Details

analyze508.0ms (14.4%)

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)

sample30.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	72×	body	1024	valid
4.0ms	45×	body	512	valid
3.0ms	110×	body	128	valid
2.0ms	10×	body	2048	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify8.0ms (0.2%)

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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 25 to 15 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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:

3.0ms

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

simplify70.0ms (2%)

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

41 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune18.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

0.4b

Counts

41 → 3

Alt Table

Status	Error	Program
	27.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
▶	22.6b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 473 to 170 computations (64.1% 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
▶	27.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	22.6b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 30 to 23 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	25.1b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

series33.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

23.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
9.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

rewrite15.0ms (0.4%)

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

simplify99.0ms (2.8%)

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

prune95.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	149	3	152

Error

0.4b

Counts

152 → 3

Alt Table

Status	Error	Program
✓	22.6b	(+.f64 1/2 (/.f64 1 x))
▶	48.9b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 2225 to 965 computations (56.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (pow.f64 x 3))
✓	0.2b	(/.f64 3/2 (*.f64 x x))
✓	9.6b	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
✓	25.4b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

series21.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

8.0ms	(/.f64 1 (pow.f64 x 3))
6.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
4.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
3.0ms	(/.f64 3/2 (*.f64 x x))

rewrite68.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

4 → 178

Calls

4 calls:

26.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
22.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
4.0ms	(/.f64 1 (pow.f64 x 3))
3.0ms	(/.f64 3/2 (*.f64 x x))

simplify165.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-def_binary64`
372×	`unswap-sqr_binary64`
356×	`associate-/l/_binary64`
224×	`distribute-rgt-in_binary64`
217×	`fma-neg_binary64`

Counts

214 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	185	2668
1	401	2553
2	1551	2501
3	4536	2445
4	4701	2435
5	4947	2435
6	4954	2435

prune197.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	194	4	198

Error

0.4b

Counts

198 → 4

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	49.0b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (.f64 x x)))) 3/8))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (.f64 x x)))) 3/8)))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))))
✓	22.6b	(+.f64 1/2 (/.f64 1 x))
	56.1b	(.f64 (cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (.f64 x x)))) 3/8))) (cbrt.f64 (sqrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))))

Compiler

Compiled 5027 to 3742 computations (25.6% saved)

regimes523.0ms (14.9%)

Accuracy

Total 0.1b remaining (21.4%)

Threshold costs 0.1b (21.4%)

Counts

164 → 1

Compiler

Compiled 11084 to 8683 computations (21.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end1.0ms (0%)

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

sample1.6s (46.2%)

Algorithm

1×

intervals

Results

642.0ms	2620×	body	1024	valid
170.0ms	1371×	body	512	valid
134.0ms	3107×	body	128	valid
64.0ms	251×	body	2048	valid
55.0ms	651×	body	256	valid

Compiler

Compiled 128 to 97 computations (24.2% saved)

Details

analyze508.0ms (14.4%)

sample30.0ms (0.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify70.0ms (2%)

prune18.0ms (0.5%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series33.0ms (0.9%)

rewrite15.0ms (0.4%)

simplify99.0ms (2.8%)

prune95.0ms (2.7%)

localize11.0ms (0.3%)

series21.0ms (0.6%)

rewrite68.0ms (1.9%)

simplify165.0ms (4.7%)

prune197.0ms (5.6%)

regimes523.0ms (14.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (46.2%)

Profiling