Details

analyze490.0ms (16.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (54.9%)

Results

866.0ms	2737×	body	1024	valid
300.0ms	1389×	body	512	valid
256.0ms	3178×	body	128	valid
112.0ms	287×	body	2048	valid
98.0ms	665×	body	256	valid
1.0ms	4×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite92.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
334×	`unpow-prod-down_binary64`
258×	`log-prod_binary64`
241×	`prod-diff_binary64`

Counts

1 → 67

Calls

1 calls:

90.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	98	8
2	1250	8
3	4894	8
4	5321	8
0	0	0
1	0	0

simplify124.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1111×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
754×	`fma-def_binary64`
462×	`cancel-sign-sub-inv_binary64`
454×	`neg-mul-1_binary64`

Counts

79 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	110
1	46	106
2	97	104
3	229	104
4	551	104
5	1141	104
6	1839	104
7	2317	104
8	3682	104
9	3797	104
10	4445	104
11	4865	104
12	4972	104
13	4805	104

prune36.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Error

0.6b

Counts

76 → 3

Alt Table

Status	Error	Program
▶	19.9b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
	20.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1000 to 435 computations (56.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	0.1b	(fma.f64 x 1/12 (/.f64 1 x))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x 1/12 (/.f64 1 x))
2.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))

rewrite44.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`log1p-expm1-u_binary64`
768×	`expm1-log1p-u_binary64`
144×	`log1p-udef_binary64`
122×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`

Counts

2 → 57

Calls

2 calls:

43.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
43.0ms	(fma.f64 x 1/12 (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	172	19
2	1928	19
3	5039	19
0	0	0
1	0	0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
4×	`+-commutative_binary64`
2×	`associate-+r+_binary64`
2×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

81 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	213
1	19	179
2	26	179
3	28	179
4	27	179

prune33.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	66	3	69

Error

0.6b

Counts

69 → 3

Alt Table

Status	Error	Program
✓	19.9b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
▶	20.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 939 to 749 computations (20.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1 x))

series1.0ms (0%)

Counts

1 → 3

Calls

1 calls:

1.0ms

(+.f64 1/2 (/.f64 1 x))

rewrite67.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
241×	`log-prod_binary64`
158×	`prod-diff_binary64`
109×	`expm1-udef_binary64`

Counts

1 → 39

Calls

1 calls:

66.0ms

(+.f64 1/2 (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1492	7
3	4897	7
4	5058	7
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

42 → 41

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	6	6

prune20.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	40	4	44

Error

0.6b

Counts

44 → 4

Alt Table

Status	Error	Program
▶	20.9b	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))
✓	19.9b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	20.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 471 to 392 computations (16.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/2 (/.f64 1 x))
✓	0.2b	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))
✓	0.4b	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
✓	0.6b	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)

series13.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
5.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
1.0ms	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))

rewrite47.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

768×	`log1p-expm1-u_binary64`
768×	`expm1-log1p-u_binary64`
145×	`log1p-udef_binary64`
88×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

46.0ms	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2))
46.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
46.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	193	28
2	1981	28
3	4876	28
0	0	0
1	0	0

simplify60.0ms (2%)

Algorithm

1×	egg-herbie

Rules

985×	`fma-neg_binary64`
438×	`cancel-sign-sub-inv_binary64`
328×	`fma-def_binary64`
194×	`associate-r_binary64`
191×	`distribute-rgt-out_binary64`

Counts

108 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	652
1	234	554
2	624	512
3	2211	488
4	4647	488
5	5134	488

prune135.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	230	4	234

Error

0.6b

Counts

234 → 4

Alt Table

Status	Error	Program
✓	19.9b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
	21.5b	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x)))) 3) 2))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	61.6b	(*.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) (pow.f64 (fma.f64 2/3 (/.f64 (cbrt.f64 1/2) x) (cbrt.f64 1/2)) 2))

Compiler

Compiled 4511 to 3886 computations (13.9% saved)

regimes76.0ms (2.5%)

Accuracy

Total 0.1b remaining (20.6%)

Threshold costs 0.1b (20.6%)

Counts

30 → 1

Compiler

Compiled 1292 to 1108 computations (14.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	7	11

end66.0ms (2.2%)

Compiler: Compiled 68 to 56 computations (17.6% saved)

Details

analyze490.0ms (16.2%)

sample1.7s (54.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite92.0ms (3%)

simplify124.0ms (4.1%)

prune36.0ms (1.2%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite44.0ms (1.4%)

simplify10.0ms (0.3%)

prune33.0ms (1.1%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite67.0ms (2.2%)

simplify6.0ms (0.2%)

prune20.0ms (0.7%)

localize9.0ms (0.3%)

series13.0ms (0.4%)

rewrite47.0ms (1.6%)

simplify60.0ms (2%)

prune135.0ms (4.5%)

regimes76.0ms (2.5%)

simplify2.0ms (0.1%)

end66.0ms (2.2%)

Profiling