Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample18.0s (68%)

Symmetry

(sort a b)

Results

14.1s	7847×	body	8192	exit
2.0s	1988×	body	1024	valid
798.0ms	4588×	body	128	valid
583.0ms	1030×	body	512	valid
213.0ms	174×	body	2048	valid
174.0ms	476×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify18.0ms (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

prune3.0ms (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

31.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.9b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize11.0ms (0%)

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)))

series823.0ms (3.1%)

Counts

2 → 48

Calls

2 calls:

814.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
8.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite15.0ms (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:

6.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
6.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify140.0ms (0.5%)

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

prune114.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Error

0.4b

Counts

84 → 3

Alt Table

Status	Error	Program
	35.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	32.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1365 to 624 computations (54.3% saved)

localize14.0ms (0.1%)

Local error

Found 2 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 1 (exp.f64 a))

series343.0ms (1.3%)

Counts

2 → 28

Calls

2 calls:

340.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
3.0ms	(+.f64 1 (exp.f64 a))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
7×	`add-log-exp_binary64`
6×	`fma-def_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 35

Calls

2 calls:

12.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
4.0ms	(+.f64 1 (exp.f64 a))

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-neg_binary64`
496×	`associate-+r+_binary64`
405×	`times-frac_binary64`
356×	`associate-l_binary64`
317×	`fma-def_binary64`

Counts

63 → 59

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	955
1	256	894
2	626	884
3	1780	874
4	3990	873
5	5038	873

prune88.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Error

0.4b

Counts

62 → 4

Alt Table

Status	Error	Program
	35.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
▶	0.7b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	2.4b	(.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	32.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1100 to 594 computations (46% saved)

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

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

series459.0ms (1.7%)

Counts

1 → 24

Calls

1 calls:

459.0ms

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

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`fma-def_binary64`
17×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 33

Calls

1 calls:

21.0ms

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

simplify159.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

941×	`fma-neg_binary64`
586×	`cancel-sign-sub-inv_binary64`
480×	`associate-+l+_binary64`
358×	`associate-+r+_binary64`
305×	`times-frac_binary64`

Counts

57 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	780
1	180	737
2	442	723
3	1275	715
4	2933	714
5	4893	714
6	5063	714

prune103.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Error

0.4b

Counts

81 → 4

Alt Table

Status	Error	Program
	35.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	0.7b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
▶	2.4b	(.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	32.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1449 to 769 computations (46.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	1.0b	(cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))

series3.0s (11.4%)

Counts

3 → 72

Calls

3 calls:

1.4s

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

1.0s

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

577.0ms

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

rewrite169.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`
33×	`cbrt-prod_binary64`
32×	`frac-times_binary64`

Counts

3 → 136

Calls

3 calls:

60.0ms

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

42.0ms

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

15.0ms

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

simplify452.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
330×	`times-frac_binary64`
314×	`*-commutative_binary64`
265×	`associate-/l*_binary64`
192×	`associate-/r*_binary64`

Counts

208 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	721	14348
1	2223	12657
2	4939	12458
3	4964	12458

prune1.3s (4.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	430	2	432
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	431	5	436

Error

0.4b

Counts

436 → 5

Alt Table

Status	Error	Program
	35.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	44.8b	(.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (fma.f64 1/3 (.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (exp.f64 (fma.f64 1/3 (fma.f64 -1 (log1p.f64 (exp.f64 a)) (log.f64 b)) a))) (fma.f64 1/3 (.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (cbrt.f64 (exp.f64 (fma.f64 -1 (log1p.f64 (exp.f64 a)) (log.f64 b))))) (cbrt.f64 (exp.f64 (fma.f64 -1 (log1p.f64 (exp.f64 a)) (log.f64 b)))))))
✓	0.7b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	32.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	3.4b	(expm1.f64 (log1p.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))

Compiler

Compiled 32477 to 20010 computations (38.4% saved)

regimes708.0ms (2.7%)

Accuracy

Total 0.5b remaining (53.2%)

Threshold costs 0.5b (53.2%)

Counts

62 → 1

Compiler

Compiled 6369 to 4546 computations (28.6% saved)

simplify3.0ms (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

end383.0ms (1.4%)

Compiler: Compiled 192 to 116 computations (39.6% saved)

Details

analyze2.0ms (0%)

sample18.0s (68%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0%)

series823.0ms (3.1%)

rewrite15.0ms (0.1%)

simplify140.0ms (0.5%)

prune114.0ms (0.4%)

localize14.0ms (0.1%)

series343.0ms (1.3%)

rewrite18.0ms (0.1%)

simplify112.0ms (0.4%)

prune88.0ms (0.3%)

localize13.0ms (0%)

series459.0ms (1.7%)

rewrite26.0ms (0.1%)

simplify159.0ms (0.6%)

prune103.0ms (0.4%)

localize22.0ms (0.1%)

series3.0s (11.4%)

rewrite169.0ms (0.6%)

simplify452.0ms (1.7%)

prune1.3s (4.8%)

regimes708.0ms (2.7%)

simplify3.0ms (0%)

end383.0ms (1.4%)

Profiling