Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (30.6%)

Results

948.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify146.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1355×	`fma-neg_binary64`
877×	`fma-def_binary64`
720×	`distribute-rgt-neg-in_binary64`
564×	`cancel-sign-sub-inv_binary64`
530×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	11
2	49	11
3	107	11
4	170	11
5	291	11
6	516	11
7	1002	11
8	1492	11
9	2128	11
10	2734	11
11	3154	11
12	3358	11
13	3535	11
14	4106	11
15	3099	11
16	3528	11
17	4668	11
18	4732	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Status

Error

Program

▶

0.2b

(-.f64 (*.f64 238732414637843/250000000000000 x) (*.f64 6450306886639899/50000000000000000 (*.f64 (*.f64 x x) x)))

0.2b

(*.f64 x (fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
✓	0.1b	(*.f64 238732414637843/250000000000000 x)
✓	0.1b	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
✓	0.1b	(.f64 (.f64 x x) x)

series11.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
3.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
3.0ms	(.f64 (.f64 x x) x)
1.0ms	(*.f64 238732414637843/250000000000000 x)

rewrite77.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
403×	`fma-def_binary64`
239×	`pow2_binary64`
229×	`egg-rr`
178×	`fma-neg_binary64`

Counts

4 → 229

Calls

4 calls:

71.0ms	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (.f64 (.f64 x x) x)))
71.0ms	(*.f64 238732414637843/250000000000000 x)
71.0ms	(.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x))
71.0ms	(.f64 (.f64 x x) x)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	200	26
2	2349	26
3	4869	26

simplify195.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1274×	`fma-def_binary64`
875×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
685×	`cube-prod_binary64`
665×	`cancel-sign-sub-inv_binary64`

Counts

265 → 234

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	267
1	27	249
2	64	249
3	155	249
4	313	249
5	728	249
6	1078	249
7	1590	249
8	2988	249
9	4112	249
10	4092	249
11	4547	249
12	4019	249
13	4022	249
14	3466	249
15	4267	249
16	4642	249
17	4931	249
18	4727	249

prune276.0ms (7.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	227	7	234
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	7	236

Error

0.0b

Counts

236 → 7

Alt Table

Status	Error	Program
	28.3b	(-.f64 (sqrt.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)) x (*.f64 x 238732414637843/250000000000000))
	28.8b	(.f64 (-.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (.f64 (pow.f64 x 6) 41606458931834106848498498730201/2500000000000000000000000000000000)) (/.f64 1 (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	30.9b	(-.f64 (.f64 238732414637843/250000000000000 x) (pow.f64 (.f64 (pow.f64 x 3/2) (sqrt.f64 6450306886639899/50000000000000000)) 2))
	31.0b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 238732414637843/250000000000000) (.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
▶	0.2b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	40.4b	(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3))

Compiler

Compiled 4959 to 3817 computations (23% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
✓	0.1b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))
✓	0.1b	(*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)
✓	34.6b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))

series21.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))
6.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))
5.0ms	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
3.0ms	(*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)

rewrite115.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

418×	`log-prod_binary64`
260×	`pow2_binary64`
241×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`

Counts

4 → 109

Calls

4 calls:

113.0ms	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
113.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)))
113.0ms	(*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000)
113.0ms	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	67
1	228	46
2	2333	46
3	4903	46
4	4987	46
5	4848	46

simplify197.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1274×	`fma-def_binary64`
875×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
685×	`cube-prod_binary64`
665×	`cancel-sign-sub-inv_binary64`

Counts

157 → 116

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	315
1	28	297
2	64	297
3	155	297
4	313	297
5	728	297
6	1078	297
7	1590	297
8	2988	297
9	4112	297
10	4092	297
11	4547	297
12	4019	297
13	4022	297
14	3466	297
15	4267	297
16	4642	297
17	4931	297
18	4727	297

prune131.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	116	7	123

Error

0.0b

Counts

123 → 7

Alt Table

Status	Error	Program
	28.3b	(-.f64 (sqrt.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
▶	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)) x (*.f64 x 238732414637843/250000000000000))
	28.8b	(.f64 (-.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (.f64 (pow.f64 x 6) 41606458931834106848498498730201/2500000000000000000000000000000000)) (/.f64 1 (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	30.9b	(-.f64 (.f64 238732414637843/250000000000000 x) (pow.f64 (.f64 (pow.f64 x 3/2) (sqrt.f64 6450306886639899/50000000000000000)) 2))
	31.0b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 238732414637843/250000000000000) (.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
✓	0.2b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	40.4b	(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3))

Compiler

Compiled 2440 to 1970 computations (19.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 x 238732414637843/250000000000000)
✓	0.1b	(fma.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)) x (*.f64 x 238732414637843/250000000000000))
✓	0.2b	(.f64 -6450306886639899/50000000000000000 (.f64 x x))

series7.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms

(fma.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x)) x (*.f64 x 238732414637843/250000000000000))

2.0ms

(*.f64 -6450306886639899/50000000000000000 (*.f64 x x))

1.0ms

(*.f64 x 238732414637843/250000000000000)

rewrite111.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`log1p-expm1-u_binary64`
670×	`expm1-log1p-u_binary64`
169×	`prod-diff_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`

Counts

3 → 52

Calls

3 calls:

