Details

analyze771.0ms (2.1%)

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%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample12.6s (34.4%)

Symmetry

(sort a b)

Results

9.7s	7741×	body	8192	exit
1.4s	1952×	body	1024	valid
602.0ms	4562×	body	128	valid
431.0ms	1004×	body	512	valid
189.0ms	199×	body	2048	valid
141.0ms	539×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify5.0ms (0%)

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

31.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series325.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

321.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (0%)

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

simplify83.0ms (0.2%)

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

prune45.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

0.4b

Counts

84 → 3

Alt Table

Status	Error	Program
✓	31.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1353 to 614 computations (54.6% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

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

series209.0ms (0.6%)

Counts

3 → 32

Calls

3 calls:

190.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
18.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

3 → 70

Calls

3 calls:

7.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
6.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-neg_binary64`
435×	`associate-/l*_binary64`
384×	`fma-def_binary64`
381×	`cancel-sign-sub-inv_binary64`
224×	`distribute-rgt-in_binary64`

Counts

102 → 104

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1554
1	354	1479
2	867	1463
3	2390	1452
4	4939	1451
5	5066	1451

prune89.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	5	107

Error

0.4b

Counts

107 → 5

Alt Table

Status	Error	Program
✓	31.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	19.8b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	26.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1836 to 960 computations (47.7% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.1b	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	1.4b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series637.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

416.0ms	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
221.0ms	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`log-prod_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-sum_binary64`

Counts

2 → 37

Calls

2 calls:

8.0ms	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
7.0ms	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
271×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
198×	`associate-/l/_binary64`
156×	`distribute-rgt-in_binary64`

Counts

85 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2938
1	628	2741
2	2529	2615
3	4984	2615

prune128.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	171	5	176

Error

0.4b

Counts

176 → 5

Alt Table

Status	Error	Program
▶	20.5b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
✓	31.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	48.2b	(exp.f64 (-.f64 (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))) (log.f64 (/.f64 1 b))))
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 4808 to 2879 computations (40.1% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.5b	(*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
✓	1.2b	(exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
✓	1.4b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))

series18.1s (49.6%)

Counts

4 → 96

Calls

4 calls:

13.4s	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
2.6s	(exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
1.4s	(*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
775.0ms	(cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`pow1_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 98

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
3.0ms	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
1.0ms	(exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
1.0ms	(cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

simplify1.0s (2.7%)

Algorithm

1×	egg-herbie

Rules

1116× fma-def_binary64

Counts

194 → 157

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4773	317827592675
1	5883	317827592675

prune2.0s (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	217	5	222

Error

0.4b

Counts

222 → 5

Alt Table

Status	Error	Program
✓	31.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
	48.2b	(exp.f64 (-.f64 (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))) (log.f64 (/.f64 1 b))))
	20.5b	(pow.f64 (exp.f64 (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 107630 to 83886 computations (22.1% saved)

regimes138.0ms (0.4%)

Accuracy

Total 0.5b remaining (48.4%)

Threshold costs 0.5b (48.4%)

Counts

30 → 1

Compiler

Compiled 2730 to 1916 computations (29.8% 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

end235.0ms (0.6%)

Compiler: Compiled 157 to 105 computations (33.1% saved)

Details

analyze771.0ms (2.1%)

sample12.6s (34.4%)

simplify5.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0%)

series325.0ms (0.9%)

rewrite7.0ms (0%)

simplify83.0ms (0.2%)

prune45.0ms (0.1%)

localize6.0ms (0%)

series209.0ms (0.6%)

rewrite18.0ms (0.1%)

simplify83.0ms (0.2%)

prune89.0ms (0.2%)

localize9.0ms (0%)

series637.0ms (1.7%)

rewrite16.0ms (0%)

simplify76.0ms (0.2%)

prune128.0ms (0.3%)

localize14.0ms (0%)

series18.1s (49.6%)

rewrite19.0ms (0.1%)

simplify1.0s (2.7%)

prune2.0s (5.3%)

regimes138.0ms (0.4%)

simplify2.0ms (0%)

end235.0ms (0.6%)

Profiling