Details

analyze67.0ms (1.8%)

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 (56.2%)

Symmetry

(sort a x)

Results

826.0ms	1582×	body	2048	valid
594.0ms	1824×	body	1024	valid
282.0ms	3091×	body	128	valid
259.0ms	1144×	body	512	valid
97.0ms	615×	body	256	valid
12.0ms	134×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify77.0ms (2%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))
	32.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 40 to 27 computations (32.5% 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))

rewrite75.0ms (2%)

Algorithm

2×	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:

74.0ms

(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
0	0	0
1	0	0

simplify60.0ms (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

prune21.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

0.0b

Counts

46 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
	44.5b	(.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))
▶	17.6b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

Compiler

Compiled 582 to 274 computations (52.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a x) 2)

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(pow.f64 (*.f64 a x) 2)

rewrite77.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

893×	`log1p-udef_binary64`
471×	`log1p-expm1-u_binary64`
471×	`expm1-log1p-u_binary64`
366×	`unpow-prod-down_binary64`
262×	`log-prod_binary64`

Counts

1 → 51

Calls

1 calls:

76.0ms

(pow.f64 (*.f64 a x) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	124	7
2	1250	7
3	4902	7
4	6409	7
0	0	0
1	0	0

simplify166.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1022×	`sqr-pow_binary64`
785×	`associate-l_binary64`
636×	`*-commutative_binary64`
598×	`fabs-mul_binary64`
578×	`cube-prod_binary64`

Counts

75 → 52

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	240
1	16	240
2	35	240
3	88	240
4	295	240
5	1349	240
6	1413	240
7	1542	240
8	1721	240
9	1930	240
10	2180	240
11	2322	240
12	2724	240
13	3047	240
14	3626	240
15	3983	240
16	4262	240
17	4371	240
18	4402	240
19	4414	240
20	4876	240

prune31.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	52	3	55

Error

0.0b

Counts

55 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	44.5b	(.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))
✓	17.6b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

Compiler

Compiled 892 to 476 computations (46.6% 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))
✓	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	12.2b	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
✓	20.6b	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series669.0ms (17.6%)

Counts

4 → 80

Calls

4 calls:

610.0ms	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
34.0ms	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
18.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
7.0ms	(.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))

rewrite51.0ms (1.3%)

Algorithm

2×	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:

49.0ms	(.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))
49.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
49.0ms	(pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)) 1/3)
49.0ms	(sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify90.0ms (2.4%)

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

prune112.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	204	3	207

Error

0.0b

Counts

207 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	44.5b	(.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))
✓	17.6b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))

Compiler

Compiled 4453 to 2400 computations (46.1% saved)

regimes39.0ms (1%)

Accuracy

Total 0.0b remaining (31.9%)

Threshold costs 0.0b (31.9%)

Counts

7 → 1

Compiler

Compiled 510 to 354 computations (30.6% 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

end85.0ms (2.2%)

Remove: (sort a x)
Compiler: Compiled 63 to 43 computations (31.7% saved)

Details

analyze67.0ms (1.8%)

sample2.1s (56.2%)

simplify77.0ms (2%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite75.0ms (2%)

simplify60.0ms (1.6%)

prune21.0ms (0.6%)

localize6.0ms (0.2%)

series9.0ms (0.2%)

rewrite77.0ms (2%)

simplify166.0ms (4.4%)

prune31.0ms (0.8%)

localize8.0ms (0.2%)

series669.0ms (17.6%)

rewrite51.0ms (1.3%)

simplify90.0ms (2.4%)

prune112.0ms (3%)

regimes39.0ms (1%)

simplify2.0ms (0%)

end85.0ms (2.2%)

Profiling