110.0ms

(*.f64 x 238732414637843/250000000000000)

110.0ms

(fma.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x)) x (*.f64 x 238732414637843/250000000000000))

110.0ms

(*.f64 -6450306886639899/50000000000000000 (*.f64 x x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	164	24
2	1762	22
3	4933	22
4	4949	22
5	4866	22

simplify128.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1189×	`fma-def_binary64`
1188×	`fma-neg_binary64`
505×	`unsub-neg_binary64`
503×	`neg-mul-1_binary64`
500×	`neg-sub0_binary64`

Counts

88 → 57

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	267
1	34	249
2	77	249
3	209	249
4	571	249
5	991	249
6	1848	249
7	3091	249
8	4089	249
9	3885	249
10	3986	249
11	4130	249
12	4770	249
13	5034	249

prune86.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Error

0.0b

Counts

64 → 7

Alt Table

Status	Error	Program
	28.3b	(-.f64 (sqrt.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
✓	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)) x (*.f64 x 238732414637843/250000000000000))
▶	0.5b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x))) 3) x (*.f64 x 238732414637843/250000000000000))
	28.8b	(.f64 (-.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (.f64 (pow.f64 x 6) 41606458931834106848498498730201/2500000000000000000000000000000000)) (/.f64 1 (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	31.0b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 238732414637843/250000000000000) (.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
✓	0.2b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	40.4b	(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3))

Compiler

Compiled 892 to 590 computations (33.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x))) 3) x (*.f64 x 238732414637843/250000000000000))
	0.2b	(.f64 -6450306886639899/50000000000000000 (.f64 x x))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x))) 3)
✓	18.9b	(cbrt.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)))

series269.0ms (7.2%)

Counts

3 → 36

Calls

3 calls:

113.0ms

(fma.f64 (pow.f64 (cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x))) 3) x (*.f64 x 238732414637843/250000000000000))

105.0ms

(pow.f64 (cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x))) 3)

51.0ms

(cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x)))

rewrite58.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

839×	`log1p-expm1-u_binary64`
839×	`expm1-log1p-u_binary64`
180×	`prod-diff_binary64`
97×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Counts

3 → 84

Calls

3 calls:

57.0ms

(fma.f64 (pow.f64 (cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x))) 3) x (*.f64 x 238732414637843/250000000000000))

57.0ms

(pow.f64 (cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x))) 3)

57.0ms

(cbrt.f64 (*.f64 -6450306886639899/50000000000000000 (*.f64 x x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	212	29
2	2210	29
3	5306	29

simplify165.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1467×	`fma-def_binary64`
789×	`cube-prod_binary64`
756×	`fma-neg_binary64`
573×	`sqr-pow_binary64`
525×	`cancel-sign-sub-inv_binary64`

Counts

120 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	372
1	46	372
2	105	348
3	243	348
4	608	348
5	921	348
6	1509	348
7	2527	348
8	3587	348
9	4049	348
10	3208	348
11	3215	348
12	3678	348
13	3703	348
14	4738	348
15	4949	348

prune101.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	105	7	112

Error

0.0b

Counts

112 → 7

Alt Table

Status	Error	Program
	28.3b	(-.f64 (sqrt.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000)) (.f64 6450306886639899/50000000000000000 (.f64 (*.f64 x x) x)))
✓	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x)) x (*.f64 x 238732414637843/250000000000000))
✓	0.5b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 -6450306886639899/50000000000000000 (.f64 x x))) 3) x (*.f64 x 238732414637843/250000000000000))
	28.8b	(.f64 (-.f64 (.f64 (.f64 x x) 56993165798814994692847692649/62500000000000000000000000000) (.f64 (pow.f64 x 6) 41606458931834106848498498730201/2500000000000000000000000000000000)) (/.f64 1 (fma.f64 x 238732414637843/250000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	31.0b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) 238732414637843/250000000000000) (.f64 (pow.f64 x 3) -6450306886639899/50000000000000000))
✓	0.2b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 (pow.f64 x 3) 6450306886639899/50000000000000000))))
	40.4b	(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 x 238732414637843/250000000000000)) 3))

Compiler

Compiled 1713 to 1188 computations (30.6% saved)

regimes331.0ms (8.9%)

Accuracy

Total 0.1b remaining (70.5%)

Threshold costs 0.1b (70.5%)

Counts

138 → 1

Compiler

Compiled 4058 to 3180 computations (21.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end117.0ms (3.2%)

Compiler: Compiled 125 to 92 computations (26.4% saved)

Details

analyze5.0ms (0.1%)

sample1.1s (30.6%)

simplify146.0ms (3.9%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series11.0ms (0.3%)

rewrite77.0ms (2.1%)

simplify195.0ms (5.2%)

prune276.0ms (7.4%)

localize8.0ms (0.2%)

series21.0ms (0.6%)

rewrite115.0ms (3.1%)

simplify197.0ms (5.3%)

prune131.0ms (3.5%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite111.0ms (3%)

simplify128.0ms (3.4%)

prune86.0ms (2.3%)

localize8.0ms (0.2%)

series269.0ms (7.2%)

rewrite58.0ms (1.6%)

simplify165.0ms (4.4%)

prune101.0ms (2.7%)

regimes331.0ms (8.9%)

simplify2.0ms (0.1%)

end117.0ms (3.2%)

Profiling