Details

analyze4.0ms (0.2%)

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)

sample1.0s (35.6%)

Results

831.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify147.0ms (5.2%)

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

prune3.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(-.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

0.4b

(-.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)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
2.0ms	(fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)

rewrite55.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
347×	`unpow-prod-down_binary64`
279×	`log-prod_binary64`
167×	`pow2_binary64`

Counts

2 → 56

Calls

2 calls:

54.0ms	(fma.f64 (*.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)
54.0ms	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1488	19
3	5335	19
0	0	0
1	0	0

simplify91.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
653×	`fma-def_binary64`
586×	`distribute-rgt-neg-in_binary64`
532×	`distribute-lft-neg-in_binary64`
397×	`neg-mul-1_binary64`

Counts

80 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	240
1	40	222
2	88	204
3	233	204
4	619	204
5	1050	204
6	1869	204
7	2935	204
8	4514	204
9	4934	204
10	4905	204

prune48.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	63	5	68

Error

0.0b

Counts

68 → 5

Alt Table

Status	Error	Program
✓	0.2b	(.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000))
	1.3b	(.f64 x (pow.f64 (cbrt.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)) 3))
▶	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	4.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) -6450306886639899/50000000000000000) 2) 56993165798814994692847692649/62500000000000000000000000000) (fma.f64 x (.f64 x -6450306886639899/50000000000000000) -238732414637843/250000000000000)))
	39.9b	(cbrt.f64 (pow.f64 (.f64 x (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)) 3))

Compiler

Compiled 951 to 617 computations (35.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
✓	0.2b	(*.f64 238732414637843/250000000000000 x)
✓	0.3b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))

series8.0ms (0.3%)

Counts

3 → 3

Calls

3 calls:

3.0ms

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

3.0ms

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

1.0ms

(*.f64 238732414637843/250000000000000 x)

rewrite77.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

432×	`log-prod_binary64`
370×	`fma-def_binary64`
242×	`pow2_binary64`
197×	`egg-rr`
171×	`fma-neg_binary64`

Counts

3 → 197

Calls

3 calls:

73.0ms

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

73.0ms

(*.f64 238732414637843/250000000000000 x)

73.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	205	22
2	2349	22
3	4853	22
0	0	0
1	0	0

simplify142.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
529×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
481×	`fabs-mul_binary64`
452×	`associate-l_binary64`

Counts

200 → 199

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	18	18
2	35	18
3	54	18
4	96	18
5	220	18
6	645	18
7	944	18
8	948	18
9	1078	18
10	1232	18
11	1388	18
12	1617	18
13	1918	18
14	2266	18
15	2741	18
16	3359	18
17	3555	18
18	3729	18
19	3843	18
20	3890	18
21	3942	18
22	4820	18
23	4723	18

prune165.0ms (5.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	199	5	204

Error

Counts

204 → 5

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))
▶	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 x) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
✓	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	1.3b	(.f64 x (pow.f64 (cbrt.f64 (fma.f64 (.f64 x x) -6450306886639899/50000000000000000 238732414637843/250000000000000)) 3))
	4.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) -6450306886639899/50000000000000000) 2) 56993165798814994692847692649/62500000000000000000000000000) (fma.f64 x (.f64 x -6450306886639899/50000000000000000) -238732414637843/250000000000000)))

Compiler

Compiled 4195 to 3289 computations (21.6% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

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

rewrite112.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

655×	`log1p-expm1-u_binary64`
655×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
136×	`expm1-udef_binary64`
136×	`log1p-udef_binary64`

Counts

3 → 55

Calls

3 calls:

111.0ms	(fma.f64 (.f64 -6450306886639899/50000000000000000 x) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
111.0ms	(*.f64 -6450306886639899/50000000000000000 x)
111.0ms	(*.f64 x 238732414637843/250000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	162	21
2	1721	19
3	4899	19
4	4966	19
5	4883	19
0	0	0
1	0	0

simplify188.0ms (6.7%)

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

79 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	183
1	27	165
2	64	165
3	155	165
4	313	165
5	728	165
6	1078	165
7	1590	165
8	2988	165
9	4112	165
10	4092	165
11	4547	165
12	4019	165
13	4022	165
14	3466	165
15	4267	165
16	4642	165
17	4931	165
18	4727	165

prune45.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	60	5	65

Error

Counts

65 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 x) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
	33.1b	(fma.f64 (pow.f64 (sqrt.f64 (.f64 x -6450306886639899/50000000000000000)) 2) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
▶	0.5b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))
✓	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	4.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) -6450306886639899/50000000000000000) 2) 56993165798814994692847692649/62500000000000000000000000000) (fma.f64 x (.f64 x -6450306886639899/50000000000000000) -238732414637843/250000000000000)))

Compiler

Compiled 886 to 626 computations (29.3% saved)

localize8.0ms (0.3%)

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 6450306886639899/50000000000000000 (pow.f64 x 3)))))
✓	0.3b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))))
	0.3b	(*.f64 6450306886639899/50000000000000000 (pow.f64 x 3))
✓	30.5b	(fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))

series21.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

10.0ms

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

5.0ms

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

5.0ms

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

rewrite112.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 92

Calls

3 calls:

110.0ms

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

110.0ms

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

110.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	60
1	228	39
2	2333	39
3	4903	39
4	4987	39
5	4848	39
0	0	0
1	0	0

simplify197.0ms (7%)

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

128 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	231
1	28	213
2	64	213
3	155	213
4	313	213
5	728	213
6	1078	213
7	1590	213
8	2988	213
9	4112	213
10	4092	213
11	4547	213
12	4019	213
13	4022	213
14	3466	213
15	4267	213
16	4642	213
17	4931	213
18	4727	213

prune108.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (.f64 -6450306886639899/50000000000000000 x) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
	33.1b	(fma.f64 (pow.f64 (sqrt.f64 (.f64 x -6450306886639899/50000000000000000)) 2) (.f64 x x) (*.f64 x 238732414637843/250000000000000))
✓	0.5b	(fma.f64 x 238732414637843/250000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (fma.f64 (pow.f64 x 3) -6450306886639899/50000000000000000 (*.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))))
✓	0.4b	(-.f64 (.f64 238732414637843/250000000000000 x) (.f64 6450306886639899/50000000000000000 (pow.f64 x 3)))
	4.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (.f64 (.f64 x x) -6450306886639899/50000000000000000) 2) 56993165798814994692847692649/62500000000000000000000000000) (fma.f64 x (.f64 x -6450306886639899/50000000000000000) -238732414637843/250000000000000)))

Compiler

Compiled 2322 to 1883 computations (18.9% saved)

regimes141.0ms (5%)

Accuracy

Total 0.2b remaining (94.7%)

Threshold costs 0.2b (94.7%)

Counts

65 → 1

Compiler

Compiled 1774 to 1360 computations (23.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	10	14
2	10	14

end104.0ms (3.7%)

Compiler: Compiled 95 to 68 computations (28.4% saved)

Details

analyze4.0ms (0.2%)

sample1.0s (35.6%)

simplify147.0ms (5.2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite55.0ms (2%)

simplify91.0ms (3.2%)

prune48.0ms (1.7%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite77.0ms (2.7%)

simplify142.0ms (5.1%)

prune165.0ms (5.9%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite112.0ms (4%)

simplify188.0ms (6.7%)

prune45.0ms (1.6%)

localize8.0ms (0.3%)

series21.0ms (0.7%)

rewrite112.0ms (4%)

simplify197.0ms (7%)

prune108.0ms (3.9%)

regimes141.0ms (5%)

simplify3.0ms (0.1%)

end104.0ms (3.7%)

Profiling