Details

analyze1.7s (22.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample151.0ms (2%)

Algorithm

1×

intervals

Results

100.0ms	138×	body	1024	valid
22.0ms	57×	body	512	valid
7.0ms	36×	body	256	valid
5.0ms	256×	pre	128	true
3.0ms	3×	body	2048	valid
2.0ms	22×	body	128	valid

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
5×	`+-commutative_binary64`
4×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	10
2	19	10
3	25	10
4	32	10
5	42	10
6	53	10
7	66	10
8	70	10
9	53	10

prune4.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
	60.6b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))

Compiler

Compiled 50 to 38 computations (24% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (neg.f64 x))
✓	0.0b	(log1p.f64 x)
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

series66.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

43.0ms	(log1p.f64 (neg.f64 x))
19.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
3.0ms	(log1p.f64 x)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

3.0ms	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
0.0ms	(log1p.f64 (neg.f64 x))
0.0ms	(log1p.f64 x)

simplify120.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-def_binary64`
311×	`times-frac_binary64`
280×	`fma-neg_binary64`
265×	`distribute-rgt-in_binary64`
253×	`sub-neg_binary64`

Counts

87 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	2090
1	661	1982
2	2276	1774
3	4794	1772
4	5282	1772

prune98.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
▶	0.1b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
	0.6b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x)))

Compiler

Compiled 2581 to 1534 computations (40.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 x)
✓	0.0b	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))

series71.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

54.0ms	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
17.0ms	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
0.0ms	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))

simplify122.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-/r*_binary64`
301×	`sub-neg_binary64`
290×	`associate-+r+_binary64`
232×	`+-commutative_binary64`
221×	`times-frac_binary64`

Counts

46 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	3891
1	1057	3698
2	4478	3692
3	5191	3692

prune174.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.1b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
▶	0.6b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x)))

Compiler

Compiled 7199 to 5148 computations (28.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x))

series3.0ms (0%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x))

simplify106.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

962×	`distribute-lft-in_binary64`
962×	`distribute-rgt-in_binary64`
451×	`fma-def_binary64`
244×	`associate-+r+_binary64`
244×	`associate-+l+_binary64`

Counts

22 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	352
1	49	321
2	138	319
3	637	267
4	3429	267
5	4342	267
6	4956	267
7	4797	267

prune24.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	26	3	29

Error

Counts

29 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.1b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
✓	0.6b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) (fma.f64 5/12 (pow.f64 x 3) x)))

Compiler

Compiled 454 to 309 computations (31.9% saved)

regimes58.0ms (0.8%)

Accuracy

Total 0.0b remaining (87.1%)

Threshold costs 0.0b (87.1%)

Counts

25 → 1

Compiler

Compiled 506 to 404 computations (20.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	12	10
3	13	10
4	13	10

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample4.8s (63.4%)

Algorithm

1×

intervals

Results

2.9s	4029×	body	1024	valid
737.0ms	2030×	body	512	valid
377.0ms	395×	body	2048	valid
189.0ms	996×	body	256	valid
147.0ms	8000×	pre	128	true
47.0ms	550×	body	128	valid

Compiler

Compiled 55 to 41 computations (25.5% saved)

Details

analyze1.7s (22.8%)

sample151.0ms (2%)

simplify15.0ms (0.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series66.0ms (0.9%)

rewrite6.0ms (0.1%)

simplify120.0ms (1.6%)

prune98.0ms (1.3%)

localize16.0ms (0.2%)

series71.0ms (0.9%)

rewrite1.0ms (0%)

simplify122.0ms (1.6%)

prune174.0ms (2.3%)

localize8.0ms (0.1%)

series3.0ms (0%)

rewrite1.0ms (0%)

simplify106.0ms (1.4%)

prune24.0ms (0.3%)

regimes58.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.8s (63.4%)

Profiling