Details

analyze701.0ms (26.5%)

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
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample55.0ms (2.1%)

Algorithm

1×

intervals

Results

27.0ms	94×	body	1024	valid
7.0ms	43×	body	512	valid
4.0ms	92×	body	128	valid
3.0ms	9×	body	2048	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify19.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite49.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

Compiler

Compiled 335 to 89 computations (73.4% saved)

series21.0ms (0.8%)

Error

0.2b

Counts

1 → 6

Calls

1 calls:

15.0ms

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

Compiler

Compiled 108 to 79 computations (26.9% saved)

simplify128.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

35 → 12

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	511
1	130	473
2	292	471
3	609	471
4	1403	471
5	4001	471
6	5294	471

prune17.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	9	3	12
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	4	13

Error

0.2b

Counts

13 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
	31.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
▶	19.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
	19.6b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 131 to 81 computations (38.2% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
0.1b	(fma.f64 x 1/12 (/.f64 1 x))

rewrite37.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
1.0ms	(fma.f64 x 1/12 (/.f64 1 x))

Compiler

Compiled 397 to 313 computations (21.2% saved)

series34.0ms (1.3%)

Error

0.2b

Counts

2 → 15

Calls

2 calls:

16.0ms	(fma.f64 x 1/12 (/.f64 1 x))
15.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))

Compiler

Compiled 194 to 155 computations (20.1% saved)

simplify88.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

930×	`distribute-rgt-in_binary64`
900×	`distribute-lft-in_binary64`
726×	`fma-def_binary64`
566×	`associate-+l+_binary64`
388×	`fma-neg_binary64`

Counts

43 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	466
1	94	435
2	242	435
3	989	433
4	4674	433
5	4932	433

prune19.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	26	4	30

Error

0.2b

Counts

30 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
	31.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	19.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
▶	19.6b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 257 to 201 computations (21.8% saved)

localize7.0ms (0.3%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune4.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.2b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	31.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	19.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	19.6b	(+.f64 (/.f64 1 x) 1/2)

Compiler

Compiled 39 to 30 computations (23.1% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.1b	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
29.5b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

rewrite98.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

45×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
41×	`add-cube-cbrt_binary64`
32×	`cbrt-prod_binary64`

Counts

3 → 121

Calls

3 calls:

8.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
6.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1458 to 584 computations (59.9% saved)

series55.0ms (2.1%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

17.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
17.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

Compiler

Compiled 438 to 345 computations (21.2% saved)

simplify112.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

772×	`times-frac_binary64`
506×	`associate-/l*_binary64`
444×	`log-div_binary64`
338×	`unswap-sqr_binary64`
215×	`associate-/l/_binary64`

Counts

139 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	2348
1	354	2099
2	1075	2079
3	4360	2079
4	5134	2079

prune42.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	102	3	105

Error

0.2b

Counts

105 → 3

Alt Table

Status	Error	Program
	50.8b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
	19.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))

Compiler

Compiled 634 to 305 computations (51.9% saved)

regimes78.0ms (3%)

Accuracy

Total 0.1b remaining (22.1%)

Threshold costs 0.1b (22.1%)

Compiler

Compiled 1394 to 892 computations (36% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11
2	8	11

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample1.0s (38.8%)

Algorithm

1×

intervals

Results

436.0ms	2645×	body	1024	valid
169.0ms	1333×	body	512	valid
90.0ms	3100×	body	128	valid
47.0ms	262×	body	2048	valid
38.0ms	660×	body	256	valid

Compiler

Compiled 52 to 39 computations (25% saved)

Details

analyze701.0ms (26.5%)

sample55.0ms (2.1%)

simplify19.0ms (0.7%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite49.0ms (1.9%)

series21.0ms (0.8%)

simplify128.0ms (4.8%)

prune17.0ms (0.6%)

localize9.0ms (0.4%)

rewrite37.0ms (1.4%)

series34.0ms (1.3%)

simplify88.0ms (3.3%)

prune19.0ms (0.7%)

localize7.0ms (0.3%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify16.0ms (0.6%)

prune4.0ms (0.2%)

localize11.0ms (0.4%)

rewrite98.0ms (3.7%)

series55.0ms (2.1%)

simplify112.0ms (4.2%)

prune42.0ms (1.6%)

regimes78.0ms (3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (38.8%)

Profiling