Details

analyze980.0ms (13.3%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.7%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.9%	0.1%	8
16.4%	83.5%	0.1%	9
19.1%	80.8%	0.1%	10
20.5%	79.4%	0.1%	11
22%	78%	0.1%	12
22.7%	77.2%	0.1%	13
23.4%	76.5%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.6s (48.4%)

Symmetry

(sort a x)

Results

1.3s	2672×	body	8192	exit
842.0ms	1524×	body	2048	valid
663.0ms	1839×	body	1024	valid
333.0ms	3113×	body	128	valid
292.0ms	1172×	body	512	valid
114.0ms	608×	body	256	valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify73.0ms (1%)

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%)

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%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(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))

simplify68.0ms (0.9%)

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 (0.1%)

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

0.0b

Counts

20 → 2

Alt Table

Status	Error	Program
▶	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 245 to 121 computations (50.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series30.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite6.0ms (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:

2.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
2.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

simplify85.0ms (1.2%)

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 → 70

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

prune45.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Error

0.0b

Counts

91 → 3

Alt Table

Status	Error	Program
✓	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	48.8b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

Compiler

Compiled 1312 to 701 computations (46.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	26.1b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

series618.0ms (8.4%)

Counts

1 → 24

Calls

1 calls:

618.0ms

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

rewrite5.0ms (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:

3.0ms

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

simplify55.0ms (0.7%)

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 → 49

Iterations

Useful iterations: 3 (0.0ms)

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

prune56.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	102	3	105

Error

Counts

105 → 3

Alt Table

Status	Error	Program
✓	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	48.8b	(.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))) 1/3) (pow.f64 (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1798 to 1072 computations (40.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))
✓	10.3b	(pow.f64 (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	22.5b	(pow.f64 (.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))) 1/3)

series1.1s (14.7%)

Counts

3 → 72

Calls

3 calls:

605.0ms

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

465.0ms

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

14.0ms

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

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`cbrt-prod_binary64`
69×	`add-sqr-sqrt_binary64`
47×	`unpow-prod-down_binary64`
31×	`cube-prod_binary64`
29×	`*-un-lft-identity_binary64`

Counts

3 → 156

Calls

3 calls:

11.0ms

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

7.0ms

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

4.0ms

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

simplify145.0ms (2%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
539×	`*-commutative_binary64`
349×	`exp-prod_binary64`
247×	`sqr-pow_binary64`
241×	`log-prod_binary64`

Counts

228 → 216

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	239	3286
1	476	3134
2	1472	2788
3	3083	2654
4	4659	2630
5	4921	2630

prune260.0ms (3.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	324	0	324
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	324	3	327

Error

Counts

327 → 3

Alt Table

Status	Error	Program
✓	19.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	48.8b	(.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))) 1/3) (pow.f64 (cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 11010 to 6155 computations (44.1% saved)

regimes138.0ms (1.9%)

Accuracy

Total 0.0b remaining (17.3%)

Threshold costs 0.0b (17.3%)

Counts

23 → 1

Compiler

Compiled 2590 to 1764 computations (31.9% saved)

simplify3.0ms (0%)

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

end62.0ms (0.8%)

Remove: (sort a x)
Compiler: Compiled 68 to 46 computations (32.4% saved)

Details

analyze980.0ms (13.3%)

sample3.6s (48.4%)

simplify73.0ms (1%)

prune3.0ms (0%)

localize3.0ms (0%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify68.0ms (0.9%)

prune10.0ms (0.1%)

localize7.0ms (0.1%)

series30.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify85.0ms (1.2%)

prune45.0ms (0.6%)

localize7.0ms (0.1%)

series618.0ms (8.4%)

rewrite5.0ms (0.1%)

simplify55.0ms (0.7%)

prune56.0ms (0.8%)

localize14.0ms (0.2%)

series1.1s (14.7%)

rewrite38.0ms (0.5%)

simplify145.0ms (2%)

prune260.0ms (3.5%)

regimes138.0ms (1.9%)

simplify3.0ms (0%)

end62.0ms (0.8%)

Profiling