Details

analyze74.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	37.5%	12.6%	6
50%	25%	25.1%	7
50%	18.7%	31.3%	8
50%	12.5%	37.6%	9
50%	9.4%	40.7%	10
50%	6.2%	43.8%	11
50%	4.7%	45.4%	12
50%	3.1%	46.9%	13
50%	2.3%	47.7%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample156.0ms (2.9%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

38.0ms	55×	body	1024	valid
8.0ms	141×	body	128	valid
6.0ms	9×	body	2048	valid
6.0ms	23×	body	512	valid
4.0ms	28×	body	256	valid
0.0ms	8×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.7b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series569.0ms (10.6%)

Counts

2 → 48

Calls

2 calls:

565.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
418×	`associate-+l+_binary64`
392×	`fma-def_binary64`
238×	`times-frac_binary64`
229×	`associate-+r+_binary64`

Counts

82 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1238
1	334	1183
2	1034	1155
3	4062	1151
4	4828	1151
5	4973	1151

prune55.0ms (1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	1	84

Error

0.2b

Counts

84 → 1

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1321 to 592 computations (55.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))

series20.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

19.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
766×	`times-frac_binary64`
382×	`associate-l_binary64`
309×	`associate-r_binary64`
305×	`associate-/l*_binary64`

Counts

60 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	816
1	240	750
2	571	740
3	1389	730
4	4215	730
5	5275	730

prune93.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	2	73

Error

0.2b

Counts

73 → 2

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 1215 to 627 computations (48.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

series296.0ms (5.5%)

Counts

2 → 48

Calls

2 calls:

277.0ms	(log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
19.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-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 (/.f64 b (+.f64 1 (exp.f64 a))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
411×	`associate-/l*_binary64`
356×	`fma-def_binary64`
279×	`associate-/r*_binary64`
274×	`fma-neg_binary64`

Counts

70 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1445
1	432	1337
2	1553	1308
3	4857	1308
4	5021	1308

prune95.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	141	2	143

Error

0.2b

Counts

143 → 2

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
✓	0.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 3179 to 1850 computations (41.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))))
✓	0.0b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.0b	(log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

series1.1s (19.7%)

Counts

3 → 72

Calls

3 calls:

764.0ms

(log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

274.0ms

(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

19.0ms

(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 33

Calls

3 calls:

0.0ms

(log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

0.0ms

(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))))

0.0ms

(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Rules

340×	`sub-neg_binary64`
325×	`associate-+r+_binary64`
307×	`associate-/r*_binary64`
280×	`+-commutative_binary64`
254×	`times-frac_binary64`

Counts

105 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	4646
1	1115	4124
2	4602	4069
3	5189	4069

prune163.0ms (3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	164	2	166

Error

0.2b

Counts

166 → 2

Alt Table

Status	Error	Program
	17.4b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (expm1.f64 (cbrt.f64 (.f64 (.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))) (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))))
✓	0.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Status

Error

Program

17.4b

(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (expm1.f64 (cbrt.f64 (*.f64 (*.f64 (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))) (log1p.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))))

✓

0.2b

(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 7011 to 4628 computations (34% saved)

regimes243.0ms (4.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

52 → 1

Compiler

Compiled 4141 to 3222 computations (22.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end6.0ms (0.1%)

Compiler: Compiled 36 to 24 computations (33.3% saved)

sample2.2s (40.5%)

Algorithm

1×

intervals

Results

951.0ms	1889×	body	1024	valid
253.0ms	973×	body	512	valid
219.0ms	4487×	body	128	valid
135.0ms	194×	body	2048	valid
64.0ms	457×	body	256	valid
6.0ms	146×	body	128	overflowed

Compiler

Compiled 70 to 50 computations (28.6% saved)

Details

analyze74.0ms (1.4%)

sample156.0ms (2.9%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series569.0ms (10.6%)

rewrite7.0ms (0.1%)

simplify87.0ms (1.6%)

prune55.0ms (1%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify61.0ms (1.1%)

prune93.0ms (1.7%)

localize10.0ms (0.2%)

series296.0ms (5.5%)

rewrite1.0ms (0%)

simplify63.0ms (1.2%)

prune95.0ms (1.8%)

localize11.0ms (0.2%)

series1.1s (19.7%)

rewrite2.0ms (0%)

simplify105.0ms (2%)

prune163.0ms (3%)

regimes243.0ms (4.5%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample2.2s (40.5%)

Profiling