Details

analyze59.0ms (1.3%)

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)

sample2.0s (45.6%)

Symmetry

(sort a x)

Results

740.0ms	1473×	body	2048	valid
594.0ms	1835×	body	1024	valid
274.0ms	3084×	body	128	valid
268.0ms	1228×	body	512	valid
95.0ms	636×	body	256	valid
10.0ms	117×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`exp-prod_binary64`
1×	`rules-20_binary64`
1×	`rules-21_binary64`
1×	`rules-52_binary64`
1×	`1-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	15	6
2	18	6
3	17	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 (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite39.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

454×	`log1p-expm1-u_binary64`
454×	`expm1-log1p-u_binary64`
396×	`fma-neg_binary64`
246×	`log-prod_binary64`
240×	`fma-def_binary64`

Counts

1 → 36

Calls

1 calls:

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	111	6
2	1377	6
3	4974	6
0	0	0
1	0	0

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

708×	`rules-6_binary64`
613×	`rules-20_binary64`
337×	`rules-5-rev_binary64`
305×	`fma-def_binary64`
289×	`rules-14-rev_binary64`

Counts

60 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	88	284
2	354	280
3	1850	266
4	5043	266

prune21.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	40.8b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)

Compiler

Compiled 529 to 236 computations (55.4% saved)

localize5.0ms (0.1%)

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)
✓	15.7b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
6.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite58.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

607×	`log1p-expm1-u_binary64`
607×	`expm1-log1p-u_binary64`
492×	`fma-neg_binary64`
161×	`prod-diff_binary64`
117×	`expm1-udef_binary64`

Counts

2 → 115

Calls

2 calls:

55.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
55.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	159	15
2	1839	15
3	5100	15
0	0	0
1	0	0

simplify49.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-def_binary64`
515×	`rules-21_binary64`
489×	`rules-14-rev_binary64`
448×	`rules-4_binary64`
412×	`rules-10-rev_binary64`

Counts

163 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	664
1	143	664
2	593	660
3	3316	646
4	5384	646

prune89.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	175	3	178

Error

Counts

178 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
▶	37.1b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3))

Compiler

Compiled 3102 to 1446 computations (53.4% saved)

localize8.0ms (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 (pow.f64 (expm1.f64 (.f64 a x)) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3))
✓	6.7b	(pow.f64 (expm1.f64 (*.f64 a x)) 3/2)
✓	10.4b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3)

series1.6s (36.1%)

Counts

3 → 72

Calls

3 calls:

982.0ms	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3)
608.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3/2)
6.0ms	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3))

rewrite64.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
189×	`prod-diff_binary64`
121×	`egg-rr`
87×	`add-sqr-sqrt_binary64`

Counts

3 → 121

Calls

3 calls:

61.0ms	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3))
61.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3/2)
61.0ms	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	235	23
2	2307	23
3	5240	23
0	0	0
1	0	0

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Rules

731×	`rules-13_binary64`
730×	`rules-4_binary64`
327×	`rules-20_binary64`
190×	`rules-21_binary64`
189×	`fma-def_binary64`

Counts

193 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1416
1	260	1352
2	1076	1138
3	5009	1138

prune203.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	328	3	331

Error

Counts

331 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	37.1b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3/2) 1/3) (pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3/2) 1/3))

Compiler

Compiled 8086 to 4004 computations (50.5% saved)

regimes40.0ms (0.9%)

Accuracy

Total 0.0b remaining (24.7%)

Threshold costs 0.0b (24.7%)

Counts

8 → 1

Compiler

Compiled 515 to 359 computations (30.3% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	5	6

end52.0ms (1.2%)

Remove: (sort a x)
Compiler: Compiled 58 to 40 computations (31% saved)

Details

analyze59.0ms (1.3%)

sample2.0s (45.6%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite39.0ms (0.9%)

simplify32.0ms (0.7%)

prune21.0ms (0.5%)

localize5.0ms (0.1%)

series25.0ms (0.6%)

rewrite58.0ms (1.3%)

simplify49.0ms (1.1%)

prune89.0ms (2%)

localize8.0ms (0.2%)

series1.6s (36.1%)

rewrite64.0ms (1.4%)

simplify44.0ms (1%)

prune203.0ms (4.6%)

regimes40.0ms (0.9%)

simplify1.0ms (0%)

end52.0ms (1.2%)

Profiling