Details

analyze6.0ms (0.3%)

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
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample756.0ms (37.6%)

Results

744.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

preprocess54.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
80×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	33	14
2	76	12
3	182	12
4	377	9
5	542	9
6	869	9
7	1535	9
8	2446	9
9	2827	9
10	2939	9
11	3065	9
12	3071	9
13	3071	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify45.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
80×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	33	14
2	76	12
3	182	12
4	377	9
5	542	9
6	869	9
7	1535	9
8	2446	9
9	2827	9
10	2939	9
11	3065	9
12	3071	9
13	3071	9

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.2%)

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
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)	x	-inf
1.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)	x	inf
1.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)	x	0
1.0ms	(fma.f64 x 9 -12)	x	-inf
0.0ms	(fma.f64 x 9 -12)	x	inf

rewrite38.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

568×	`log1p-expm1-u_binary64`
568×	`expm1-log1p-u_binary64`
253×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`
166×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	142	14
2	1500	14

Stop Event

1×	node limit

Counts

2 → 66

simplify39.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
466×	`cancel-sign-sub-inv_binary64`
418×	`distribute-rgt-neg-in_binary64`
413×	`fma-def_binary64`
296×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	198
1	38	182
2	69	156
3	141	144
4	380	144
5	1208	144
6	2780	144
7	4663	144

Stop Event

1×	node limit

Counts

90 → 80

prune62.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

0.0b

Counts

82 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.6b	(fma.f64 x (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 9 -12))) 2) 3) (cbrt.f64 (fma.f64 x 9 -12))) 3)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 1106 to 889 computations (19.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (*.f64 9 (pow.f64 x 2)))
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series7.0ms (0.3%)

Counts

3 → 9

Calls

9 calls:

1.0ms	(*.f64 9 (pow.f64 x 2))	x	0
1.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))	x	-inf
1.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))	x	inf
1.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))	x	-inf
1.0ms	(*.f64 9 (pow.f64 x 2))	x	-inf

rewrite64.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log-prod_binary64`
395×	`fma-def_binary64`
203×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	250	29
2	3132	27

Stop Event

1×	node limit

Counts

3 → 188

simplify35.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
757×	`fma-neg_binary64`
415×	`distribute-rgt-neg-in_binary64`
350×	`cancel-sign-sub-inv_binary64`
293×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	63
1	27	59
2	52	55
3	121	51
4	331	51
5	1109	51
6	2423	51
7	4614	51

Stop Event

1×	node limit

Counts

197 → 195

prune252.0ms (12.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	193	6	199

Error

Counts

199 → 6

Alt Table

Status	Error	Program
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
	10.5b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	10.6b	(-.f64 (/.f64 (-.f64 9 (.f64 (pow.f64 x 4) 81)) (+.f64 3 (.f64 -9 (.f64 x x)))) (.f64 12 x))
	0.6b	(fma.f64 x (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 9 -12))) 2) 3) (cbrt.f64 (fma.f64 x 9 -12))) 3)

Compiler

Compiled 3712 to 2544 computations (31.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
✓	0.1b	(fma.f64 9 (.f64 x x) (.f64 x -12))

series5.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 9 (.f64 x x) (.f64 x -12))	x	-inf
1.0ms	(fma.f64 9 (.f64 x x) (.f64 x -12))	x	inf
1.0ms	(fma.f64 9 (.f64 x x) (.f64 x -12))	x	0
1.0ms	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))	x	-inf
1.0ms	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))	x	inf

rewrite47.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
155×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	191	25
2	2208	25

Stop Event

1×	node limit

Counts

2 → 55

simplify38.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
463×	`cancel-sign-sub-inv_binary64`
418×	`distribute-rgt-neg-in_binary64`
406×	`fma-def_binary64`
295×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	279
1	34	245
2	64	220
3	152	180
4	401	180
5	1245	180
6	2815	180
7	4694	180

Stop Event

1×	node limit

Counts

79 → 65

prune75.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	65	6	71

Error

Counts

71 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
	10.5b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	10.6b	(-.f64 (/.f64 (-.f64 9 (.f64 (pow.f64 x 4) 81)) (+.f64 3 (.f64 -9 (.f64 x x)))) (.f64 12 x))
	0.6b	(fma.f64 x (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x 9 -12))) 2) 3) (cbrt.f64 (fma.f64 x 9 -12))) 3)

Compiler

Compiled 1237 to 853 computations (31% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.2b	(.f64 (.f64 x 3) x)

series5.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(.f64 (.f64 x 3) x)	x	0
1.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))	x	-inf
1.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))	x	inf
1.0ms	(.f64 (.f64 x 3) x)	x	-inf
1.0ms	(.f64 (.f64 x 3) x)	x	inf

rewrite47.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

707×	`fma-def_binary64`
400×	`fma-neg_binary64`
206×	`log1p-udef_binary64`
204×	`expm1-udef_binary64`
118×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	256	21
2	3290	19

Stop Event

1×	node limit

Counts

2 → 45

simplify38.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-neg_binary64`
465×	`cancel-sign-sub-inv_binary64`
417×	`distribute-rgt-neg-in_binary64`
405×	`fma-def_binary64`
296×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	228
1	35	212
2	70	196
3	169	174
4	454	174
5	1419	174
6	2989	174
7	4871	174

Stop Event

1×	node limit

Counts

69 → 56

prune53.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	57	5	62

Error

Counts

62 → 5

Alt Table

Status	Error	Program
	10.5b	(-.f64 (+.f64 3 (sqrt.f64 (.f64 (pow.f64 x 4) 81))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.1b	(fma.f64 3 (*.f64 x (fma.f64 x 3 -4)) 3)
✓	0.1b	(+.f64 3 (fma.f64 9 (.f64 x x) (.f64 x -12)))
	10.6b	(-.f64 (/.f64 (-.f64 9 (.f64 (pow.f64 x 4) 81)) (+.f64 3 (.f64 -9 (.f64 x x)))) (.f64 12 x))

Compiler

Compiled 872 to 702 computations (19.5% saved)

regimes172.0ms (8.5%)

Accuracy

Total 0.1b remaining (91.3%)

Threshold costs 0.1b (91.3%)

Counts

44 → 1

Compiler

Compiled 2348 to 1829 computations (22.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end137.0ms (6.8%)

Stop Event

1×

fuel

Compiler

Compiled 84 to 65 computations (22.6% saved)

Details

analyze6.0ms (0.3%)

sample756.0ms (37.6%)

preprocess54.0ms (2.7%)

simplify45.0ms (2.2%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite38.0ms (1.9%)

simplify39.0ms (1.9%)

prune62.0ms (3.1%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite64.0ms (3.2%)

simplify35.0ms (1.8%)

prune252.0ms (12.6%)

localize5.0ms (0.3%)

series5.0ms (0.2%)

rewrite47.0ms (2.4%)

simplify38.0ms (1.9%)

prune75.0ms (3.8%)

localize8.0ms (0.4%)

series5.0ms (0.2%)

rewrite47.0ms (2.3%)

simplify38.0ms (1.9%)

prune53.0ms (2.6%)

regimes172.0ms (8.5%)

simplify2.0ms (0.1%)

end137.0ms (6.8%)

Profiling