Details

analyze385.0ms (4.9%)

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.8s (60.7%)

Results

2.6s	2566×	body	8192	exit
1.8s	7664×	body	128	valid
118.0ms	196×	body	1024	valid
106.0ms	262×	body	512	valid
32.0ms	133×	body	256	valid
10.0ms	78×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
✓	0.2b	(log.f64 (+.f64 1 (exp.f64 x)))

series265.0ms (3.4%)

Counts

3 → 32

Calls

3 calls:

180.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
84.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`log-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

3 → 63

Calls

3 calls:

5.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
2.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

343×	`fma-def_binary64`
310×	`distribute-rgt-in_binary64`
305×	`cancel-sign-sub-inv_binary64`
244×	`associate-+l+_binary64`
238×	`distribute-lft-in_binary64`

Counts

95 → 109

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	115	1097
1	272	1018
2	652	1004
3	2057	999
4	4440	999
5	4970	993
6	5000	993
7	4880	993

prune123.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	2	111

Error

0.2b

Counts

111 → 2

Alt Table

Status	Error	Program
	10.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
▶	0.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))

Compiler

Compiled 1692 to 872 computations (48.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))
✓	0.2b	(log1p.f64 (exp.f64 x))
✓	1.0b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

series602.0ms (7.6%)

Counts

3 → 40

Calls

3 calls:

236.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
184.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))
182.0ms	(log1p.f64 (exp.f64 x))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`log-prod_binary64`
8×	`sqrt-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 68

Calls

3 calls:

10.0ms	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))
3.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
0.0ms	(log1p.f64 (exp.f64 x))

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
583×	`fma-def_binary64`
575×	`associate-+r+_binary64`
363×	`associate--l+_binary64`
208×	`distribute-rgt-in_binary64`

Counts

108 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2303
1	442	2044
2	1270	1958
3	4928	1952
4	5624	1952

prune94.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	143	2	145

Error

0.2b

Counts

145 → 2

Alt Table

Status	Error	Program
▶	10.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))

Compiler

Compiled 3486 to 2085 computations (40.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series13.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
478×	`neg-sub0_binary64`
433×	`neg-mul-1_binary64`
375×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	459
1	52	346
2	104	346
3	328	346
4	1670	346
5	2981	346
6	4467	346
7	4969	346

prune18.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Error

0.2b

Counts

24 → 3

Alt Table

Status	Error	Program
▶	12.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	10.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))

Compiler

Compiled 289 to 218 computations (24.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	0.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))
✓	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

series192.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

126.0ms

(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

53.0ms

(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

rewrite17.0ms (0.2%)

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 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))))

1.0ms

(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

simplify145.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

734×	`times-frac_binary64`
597×	`fma-def_binary64`
506×	`associate-/l*_binary64`
250×	`*-commutative_binary64`
137×	`+-commutative_binary64`

Counts

165 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	669	9535
1	2330	8681
2	5361	8681

prune550.0ms (7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	393	3	396

Error

0.2b

Counts

396 → 3

Alt Table

Status	Error	Program
	60.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))) (fma.f64 1/3 (/.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x))) (/.f64 (-.f64 1/2 y) (/.f64 (log.f64 2) x))) (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (-.f64 1/2 y)) (log.f64 x)))))
✓	10.8b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(+.f64 (log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) (.f64 x y)))

Compiler

Compiled 24154 to 18810 computations (22.1% saved)

regimes153.0ms (1.9%)

Accuracy

Total 0.2b remaining (45.9%)

Threshold costs 0.2b (45.9%)

Counts

53 → 1

Compiler

Compiled 2294 to 1765 computations (23.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	18	24
2	28	24
3	34	24
4	38	24
5	39	24
6	39	24

end96.0ms (1.2%)

Compiler: Compiled 112 to 82 computations (26.8% saved)

Details

analyze385.0ms (4.9%)

sample4.8s (60.7%)

simplify99.0ms (1.3%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series265.0ms (3.4%)

rewrite12.0ms (0.2%)

simplify118.0ms (1.5%)

prune123.0ms (1.6%)

localize12.0ms (0.2%)

series602.0ms (7.6%)

rewrite17.0ms (0.2%)

simplify92.0ms (1.2%)

prune94.0ms (1.2%)

localize5.0ms (0.1%)

series13.0ms (0.2%)

rewrite1.0ms (0%)

simplify64.0ms (0.8%)

prune18.0ms (0.2%)

localize9.0ms (0.1%)

series192.0ms (2.4%)

rewrite17.0ms (0.2%)

simplify145.0ms (1.8%)

prune550.0ms (7%)

regimes153.0ms (1.9%)

simplify3.0ms (0%)

end96.0ms (1.2%)

Profiling