Details

analyze80.0ms (1.2%)

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)

sample116.0ms (1.8%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

37.0ms	67×	body	1024	valid
7.0ms	29×	body	512	valid
7.0ms	144×	body	128	valid
3.0ms	4×	body	2048	valid
2.0ms	12×	body	256	valid
0.0ms	4×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify6.0ms (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

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

29.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.9b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series585.0ms (9%)

Counts

2 → 48

Calls

2 calls:

581.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (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:

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

simplify82.0ms (1.3%)

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

prune89.0ms (1.4%)

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

0.6b

Counts

84 → 3

Alt Table

Status	Error	Program
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1405 to 648 computations (53.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
✓	0.0b	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))
✓	0.0b	(/.f64 1/2 (+.f64 1 (exp.f64 a)))
✓	0.0b	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))

series381.0ms (5.9%)

Counts

4 → 64

Calls

4 calls:

309.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
52.0ms	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))
10.0ms	(/.f64 1/2 (+.f64 1 (exp.f64 a)))
9.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))

rewrite96.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
166×	`add-cube-cbrt_binary64`
162×	`prod-diff_binary64`
158×	`times-frac_binary64`

Counts

4 → 323

Calls

4 calls:

22.0ms	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))
12.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
10.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
4.0ms	(/.f64 1/2 (+.f64 1 (exp.f64 a)))

simplify476.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-l_binary64`
535×	`associate-r_binary64`
250×	`associate-*r/_binary64`
227×	`associate-*l/_binary64`
216×	`*-commutative_binary64`

Counts

387 → 386

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	522	18026
1	1439	13892
2	4119	11991
3	4650	11991
4	4873	11991

prune545.0ms (8.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	386	3	389

Error

0.6b

Counts

389 → 3

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	21.6b	(/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 a)) 3) (pow.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) 3)) (fma.f64 (log1p.f64 (exp.f64 a)) (log1p.f64 (exp.f64 a)) (.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (-.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (log1p.f64 (exp.f64 a))))))
	32.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 21436 to 14091 computations (34.3% saved)

localize6.0ms (0.1%)

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))))

series285.0ms (4.4%)

Counts

3 → 32

Calls

3 calls:

263.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
20.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite16.0ms (0.2%)

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)))
2.0ms	(+.f64 1 (exp.f64 a))

simplify83.0ms (1.3%)

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

prune123.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Error

0.6b

Counts

106 → 5

Alt Table

Status	Error	Program
	18.5b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	21.6b	(/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 a)) 3) (pow.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) 3)) (fma.f64 (log1p.f64 (exp.f64 a)) (log1p.f64 (exp.f64 a)) (.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (-.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (log1p.f64 (exp.f64 a))))))
▶	1.8b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	27.8b	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 1/2 b))
	32.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 2011 to 1066 computations (47% saved)

localize8.0ms (0.1%)

Local error

Found 4 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)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

series280.0ms (4.3%)

Counts

2 → 48

Calls

2 calls:

260.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
20.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

486×	`distribute-rgt-neg-in_binary64`
438×	`associate-+r+_binary64`
366×	`cancel-sign-sub-inv_binary64`
347×	`associate-l_binary64`
332×	`sub-neg_binary64`

Counts

78 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1175
1	204	1119
2	532	1103
3	1544	1099
4	3675	1099
5	4727	1099
6	5033	1099

prune149.0ms (2.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Error

0.6b

Counts

141 → 5

Alt Table

Status	Error	Program
	1.8b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
	25.6b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
	21.6b	(/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 a)) 3) (pow.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) 3)) (fma.f64 (log1p.f64 (exp.f64 a)) (log1p.f64 (exp.f64 a)) (.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (-.f64 (fma.f64 (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))) (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a)))) (log1p.f64 (exp.f64 a))))))
	27.8b	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 1/2 b))
	32.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 2624 to 1477 computations (43.7% saved)

regimes795.0ms (12.3%)

Accuracy

Total 0.4b remaining (42.5%)

Threshold costs 0.4b (42.5%)

Counts

154 → 1

Compiler

Compiled 18897 to 12689 computations (32.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
1	24	44
2	31	44
3	33	44
4	34	44
5	32	44

end8.0ms (0.1%)

Compiler: Compiled 90 to 60 computations (33.3% saved)

sample2.1s (33.1%)

Algorithm

1×

intervals

Results

963.0ms	1934×	body	1024	valid
243.0ms	939×	body	512	valid
223.0ms	4432×	body	128	valid
139.0ms	211×	body	2048	valid
65.0ms	484×	body	256	valid
6.0ms	133×	body	128	overflowed

Compiler

Compiled 186 to 121 computations (34.9% saved)

Details

analyze80.0ms (1.2%)

sample116.0ms (1.8%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series585.0ms (9%)

rewrite7.0ms (0.1%)

simplify82.0ms (1.3%)

prune89.0ms (1.4%)

localize13.0ms (0.2%)

series381.0ms (5.9%)

rewrite96.0ms (1.5%)

simplify476.0ms (7.3%)

prune545.0ms (8.4%)

localize6.0ms (0.1%)

series285.0ms (4.4%)

rewrite16.0ms (0.2%)

simplify83.0ms (1.3%)

prune123.0ms (1.9%)

localize8.0ms (0.1%)

series280.0ms (4.3%)

rewrite4.0ms (0.1%)

simplify89.0ms (1.4%)

prune149.0ms (2.3%)

regimes795.0ms (12.3%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample2.1s (33.1%)

Profiling