Details

analyze813.0ms (4.8%)

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)

sample12.8s (75.6%)

Symmetry

(sort a b)

Results

9.8s	7735×	body	8192	exit
1.5s	2059×	body	1024	valid
630.0ms	4561×	body	128	valid
467.0ms	967×	body	512	valid
185.0ms	201×	body	2048	valid
133.0ms	468×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (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

30.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series420.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

416.0ms	(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)))

simplify86.0ms (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

prune65.0ms (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
	31.7b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))) (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (log.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	33.3b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1393 to 628 computations (54.9% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

17.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite9.0ms (0.1%)

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)))
3.0ms	(+.f64 1 (exp.f64 a))

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

60 → 71

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

prune47.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Error

0.4b

Counts

74 → 3

Alt Table

Status	Error	Program
	33.3b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	31.7b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))) (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (log.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 1266 to 651 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
✓	0.4b	(log1p.f64 (+.f64 1 (exp.f64 a)))

series278.0ms (1.6%)

Counts

3 → 48

Calls

3 calls:

258.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))
19.0ms	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
2.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

rewrite5.0ms (0%)

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:

2.0ms	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
0.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
750×	`times-frac_binary64`
434×	`associate-l_binary64`
330×	`associate-r_binary64`
307×	`associate-/l*_binary64`

Counts

99 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1162
1	229	1079
2	584	1069
3	1403	1056
4	4082	1056
5	5105	1056

prune93.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Error

0.4b

Counts

142 → 4

Alt Table

Status	Error	Program
✓	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
▶	2.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))
	33.3b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	31.7b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))) (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (log.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2531 to 1429 computations (43.5% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
	0.4b	(log1p.f64 (+.f64 1 (exp.f64 a)))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
✓	0.8b	(cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

series1.1s (6.2%)

Counts

3 → 36

Calls

3 calls:

458.0ms

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

406.0ms

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

186.0ms

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify127.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
481×	`fma-neg_binary64`
451×	`unswap-sqr_binary64`
300×	`*-commutative_binary64`
284×	`associate-+l+_binary64`

Counts

129 → 144

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2509
1	393	2311
2	1233	2026
3	3317	1983
4	4921	1906
5	4974	1906
6	4954	1906

prune260.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	271	4	275

Error

0.4b

Counts

275 → 4

Alt Table

Status	Error	Program
	33.3b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	31.7b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))) (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))) (log.f64 (cbrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	3.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))) 8) (cbrt.f64 (cbrt.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))))))
✓	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 9222 to 6342 computations (31.2% saved)

regimes385.0ms (2.3%)

Accuracy

Total 0.5b remaining (57.9%)

Threshold costs 0.5b (57.9%)

Counts

74 → 1

Compiler

Compiled 7276 to 5089 computations (30.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	18	16
2	26	16
3	31	16
4	33	16
5	33	16

end229.0ms (1.3%)

Compiler: Compiled 124 to 80 computations (35.5% saved)

Details

analyze813.0ms (4.8%)

sample12.8s (75.6%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series420.0ms (2.5%)

rewrite7.0ms (0%)

simplify86.0ms (0.5%)

prune65.0ms (0.4%)

localize6.0ms (0%)

series19.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify63.0ms (0.4%)

prune47.0ms (0.3%)

localize9.0ms (0.1%)

series278.0ms (1.6%)

rewrite5.0ms (0%)

simplify71.0ms (0.4%)

prune93.0ms (0.5%)

localize55.0ms (0.3%)

series1.1s (6.2%)

rewrite18.0ms (0.1%)

simplify127.0ms (0.8%)

prune260.0ms (1.5%)

regimes385.0ms (2.3%)

simplify2.0ms (0%)

end229.0ms (1.3%)

Profiling