Details

analyze60.0ms (1.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (61%)

Symmetry

(sort a x)

Results

756.0ms	1496×	body	2048	valid
570.0ms	1800×	body	1024	valid
273.0ms	3123×	body	128	valid
258.0ms	1174×	body	512	valid
109.0ms	663×	body	256	valid
12.0ms	135×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify77.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

prune6.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (*.f64 a x))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
785×	`fma-neg_binary64`
383×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`

Counts

35 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	382
1	96	369
2	262	363
3	966	347
4	2376	333
5	3696	333
6	4842	333
7	5375	333

prune9.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	1	20

Error

0.0b

Counts

20 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 237 to 115 computations (51.5% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
✓	0.0b	(expm1.f64 (expm1.f64 (*.f64 a x)))
	0.0b	(expm1.f64 (*.f64 a x))

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(expm1.f64 (expm1.f64 (*.f64 a x)))
9.0ms	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (expm1.f64 (*.f64 a x)))
0.0ms	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))

simplify77.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

591×	`distribute-rgt-in_binary64`
563×	`*-commutative_binary64`
525×	`distribute-lft-in_binary64`
499×	`fma-neg_binary64`
308×	`unswap-sqr_binary64`

Counts

70 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	806
1	143	776
2	398	764
3	1490	756
4	2768	728
5	4828	728
6	5151	728

prune29.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Error

0.0b

Counts

64 → 3

Alt Table

Status	Error	Program
	37.6b	(log1p.f64 (.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
▶	22.6b	(log1p.f64 (cbrt.f64 (.f64 (.f64 (expm1.f64 (expm1.f64 (.f64 a x))) (expm1.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 898 to 382 computations (57.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (.f64 (expm1.f64 (expm1.f64 (.f64 a x))) (expm1.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x))))
✓	0.1b	(.f64 (expm1.f64 (expm1.f64 (.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x))))
✓	22.3b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (expm1.f64 (.f64 a x))) (expm1.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x)))))

series56.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

29.0ms

(*.f64 (*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x))))

17.0ms

(*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x))))

10.0ms

(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x)))))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 70

Calls

3 calls:

4.0ms

(*.f64 (*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x))))

3.0ms

(cbrt.f64 (*.f64 (*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x)))))

3.0ms

(*.f64 (expm1.f64 (expm1.f64 (*.f64 a x))) (expm1.f64 (expm1.f64 (*.f64 a x))))

simplify119.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

688×	`unswap-sqr_binary64`
424×	`fma-def_binary64`
258×	`fma-neg_binary64`
239×	`*-commutative_binary64`
221×	`exp-prod_binary64`

Counts

142 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2141
1	257	1924
2	800	1894
3	2136	1834
4	4057	1753
5	4752	1753
6	4920	1753

prune82.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	169	3	172

Error

0.0b

Counts

172 → 3

Alt Table

Status	Error	Program
▶	37.6b	(log1p.f64 (.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
✓	22.6b	(log1p.f64 (cbrt.f64 (.f64 (.f64 (expm1.f64 (expm1.f64 (.f64 a x))) (expm1.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 4155 to 1320 computations (68.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (expm1.f64 (*.f64 a x)))
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x)))))
✓	8.3b	(sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))

series38.0ms (1.1%)

Counts

2 → 40

Calls

2 calls:

28.0ms	(sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
10.0ms	(.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x)))))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 (expm1.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x)))))
1.0ms	(sqrt.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))

simplify73.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-def_binary64`
522×	`distribute-lft-out_binary64`
475×	`*-commutative_binary64`
358×	`unswap-sqr_binary64`
322×	`associate-l_binary64`

Counts

108 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	1443
1	151	1362
2	414	1323
3	1444	1251
4	3634	1157
5	5107	1157

prune94.0ms (2.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	183	2	185

Error

0.0b

Counts

185 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))
	19.2b	(log1p.f64 (fma.f64 a (.f64 (fma.f64 a x 1) x) (fma.f64 5/6 (pow.f64 (.f64 a x) 3) (.f64 5/8 (pow.f64 (.f64 a x) 4)))))

Compiler

Compiled 3624 to 1015 computations (72% saved)

regimes386.0ms (11.5%)

Accuracy

Total 0.0b remaining (12.1%)

Threshold costs 0.0b (12.1%)

Counts

80 → 1

Compiler

Compiled 6710 to 4209 computations (37.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end53.0ms (1.6%)

Remove: (sort a x)
Compiler: Compiled 65 to 46 computations (29.2% saved)

Details

analyze60.0ms (1.8%)

sample2.0s (61%)

simplify77.0ms (2.3%)

prune6.0ms (0.2%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify67.0ms (2%)

prune9.0ms (0.3%)

localize5.0ms (0.1%)

series20.0ms (0.6%)

rewrite1.0ms (0%)

simplify77.0ms (2.3%)

prune29.0ms (0.9%)

localize9.0ms (0.3%)

series56.0ms (1.7%)

rewrite13.0ms (0.4%)

simplify119.0ms (3.6%)

prune82.0ms (2.4%)

localize7.0ms (0.2%)

series38.0ms (1.1%)

rewrite10.0ms (0.3%)

simplify73.0ms (2.2%)

prune94.0ms (2.8%)

regimes386.0ms (11.5%)

simplify2.0ms (0.1%)

end53.0ms (1.6%)

Profiling