Details

analyze64.0ms (1.7%)

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 (58%)

Symmetry

(sort a x)

Results

784.0ms	1511×	body	2048	valid
604.0ms	1789×	body	1024	valid
301.0ms	3131×	body	128	valid
270.0ms	1162×	body	512	valid
107.0ms	663×	body	256	valid
13.0ms	139×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify78.0ms (2.1%)

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 (0.1%)

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))

series5.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

5.0ms

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

rewrite76.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

736×	`log1p-udef_binary64`
405×	`log1p-expm1-u_binary64`
405×	`expm1-log1p-u_binary64`
342×	`pow1_binary64`
287×	`unpow-prod-down_binary64`

Counts

1 → 37

Calls

1 calls:

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	95	6
2	1080	6
3	4662	6
4	5883	6

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1324×	`distribute-lft-out_binary64`
882×	`fma-def_binary64`
423×	`associate-/l/_binary64`
368×	`*-commutative_binary64`
362×	`associate-/r/_binary64`

Counts

61 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	86	284
2	234	278
3	888	262
4	2148	248
5	2915	248
6	3566	248
7	5038	248

prune19.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	2	45

Error

0.0b

Counts

45 → 2

Alt Table

Status	Error	Program
▶	46.4b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 558 to 258 computations (53.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	11.1b	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
✓	19.4b	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series616.0ms (16.7%)

Counts

4 → 80

Calls

4 calls:

559.0ms	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
33.0ms	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
18.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
6.0ms	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

781×	`log1p-expm1-u_binary64`
781×	`expm1-log1p-u_binary64`
157×	`log1p-udef_binary64`
98×	`egg-rr`
94×	`add-sqr-sqrt_binary64`

Counts

4 → 98

Calls

4 calls:

50.0ms	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
50.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
50.0ms	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
50.0ms	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	226	32
2	2089	32
3	4836	32

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-neg_binary64`
356×	`associate-l_binary64`
348×	`associate-r_binary64`
322×	`distribute-lft-in_binary64`
317×	`distribute-rgt-in_binary64`

Counts

178 → 116

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	50	968
1	140	968
2	414	930
3	1822	920
4	2833	894
5	4245	864
6	4970	864
7	5200	864

prune118.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	203	3	206

Error

Counts

206 → 3

Alt Table

Status	Error	Program
✓	46.4b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	52.9b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 4479 to 2418 computations (46% saved)

localize31.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
✓	8.5b	(sqrt.f64 (expm1.f64 (*.f64 a x)))
	11.1b	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
	19.4b	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series42.0ms (1.1%)

Counts

2 → 32

Calls

2 calls:

26.0ms	(log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
16.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

rewrite49.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

536×	`log1p-expm1-u_binary64`
536×	`expm1-log1p-u_binary64`
429×	`unpow-prod-down_binary64`
311×	`log-prod_binary64`
163×	`pow2_binary64`

Counts

2 → 84

Calls

2 calls:

48.0ms	(log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x)))))
48.0ms	(sqrt.f64 (expm1.f64 (*.f64 a x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	130	16
2	1441	16
3	5291	16

simplify85.0ms (2.3%)

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

116 → 44

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	256
1	17	256
2	24	256
3	36	256
4	71	256
5	161	256
6	433	256
7	1565	256
8	3491	256
9	4955	256
10	4994	256
11	4875	256

prune45.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	99	3	102

Error

Counts

102 → 3

Alt Table

Status	Error	Program
✓	46.4b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3))
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	52.9b	(.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)) 1/3) (log.f64 (exp.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))))))

Compiler

Compiled 2137 to 881 computations (58.8% saved)

regimes44.0ms (1.2%)

Accuracy

Total 0.0b remaining (8.5%)

Threshold costs 0.0b (8.5%)

Counts

8 → 1

Compiler

Compiled 635 to 439 computations (30.9% saved)

simplify2.0ms (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

end58.0ms (1.6%)

Remove: (sort a x)
Compiler: Compiled 70 to 48 computations (31.4% saved)

Details

analyze64.0ms (1.7%)

sample2.1s (58%)

simplify78.0ms (2.1%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite76.0ms (2.1%)

simplify58.0ms (1.6%)

prune19.0ms (0.5%)

localize8.0ms (0.2%)

series616.0ms (16.7%)

rewrite52.0ms (1.4%)

simplify96.0ms (2.6%)

prune118.0ms (3.2%)

localize31.0ms (0.8%)

series42.0ms (1.1%)

rewrite49.0ms (1.3%)

simplify85.0ms (2.3%)

prune45.0ms (1.2%)

regimes44.0ms (1.2%)

simplify2.0ms (0%)

end58.0ms (1.6%)

Profiling