Details

analyze783.0ms (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)

sample12.9s (70.3%)

Symmetry

(sort a b)

Results

10.1s	7975×	body	8192	exit
1.4s	1995×	body	1024	valid
612.0ms	4582×	body	128	valid
450.0ms	1028×	body	512	valid
190.0ms	207×	body	2048	valid
117.0ms	444×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify8.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series447.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

443.0ms	(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))

simplify136.0ms (0.7%)

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

prune49.0ms (0.3%)

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

1.2b

Counts

84 → 3

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (expm1.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	30.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1361 to 624 computations (54.2% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

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

series303.0ms (1.6%)

Counts

3 → 32

Calls

3 calls:

254.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
29.0ms	(+.f64 1 (exp.f64 a))
20.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))

rewrite16.0ms (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))

simplify91.0ms (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

prune78.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Error

1.2b

Counts

106 → 5

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (expm1.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	2.4b	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 1867 to 985 computations (47.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a))))
✓	0.0b	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
✓	2.4b	(-.f64 1 (exp.f64 a))

series366.0ms (2%)

Counts

4 → 76

Calls

4 calls:

301.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a))))
35.0ms	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
28.0ms	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))
2.0ms	(-.f64 1 (exp.f64 a))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 219

Calls

4 calls:

12.0ms	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
6.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a))))
4.0ms	(-.f64 1 (exp.f64 a))
3.0ms	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))

simplify215.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
309×	`cancel-sign-sub-inv_binary64`
185×	`associate-l_binary64`
173×	`associate-r_binary64`
173×	`distribute-lft-neg-out_binary64`

Counts

295 → 351

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	332	6612
1	789	6269
2	2683	5855
3	4486	5849
4	4995	5841
5	4900	5841

prune357.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	350	1	351
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	351	5	356

Error

1.2b

Counts

356 → 5

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (expm1.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
▶	2.4b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))))

Compiler

Compiled 10136 to 2973 computations (70.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a)))
✓	0.0b	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))
✓	0.0b	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
✓	2.4b	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))

series330.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

242.0ms	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
54.0ms	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))
31.0ms	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))
3.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a)))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
46×	`associate-r_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
30×	`times-frac_binary64`

Counts

4 → 144

Calls

4 calls:

10.0ms	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))
7.0ms	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))
5.0ms	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
5.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a)))

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
623×	`associate-l_binary64`
423×	`associate-r_binary64`
264×	`fma-neg_binary64`
189×	`*-commutative_binary64`

Counts

216 → 262

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	3862
1	766	3605
2	3738	3499
3	4965	3499

prune275.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	261	6	267

Error

1.2b

Counts

267 → 6

Alt Table

Status	Error	Program
	30.2b	(log1p.f64 (expm1.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	2.4b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (exp.f64 a) (/.f64 b (expm1.f64 (+.f64 a a))))))
	40.8b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (*.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (exp.f64 (+.f64 a (log.f64 (neg.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	3.0b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 10207 to 2358 computations (76.9% saved)

regimes1.5s (8.3%)

Accuracy

Total 0.6b remaining (52.1%)

Threshold costs 0.6b (52.1%)

Counts

298 → 1

Compiler

Compiled 51257 to 28832 computations (43.8% 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	11	20
1	15	20
2	14	20

end240.0ms (1.3%)

Compiler: Compiled 160 to 106 computations (33.8% saved)

Details

analyze783.0ms (4.3%)

sample12.9s (70.3%)

simplify8.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0%)

series447.0ms (2.4%)

rewrite7.0ms (0%)

simplify136.0ms (0.7%)

prune49.0ms (0.3%)

localize6.0ms (0%)

series303.0ms (1.6%)

rewrite16.0ms (0.1%)

simplify91.0ms (0.5%)

prune78.0ms (0.4%)

localize10.0ms (0.1%)

series366.0ms (2%)

rewrite45.0ms (0.2%)

simplify215.0ms (1.2%)

prune357.0ms (1.9%)

localize15.0ms (0.1%)

series330.0ms (1.8%)

rewrite41.0ms (0.2%)

simplify107.0ms (0.6%)

prune275.0ms (1.5%)

regimes1.5s (8.3%)

simplify3.0ms (0%)

end240.0ms (1.3%)

Profiling