Details

analyze153.0ms (3.3%)

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%	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)

sample174.0ms (3.7%)

Algorithm

1×

intervals

Results

37.0ms	72×	body	1024	valid
11.0ms	41×	body	512	valid
7.0ms	129×	body	128	valid
3.0ms	5×	body	2048	valid
1.0ms	9×	body	256	valid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

32.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
3.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite124.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

32.5b

Rules

16×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
10×	`flip3-+_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 80

Calls

2 calls:

56.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
10.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 1221 to 288 computations (76.4% saved)

series46.0ms (1%)

Error

0.7b

Counts

2 → 19

Calls

2 calls:

24.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
11.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 533 to 392 computations (26.5% saved)

simplify107.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
419×	`fma-def_binary64`
401×	`cancel-sign-sub-inv_binary64`
315×	`associate-l_binary64`
262×	`associate-r_binary64`

Counts

99 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1679
1	325	1541
2	928	1427
3	2943	1374
4	4240	1374
5	4895	1374

prune33.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Error

0.4b

Counts

58 → 3

Alt Table

Status	Error	Program
▶	1.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(-.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))) 1)
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 856 to 354 computations (58.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite57.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

12×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`expm1-log1p-u_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 70

Calls

2 calls:

14.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
9.0ms	(log1p.f64 (exp.f64 a))

Compiler

Compiled 1043 to 491 computations (52.9% saved)

series75.0ms (1.6%)

Error

0.4b

Counts

2 → 14

Calls

2 calls:

63.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
8.0ms	(log1p.f64 (exp.f64 a))

Compiler

Compiled 385 to 284 computations (26.2% saved)

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
544×	`associate-/l*_binary64`
337×	`distribute-rgt-in_binary64`
313×	`cancel-sign-sub-inv_binary64`
293×	`distribute-lft-in_binary64`

Counts

84 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1162
1	181	1123
2	575	1092
3	1943	1078
4	4715	1077
5	5005	1077

prune18.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Error

0.4b

Counts

38 → 5

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	23.8b	(cbrt.f64 (pow.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
▶	2.5b	(+.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(-.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))) 1)
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 565 to 320 computations (43.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
0.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6))
0.5b	(pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)
0.9b	(cbrt.f64 (log1p.f64 (exp.f64 a)))

rewrite126.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

28×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 144

Calls

4 calls:

14.0ms	(+.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
13.0ms	(pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)
10.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6))
10.0ms	(cbrt.f64 (log1p.f64 (exp.f64 a)))

Compiler

Compiled 2430 to 1318 computations (45.8% saved)

series87.0ms (1.9%)

Error

0.4b

Counts

4 → 22

Calls

4 calls:

29.0ms	(+.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
24.0ms	(pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6)
19.0ms	(cbrt.f64 (log1p.f64 (exp.f64 a)))
9.0ms	(sqrt.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 6))

Compiler

Compiled 802 to 625 computations (22.1% saved)

simplify140.0ms (3%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-neg_binary64`
415×	`cancel-sign-sub-inv_binary64`
358×	`log-prod_binary64`
357×	`exp-prod_binary64`
270×	`fma-def_binary64`

Counts

166 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2008
1	294	1720
2	867	1559
3	2594	1540
4	3986	1540
5	4762	1540
6	4863	1540

prune43.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Error

0.4b

Counts

98 → 5

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(-.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))) 1)
	33.6b	(-.f64 (exp.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) 1)
▶	1.9b	(+.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1206 to 685 computations (43.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a)))))
0.2b	(sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6))
0.5b	(pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6)
1.2b	(log.f64 (log1p.f64 (exp.f64 a)))

rewrite154.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

30×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`pow1_binary64`
13×	`add-log-exp_binary64`
12×	`add-cbrt-cube_binary64`

Counts

4 → 141

Calls

4 calls:

39.0ms	(pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6)
13.0ms	(exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a)))))
12.0ms	(sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6))
11.0ms	(log.f64 (log1p.f64 (exp.f64 a)))

Compiler

Compiled 2615 to 1498 computations (42.7% saved)

series74.0ms (1.6%)

Error

0.4b

Counts

4 → 16

Calls

4 calls:

23.0ms	(pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6)
19.0ms	(exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a)))))
15.0ms	(log.f64 (log1p.f64 (exp.f64 a)))
10.0ms	(sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6))

Compiler

Compiled 786 to 636 computations (19.1% saved)

simplify101.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

995×	`fma-neg_binary64`
612×	`log-prod_binary64`
325×	`cancel-sign-sub-inv_binary64`
261×	`exp-prod_binary64`
230×	`associate-l_binary64`

Counts

157 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1581
1	257	1182
2	485	1038
3	1801	999
4	3817	999
5	5014	999

prune37.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	79	5	84

Error

0.4b

Counts

84 → 5

Alt Table

Status	Error	Program
	1.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(-.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))))) 1)
	33.6b	(-.f64 (exp.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) 1)
	1.9b	(+.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 1/3 (log.f64 (log1p.f64 (exp.f64 a))))) 6)) (/.f64 b (+.f64 1 (exp.f64 a))))
	34.8b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 954 to 561 computations (41.2% saved)

regimes630.0ms (13.5%)

Accuracy

Total 0.4b remaining (45.1%)

Threshold costs 0.4b (45.1%)

Compiler

Compiled 10875 to 7080 computations (34.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	24	44
2	23	44

end8.0ms (0.2%)

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

sample2.3s (50%)

Algorithm

1×

intervals

Results

1.0s	1949×	body	1024	valid
272.0ms	995×	body	512	valid
233.0ms	4362×	body	128	valid
142.0ms	209×	body	2048	valid
75.0ms	485×	body	256	valid
6.0ms	126×	body	128	overflowed

Compiler

Compiled 112 to 82 computations (26.8% saved)

Details

analyze153.0ms (3.3%)

sample174.0ms (3.7%)

simplify9.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite124.0ms (2.7%)

series46.0ms (1%)

simplify107.0ms (2.3%)

prune33.0ms (0.7%)

localize6.0ms (0.1%)

rewrite57.0ms (1.2%)

series75.0ms (1.6%)

simplify94.0ms (2%)

prune18.0ms (0.4%)

localize10.0ms (0.2%)

rewrite126.0ms (2.7%)

series87.0ms (1.9%)

simplify140.0ms (3%)

prune43.0ms (0.9%)

localize13.0ms (0.3%)

rewrite154.0ms (3.3%)

series74.0ms (1.6%)

simplify101.0ms (2.2%)

prune37.0ms (0.8%)

regimes630.0ms (13.5%)

simplify4.0ms (0.1%)

end8.0ms (0.2%)

sample2.3s (50%)

Profiling