Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (48.8%)

Symmetry

(sort a x)

Results

462.0ms	1118×	body	2048	valid
353.0ms	1375×	body	1024	valid
292.0ms	4414×	body	128	valid
189.0ms	867×	body	512	valid
114.0ms	482×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify73.0ms (2.4%)

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))

simplify66.0ms (2.2%)

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

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
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	29.4b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 253 to 119 computations (53% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	6.2b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series51.0ms (1.7%)

Counts

2 → 40

Calls

2 calls:

44.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))
7.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))

rewrite11.0ms (0.4%)

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:

6.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
1.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

simplify109.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-neg_binary64`
462×	`unswap-sqr_binary64`
338×	`associate-l_binary64`
279×	`associate-r_binary64`
264×	`difference-of-squares_binary64`

Counts

108 → 85

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	76	1213
1	148	1154
2	421	1125
3	1479	1077
4	3607	999
5	4448	993
6	4981	993
7	5027	993

prune62.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	141	3	144

Error

0.0b

Counts

144 → 3

Alt Table

Status	Error	Program
▶	30.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(expm1.f64 (*.f64 a x))
	33.8b	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))

Compiler

Compiled 2379 to 612 computations (74.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
✓	0.3b	(log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
✓	1.2b	(exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
	6.2b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series597.0ms (19.8%)

Counts

3 → 56

Calls

3 calls:

542.0ms	(log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))
47.0ms	(exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
7.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`log-prod_binary64`
17×	`sqrt-prod_binary64`
16×	`exp-sum_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
5.0ms	(exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
1.0ms	(log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))

simplify104.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-neg_binary64`
446×	`*-commutative_binary64`
410×	`unswap-sqr_binary64`
338×	`distribute-rgt-in_binary64`
304×	`distribute-lft-in_binary64`

Counts

131 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	1622
1	168	1541
2	429	1500
3	1384	1480
4	2590	1466
5	4263	1466
6	4915	1466

prune53.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	144	3	147

Error

0.0b

Counts

147 → 3

Alt Table

Status	Error	Program
✓	30.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	33.8b	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))

Compiler

Compiled 2700 to 533 computations (80.3% 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	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4)
✓	4.5b	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))
	6.2b	(sqrt.f64 (expm1.f64 (*.f64 a x)))

series91.0ms (3%)

Counts

2 → 40

Calls

2 calls:

84.0ms	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4)
7.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`sqrt-prod_binary64`
14×	`unpow-prod-down_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

2.0ms	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))
2.0ms	(pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4)

simplify106.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-def_binary64`
524×	`unswap-sqr_binary64`
493×	`*-commutative_binary64`
350×	`exp-prod_binary64`
268×	`distribute-rgt-in_binary64`

Counts

90 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	1214
1	168	1012
2	394	906
3	1342	890
4	3859	872
5	4517	872
6	4973	872
7	4920	872

prune52.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	114	3	117

Error

0.0b

Counts

117 → 3

Alt Table

Status	Error	Program
✓	30.1b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (exp.f64 (log.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	33.8b	(sqrt.f64 (pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 4))

Compiler

Compiled 1582 to 754 computations (52.3% saved)

regimes46.0ms (1.5%)

Accuracy

Total 0.0b remaining (18%)

Threshold costs 0.0b (18%)

Counts

10 → 1

Compiler

Compiled 620 to 369 computations (40.5% 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

end51.0ms (1.7%)

Remove: (sort a x)
Compiler: Compiled 55 to 36 computations (34.5% saved)

Details

analyze1.0ms (0%)

sample1.5s (48.8%)

simplify73.0ms (2.4%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify66.0ms (2.2%)

prune9.0ms (0.3%)

localize5.0ms (0.2%)

series51.0ms (1.7%)

rewrite11.0ms (0.4%)

simplify109.0ms (3.6%)

prune62.0ms (2.1%)

localize8.0ms (0.3%)

series597.0ms (19.8%)

rewrite19.0ms (0.6%)

simplify104.0ms (3.5%)

prune53.0ms (1.7%)

localize9.0ms (0.3%)

series91.0ms (3%)

rewrite7.0ms (0.2%)

simplify106.0ms (3.5%)

prune52.0ms (1.7%)

regimes46.0ms (1.5%)

simplify2.0ms (0.1%)

end51.0ms (1.7%)

Profiling