Details

analyze170.0ms (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)

sample77.0ms (0.6%)

Algorithm

1×

intervals

Results

31.0ms	64×	body	1024	valid
8.0ms	29×	body	512	valid
7.0ms	143×	body	128	valid
6.0ms	3×	body	128	overflowed
6.0ms	8×	body	2048	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify67.0ms (0.6%)

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

29.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 a)
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.9b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series900.0ms (7.4%)

Counts

3 → 52

Calls

3 calls:

888.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
9.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
3.0ms	(exp.f64 a)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 47

Calls

3 calls:

7.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
6.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
2.0ms	(exp.f64 a)

simplify142.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
433×	`associate-+l+_binary64`
430×	`fma-def_binary64`
238×	`times-frac_binary64`
231×	`associate-+r+_binary64`

Counts

99 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1338
1	362	1283
2	1079	1255
3	4133	1251
4	4928	1251
5	4982	1251

prune197.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	3	105

Error

0.2b

Counts

105 → 3

Alt Table

Status	Error	Program
	32.5b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
	29.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1628 to 751 computations (53.9% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series589.0ms (4.8%)

Counts

2 → 28

Calls

2 calls:

585.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
3.0ms	(+.f64 1 (exp.f64 a))

rewrite25.0ms (0.2%)

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:

17.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
6.0ms	(+.f64 1 (exp.f64 a))

simplify107.0ms (0.9%)

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

prune146.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	100	4	104

Error

0.2b

Counts

104 → 4

Alt Table

Status	Error	Program
	32.5b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
	29.9b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.3b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1686 to 886 computations (47.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.8s (14.4%)

Counts

2 → 48

Calls

2 calls:

1.3s	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
486.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite3.0ms (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:

1.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
1.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify220.0ms (1.8%)

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

prune324.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	151	4	155

Error

0.2b

Counts

155 → 4

Alt Table

Status	Error	Program
	32.5b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
▶	29.6b	(-.f64 (+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 1)
	63.2b	(expm1.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (-.f64 (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (*.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (exp.f64 a)))) (log1p.f64 (exp.f64 a))) (log.f64 b))))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 5377 to 3274 computations (39.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 a)
✓	0.0b	(+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	3.1b	(-.f64 (+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 1)

series959.0ms (7.8%)

Counts

2 → 48

Calls

2 calls:

484.0ms	(+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
475.0ms	(-.f64 (+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 1)

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
21×	`add-log-exp_binary64`
18×	`distribute-lft-out_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`prod-diff_binary64`

Counts

2 → 68

Calls

2 calls:

29.0ms	(-.f64 (+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 1)
19.0ms	(+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify204.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-neg_binary64`
544×	`associate-+l+_binary64`
436×	`fma-def_binary64`
363×	`associate-+r+_binary64`
332×	`distribute-rgt-in_binary64`

Counts

116 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	2329
1	278	2193
2	831	2109
3	3514	2095
4	4802	2093
5	4951	2093

prune202.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	176	4	180

Error

0.2b

Counts

180 → 4

Alt Table

Status	Error	Program
	32.5b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
✓	29.6b	(-.f64 (+.f64 1 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 1)
	63.2b	(expm1.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (-.f64 (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (*.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (exp.f64 a)))) (log1p.f64 (exp.f64 a))) (log.f64 b))))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 3926 to 2481 computations (36.8% saved)

regimes1.9s (15.9%)

Accuracy

Total 0.6b remaining (47.1%)

Threshold costs 0.6b (47.1%)

Counts

190 → 1

Compiler

Compiled 21552 to 15614 computations (27.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	16	18
2	15	18

end15.0ms (0.1%)

Compiler: Compiled 39 to 30 computations (23.1% saved)

sample4.0s (33%)

Algorithm

1×

intervals

Results

1.8s	1957×	body	1024	valid
472.0ms	972×	body	512	valid
404.0ms	4413×	body	128	valid
232.0ms	186×	body	2048	valid
120.0ms	472×	body	256	valid
12.0ms	145×	body	128	overflowed

Compiler

Compiled 115 to 75 computations (34.8% saved)

Details

analyze170.0ms (1.4%)

sample77.0ms (0.6%)

simplify67.0ms (0.6%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series900.0ms (7.4%)

rewrite19.0ms (0.2%)

simplify142.0ms (1.2%)

prune197.0ms (1.6%)

localize14.0ms (0.1%)

series589.0ms (4.8%)

rewrite25.0ms (0.2%)

simplify107.0ms (0.9%)

prune146.0ms (1.2%)

localize21.0ms (0.2%)

series1.8s (14.4%)

rewrite3.0ms (0%)

simplify220.0ms (1.8%)

prune324.0ms (2.7%)

localize18.0ms (0.1%)

series959.0ms (7.8%)

rewrite59.0ms (0.5%)

simplify204.0ms (1.7%)

prune202.0ms (1.7%)

regimes1.9s (15.9%)

simplify4.0ms (0%)

end15.0ms (0.1%)

sample4.0s (33%)

Profiling