Details

analyze182.0ms (2.5%)

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)

sample90.0ms (1.2%)

Algorithm

1×

intervals

Results

29.0ms	49×	body	2048	valid
21.0ms	53×	body	1024	valid
6.0ms	36×	body	512	valid
5.0ms	94×	body	128	valid
3.0ms	24×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify93.0ms (1.3%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))
	30.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite2.0ms (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:

1.0ms

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

series11.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

simplify105.0ms (1.5%)

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 → 59

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

prune21.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	58	3	61

Error

0.0b

Counts

61 → 3

Alt Table

Status	Error	Program
▶	17.8b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
	30.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 261 to 133 computations (49% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	17.8b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

3.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
3.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)

series67.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

57.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
10.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

simplify160.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

674×	`associate-l_binary64`
587×	`associate-r_binary64`
337×	`log-prod_binary64`
288×	`fma-def_binary64`
278×	`exp-prod_binary64`

Counts

96 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1262
1	202	1199
2	629	1177
3	3098	1171
4	4791	1171
5	4962	1171

prune80.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	235	3	238

Error

0.0b

Counts

238 → 3

Alt Table

Status	Error	Program
✓	17.8b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	44.0b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1256 to 673 computations (46.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	25.0b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`unpow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`pow-exp_binary64`

Counts

1 → 31

Calls

1 calls:

5.0ms

(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

series1.2s (16.3%)

Counts

1 → 24

Calls

1 calls:

1.2s	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

simplify122.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

746×	`distribute-rgt-in_binary64`
551×	`associate-l_binary64`
462×	`associate-r_binary64`
447×	`log-prod_binary64`
296×	`fma-def_binary64`

Counts

55 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	1018
1	230	903
2	648	619
3	2618	591
4	5595	591

prune99.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	310	4	314

Error

0.0b

Counts

314 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
	50.8b	(pow.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3) 1/3)
✓	17.8b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	38.8b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 1746 to 1044 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	10.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
✓	10.3b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`cbrt-prod_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 66

Calls

3 calls:

10.0ms	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
3.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
1.0ms	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.8s (24.8%)

Counts

3 → 72

Calls

3 calls:

1.2s	(pow.f64 (expm1.f64 (*.f64 a x)) 2/3)
606.0ms	(cbrt.f64 (expm1.f64 (*.f64 a x)))
11.0ms	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

simplify274.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
437×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`
398×	`*-commutative_binary64`
232×	`unswap-sqr_binary64`

Counts

138 → 254

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	153	2314
1	370	2252
2	1044	1905
3	2476	1793
4	4839	1765
5	4978	1765
6	4970	1765
7	4890	1765

prune175.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	490	4	494

Error

0.0b

Counts

494 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
	50.8b	(pow.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3) 1/3)
	38.8b	(.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2/3) (.f64 (sqrt.f64 (cbrt.f64 (expm1.f64 (.f64 a x)))) (sqrt.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
✓	17.8b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 2918 to 1132 computations (61.2% saved)

regimes125.0ms (1.7%)

Accuracy

Total 0.0b remaining (37.9%)

Threshold costs 0.0b (37.9%)

Compiler

Compiled 810 to 514 computations (36.5% saved)

simplify5.0ms (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

end11.0ms (0.2%)

Remove: (sort a x)
Compiler: Compiled 18 to 12 computations (33.3% saved)

sample2.5s (35.1%)

Algorithm

1×

intervals

Results

893.0ms	1455×	body	2048	valid
568.0ms	1727×	body	1024	valid
231.0ms	3070×	body	128	valid
210.0ms	1093×	body	512	valid
76.0ms	655×	body	256	valid
7.0ms	128×	body	128	invalid

Compiler

Compiled 66 to 44 computations (33.3% saved)

Details

analyze182.0ms (2.5%)

sample90.0ms (1.2%)

simplify93.0ms (1.3%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite2.0ms (0%)

series11.0ms (0.2%)

simplify105.0ms (1.5%)

prune21.0ms (0.3%)

localize12.0ms (0.2%)

rewrite9.0ms (0.1%)

series67.0ms (0.9%)

simplify160.0ms (2.2%)

prune80.0ms (1.1%)

localize13.0ms (0.2%)

rewrite8.0ms (0.1%)

series1.2s (16.3%)

simplify122.0ms (1.7%)

prune99.0ms (1.4%)

localize14.0ms (0.2%)

rewrite20.0ms (0.3%)

series1.8s (24.8%)

simplify274.0ms (3.8%)

prune175.0ms (2.4%)

regimes125.0ms (1.7%)

simplify5.0ms (0.1%)

end11.0ms (0.2%)

sample2.5s (35.1%)

Profiling