Details

analyze788.0ms (4.3%)

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)

sample13.1s (71.6%)

Symmetry

(sort a b)

Results

10.2s	7961×	body	8192	exit
1.5s	2060×	body	1024	valid
601.0ms	4499×	body	128	valid
428.0ms	984×	body	512	valid
176.0ms	193×	body	2048	valid
138.0ms	520×	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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series320.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

316.0ms	(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	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify89.0ms (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

prune61.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Error

0.2b

Counts

84 → 4

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.4b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	30.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1429 to 642 computations (55.1% 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 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

series211.0ms (1.2%)

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)))
2.0ms	(+.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))))
4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))

simplify85.0ms (0.5%)

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 → 103

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

prune74.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Error

0.2b

Counts

107 → 5

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.4b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	30.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	0.7b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 1877 to 968 computations (48.4% 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)))
✓	0.0b	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series712.0ms (3.9%)

Counts

2 → 48

Calls

2 calls:

452.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
259.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.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 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-+r+_binary64`
269×	`associate-+l+_binary64`
268×	`+-commutative_binary64`
226×	`cancel-sign-sub-inv_binary64`
216×	`times-frac_binary64`

Counts

70 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	3342
1	879	3194
2	3748	3133
3	4963	3133
4	4976	3133

prune197.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	153	5	158

Error

0.2b

Counts

158 → 5

Alt Table

Status	Error	Program
	30.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	63.7b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.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))))
▶	1.9b	(expm1.f64 (+.f64 (log1p.f64 (log1p.f64 (exp.f64 a))) (/.f64 b (*.f64 (+.f64 1 (exp.f64 a)) (+.f64 1 (log1p.f64 (exp.f64 a)))))))
✓	0.4b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 5584 to 3385 computations (39.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (log1p.f64 (log1p.f64 (exp.f64 a))) (/.f64 b (*.f64 (+.f64 1 (exp.f64 a)) (+.f64 1 (log1p.f64 (exp.f64 a))))))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(expm1.f64 (+.f64 (log1p.f64 (log1p.f64 (exp.f64 a))) (/.f64 b (*.f64 (+.f64 1 (exp.f64 a)) (+.f64 1 (log1p.f64 (exp.f64 a)))))))
✓	0.1b	(/.f64 b (*.f64 (+.f64 1 (exp.f64 a)) (+.f64 1 (log1p.f64 (exp.f64 a)))))

series1.6s (8.7%)

Counts

3 → 72

Calls

3 calls:

629.0ms

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

532.0ms

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

438.0ms

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/r/_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`flip-+_binary64`

Counts

3 → 60

Calls

3 calls:

8.0ms

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

6.0ms

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

0.0ms

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

simplify113.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

492×	`times-frac_binary64`
425×	`fma-def_binary64`
414×	`associate-r_binary64`
361×	`associate-/l*_binary64`
311×	`associate-/r*_binary64`

Counts

132 → 129

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	455	6958
1	1483	6821
2	5385	6821

prune208.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	155	5	160

Error

0.2b

Counts

160 → 5

Alt Table

Status	Error	Program
	30.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	63.7b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.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))))
✓	1.9b	(expm1.f64 (+.f64 (log1p.f64 (log1p.f64 (exp.f64 a))) (/.f64 b (*.f64 (+.f64 1 (exp.f64 a)) (+.f64 1 (log1p.f64 (exp.f64 a)))))))
✓	0.4b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 8859 to 6337 computations (28.5% saved)

regimes319.0ms (1.7%)

Accuracy

Total 0.5b remaining (51.9%)

Threshold costs 0.5b (51.9%)

Counts

65 → 1

Compiler

Compiled 5231 to 3949 computations (24.5% 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

end225.0ms (1.2%)

Compiler: Compiled 152 to 98 computations (35.5% saved)

Details

analyze788.0ms (4.3%)

sample13.1s (71.6%)

simplify5.0ms (0%)

prune2.0ms (0%)

localize8.0ms (0%)

series320.0ms (1.8%)

rewrite7.0ms (0%)

simplify89.0ms (0.5%)

prune61.0ms (0.3%)

localize6.0ms (0%)

series211.0ms (1.2%)

rewrite18.0ms (0.1%)

simplify85.0ms (0.5%)

prune74.0ms (0.4%)

localize9.0ms (0%)

series712.0ms (3.9%)

rewrite1.0ms (0%)

simplify103.0ms (0.6%)

prune197.0ms (1.1%)

localize12.0ms (0.1%)

series1.6s (8.7%)

rewrite19.0ms (0.1%)

simplify113.0ms (0.6%)

prune208.0ms (1.1%)

regimes319.0ms (1.7%)

simplify2.0ms (0%)

end225.0ms (1.2%)

Profiling