Details

analyze58.0ms (2%)

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 (73.2%)

Symmetry

(sort a x)

Results

784.0ms	1479×	body	2048	valid
593.0ms	1713×	body	1024	valid
289.0ms	3235×	body	128	valid
263.0ms	1214×	body	512	valid
92.0ms	615×	body	256	valid
13.0ms	142×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify72.0ms (2.5%)

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))

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 (2.3%)

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

prune13.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Error

0.0b

Counts

20 → 3

Alt Table

Status	Error	Program
▶	19.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	25.6b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 297 to 153 computations (48.5% saved)

localize7.0ms (0.2%)

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)
✓	19.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series28.0ms (1%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
6.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite5.0ms (0.2%)

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	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
1.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)

simplify91.0ms (3.1%)

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

prune47.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	89	3	92

Error

0.0b

Counts

92 → 3

Alt Table

Status	Error	Program
✓	19.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	25.6b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1344 to 717 computations (46.7% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a x) 4)
✓	0.3b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	7.5b	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
✓	11.8b	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))

series77.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
17.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
17.0ms	(pow.f64 (*.f64 a x) 4)
12.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

4 → 49

Calls

4 calls:

2.0ms	(pow.f64 (*.f64 a x) 4)
0.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
0.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
0.0ms	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))

simplify84.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

581×	`exp-prod_binary64`
519×	`associate-l_binary64`
435×	`associate-r_binary64`
337×	`distribute-rgt-out_binary64`
324×	`swap-sqr_binary64`

Counts

145 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	2650
1	176	2274
2	475	2252
3	2536	2220
4	5284	2220

prune76.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	96	3	99

Error

0.0b

Counts

99 → 3

Alt Table

Status	Error	Program
✓	19.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	25.6b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 2855 to 1556 computations (45.5% saved)

regimes61.0ms (2.1%)

Accuracy

Total 0.0b remaining (22.9%)

Threshold costs 0.0b (22.9%)

Counts

12 → 1

Compiler

Compiled 880 to 569 computations (35.3% 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

end59.0ms (2%)

Remove: (sort a x)
Compiler: Compiled 65 to 43 computations (33.8% saved)

Details

analyze58.0ms (2%)

sample2.1s (73.2%)

simplify72.0ms (2.5%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify67.0ms (2.3%)

prune13.0ms (0.5%)

localize7.0ms (0.2%)

series28.0ms (1%)

rewrite5.0ms (0.2%)

simplify91.0ms (3.1%)

prune47.0ms (1.6%)

localize13.0ms (0.5%)

series77.0ms (2.7%)

rewrite5.0ms (0.2%)

simplify84.0ms (2.9%)

prune76.0ms (2.6%)

regimes61.0ms (2.1%)

simplify2.0ms (0.1%)

end59.0ms (2%)

Profiling