Details

analyze413.0ms (18.7%)

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)

sample46.0ms (2.1%)

Algorithm

1×

intervals

Results

15.0ms	93×	body	1024	valid
3.0ms	37×	body	512	valid
3.0ms	100×	body	128	valid
1.0ms	7×	body	2048	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	40.4b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 41 to 25 computations (39% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

series11.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
2.0ms	(expm1.f64 x)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
0.0ms	(expm1.f64 x)

simplify76.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

942×	`fma-neg_binary64`
666×	`times-frac_binary64`
570×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
262×	`associate-l_binary64`

Counts

64 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	688
1	165	643
2	385	641
3	904	635
4	2629	635
5	4940	635
6	5241	635

prune39.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.4b

Counts

61 → 3

Alt Table

Status	Error	Program
	29.8b	(/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 3)))
	22.0b	(+.f64 1/2 (/.f64 1 x))
▶	0.5b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

Compiler

Compiled 677 to 262 computations (61.3% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 x)
✓	0.0b	(sqrt.f64 (exp.f64 x))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓	0.5b	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

series22.0ms (1%)

Counts

3 → 28

Calls

3 calls:

11.0ms	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
8.0ms	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
3.0ms	(sqrt.f64 (exp.f64 x))

rewrite25.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
32×	`sqrt-prod_binary64`

Counts

3 → 109

Calls

3 calls:

10.0ms	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
5.0ms	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))
2.0ms	(sqrt.f64 (exp.f64 x))

simplify110.0ms (5%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
372×	`associate-/l*_binary64`
321×	`associate-l_binary64`
300×	`times-frac_binary64`
274×	`div-sub_binary64`

Counts

137 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2083
1	314	1996
2	980	1949
3	2903	1940
4	4478	1940
5	5195	1940

prune89.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	195	3	198

Error

0.4b

Counts

198 → 3

Alt Table

Status	Error	Program
	29.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
▶	22.0b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

Compiler

Compiled 3198 to 826 computations (74.2% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.4b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	29.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	22.0b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 x)
✓	0.1b	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	27.4b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

series28.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
9.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 92

Calls

2 calls:

4.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
3.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

simplify94.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

647×	`log-div_binary64`
612×	`associate-*l/_binary64`
596×	`times-frac_binary64`
400×	`associate-/l*_binary64`
290×	`unswap-sqr_binary64`

Counts

116 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1991
1	332	1774
2	994	1756
3	4845	1756
4	5967	1756

prune72.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	168	3	171

Error

0.4b

Counts

171 → 3

Alt Table

Status	Error	Program
✓	29.7b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	22.0b	(+.f64 1/2 (/.f64 1 x))
	51.1b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

Compiler

Compiled 2454 to 1093 computations (55.5% saved)

regimes97.0ms (4.4%)

Accuracy

Total 0.0b remaining (6.9%)

Threshold costs 0.0b (6.9%)

Counts

46 → 1

Compiler

Compiled 1520 to 1096 computations (27.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8
2	9	8

end0.0ms (0%)

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

sample1.0s (47%)

Algorithm

1×

intervals

Results

459.0ms	2711×	body	1024	valid
126.0ms	1334×	body	512	valid
99.0ms	3039×	body	128	valid
52.0ms	275×	body	2048	valid
39.0ms	641×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

Details

analyze413.0ms (18.7%)

sample46.0ms (2.1%)

simplify6.0ms (0.3%)

prune4.0ms (0.2%)

localize3.0ms (0.2%)

series11.0ms (0.5%)

rewrite5.0ms (0.2%)

simplify76.0ms (3.5%)

prune39.0ms (1.8%)

localize5.0ms (0.2%)

series22.0ms (1%)

rewrite25.0ms (1.1%)

simplify110.0ms (5%)

prune89.0ms (4%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series28.0ms (1.3%)

rewrite14.0ms (0.6%)

simplify94.0ms (4.3%)

prune72.0ms (3.3%)

regimes97.0ms (4.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (47%)

Profiling