Details

analyze63.0ms (2.3%)

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
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)

sample2.1s (74.7%)

Symmetry

(sort a x)

Results

754.0ms	1534×	body	2048	valid
567.0ms	1776×	body	1024	valid
289.0ms	3134×	body	128	valid
262.0ms	1176×	body	512	valid
108.0ms	636×	body	256	valid
14.0ms	135×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify72.0ms (2.6%)

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

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

0.0b

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))

series5.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(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))

simplify71.0ms (2.6%)

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

prune10.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Error

Counts

20 → 2

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	16.1b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

Compiler

Compiled 261 to 121 computations (53.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x)))
✓	0.2b	(.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (*.f64 a x)))
✓	16.1b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

series33.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

17.0ms

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

11.0ms

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

5.0ms

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

rewrite14.0ms (0.5%)

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

3.0ms

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

3.0ms

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

simplify108.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-neg_binary64`
445×	`fma-def_binary64`
248×	`distribute-neg-in_binary64`
237×	`*-commutative_binary64`
233×	`sqr-pow_binary64`

Counts

142 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	1870
1	246	1686
2	778	1664
3	2126	1610
4	2909	1543
5	4766	1543
6	5251	1543

prune85.0ms (3.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	169	2	171

Error

Counts

171 → 2

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	16.1b	(cbrt.f64 (.f64 (.f64 (expm1.f64 (.f64 a x)) (expm1.f64 (.f64 a x))) (expm1.f64 (*.f64 a x))))

Compiler

Compiled 3479 to 1079 computations (69% saved)

regimes178.0ms (6.5%)

Accuracy

Total 0.0b remaining (18.5%)

Threshold costs 0.0b (18.5%)

Counts

34 → 1

Compiler

Compiled 2371 to 1539 computations (35.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end41.0ms (1.5%)

Remove: (sort a x)
Compiler: Compiled 47 to 27 computations (42.6% saved)

Details

analyze63.0ms (2.3%)

sample2.1s (74.7%)

simplify72.0ms (2.6%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.2%)

rewrite1.0ms (0%)

simplify71.0ms (2.6%)

prune10.0ms (0.4%)

localize6.0ms (0.2%)

series33.0ms (1.2%)

rewrite14.0ms (0.5%)

simplify108.0ms (3.9%)

prune85.0ms (3.1%)

regimes178.0ms (6.5%)

simplify2.0ms (0.1%)

end41.0ms (1.5%)

Profiling