 84 to 65 computations (22.6% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12)))
	0.2b	(.f64 (.f64 x x) 1/144)
✓	0.3b	(*.f64 x -1/12)
✓	11.1b	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12))

Compiler

Compiled 57 to 35 computations (38.6% saved)

series6.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12))
1.0ms	x	@	inf	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12))
1.0ms	x	@	0	(/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12))
0.0ms	x	@	0	(*.f64 x -1/12)
0.0ms	x	@	0	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12)))

rewrite84.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`log-prod_binary64`
316×	`fma-def_binary64`
244×	`pow1/3_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	306	43
2	4476	39

Stop Event

1×	node limit

Counts

3 → 165

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x -2) (/.f64 -12 x)) (neg.f64 (*.f64 -1/12 (/.f64 (*.f64 x x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2)) (/.f64 -12 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2))) (/.f64 -12 x))) (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2))) (/.f64 -12 x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2))) (/.f64 -12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2))) (/.f64 -12 x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x (*.f64 x 1/144) (pow.f64 x -2))) (/.f64 -12 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (pow.f64 x -2) (/.f64 -12 x)) (*.f64 -1/12 (/.f64 (*.f64 x x) x)))))) (#(struct:change #<rule egg-rr> (2) 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simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-neg_binary64`
732×	`times-frac_binary64`
559×	`associate-/r*_binary64`
517×	`associate-/l/_binary64`
362×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	315
1	46	281
2	91	281
3	197	281
4	456	281
5	1320	281
6	5786	281

Stop Event

1×	node limit

Counts

201 → 178

Calls

Call 1

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

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

eval88.0ms (2.4%)

Compiler: Compiled 4168 to 3040 computations (27.1% saved)

prune28.0ms (0.8%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	0	0
Picked	1	0	1
Done	0	7	7
Total	196	8	204

Error

0.6b

Counts

204 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	63.2b	(+.f64 1/2 (-.f64 (.f64 1/12 x) (.f64 12 (/.f64 1 (pow.f64 x 3)))))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	20.9b	(+.f64 1/2 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))))
✓	62.0b	(+.f64 1/2 (*.f64 x 1/12))
✓	20.5b	(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
✓	20.5b	(+.f64 (/.f64 1 x) 1/2)
✓	42.4b	(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (-.f64 (/.f64 1 x) (*.f64 x 1/12))))
✓	20.5b	(/.f64 1 x)

Compiler

Compiled 82 to 65 computations (20.7% saved)

regimes17.0ms (0.5%)

Counts

10 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (-.f64 (.f64 1/12 x) (.f64 12 (/.f64 1 (pow.f64 x 3)))))
(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12)))
(+.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 x 1/12))))
(/.f64 (exp.f64 x) (expm1.f64 x))
(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Outputs
(/.f64 (exp.f64 x) (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
0.8b	1	`x`
0.8b	1	`(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))`
0.8b	1	`(exp.f64 x)`

Compiler

Compiled 110 to 79 computations (28.2% saved)

regimes8.0ms (0.2%)

Accuracy

Total -43.2b remaining (-211.3%)

Threshold costs -43.2b (-211.3%)

Counts

8 → 1

Calls

Call 1

Inputs
(/.f64 1 x)
(+.f64 1/2 (*.f64 x 1/12))
(+.f64 (/.f64 1 x) 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/12 x) (/.f64 1 x)))
(+.f64 1/2 (-.f64 (.f64 1/12 x) (.f64 12 (/.f64 1 (pow.f64 x 3)))))
(+.f64 1/2 (/.f64 (-.f64 (pow.f64 x -2) (.f64 (.f64 x x) 1/144)) (*.f64 x -1/12)))
(+.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 x 1/12))))

Outputs
(/.f64 1 x)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
20.5b	1	`x`

Compiler

Compiled 87 to 66 computations (24.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	9	12

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

soundness7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 14 to 9 computations (35.7% saved)

end17.0ms (0.5%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

Details

analyze302.0ms (8.3%)

sample1.8s (49.2%)

preprocess19.0ms (0.5%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite44.0ms (1.2%)

simplify178.0ms (4.9%)

eval7.0ms (0.2%)

prune7.0ms (0.2%)

localize24.0ms (0.7%)

series6.0ms (0.2%)

rewrite85.0ms (2.3%)

simplify175.0ms (4.8%)

localize11.0ms (0.3%)

localize5.0ms (0.1%)

localize3.0ms (0.1%)

eval119.0ms (3.3%)

prune40.0ms (1.1%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite41.0ms (1.1%)

simplify11.0ms (0.3%)

localize28.0ms (0.8%)

series4.0ms (0.1%)

rewrite82.0ms (2.3%)

simplify139.0ms (3.8%)

eval124.0ms (3.4%)

prune39.0ms (1.1%)

localize21.0ms (0.6%)

series6.0ms (0.2%)

rewrite84.0ms (2.3%)

simplify53.0ms (1.5%)

eval88.0ms (2.4%)

prune28.0ms (0.8%)

regimes17.0ms (0.5%)

regimes8.0ms (0.2%)

simplify2.0ms (0.1%)

soundness7.0ms (0.2%)

end17.0ms (0.5%)

Profiling