Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.6%	50.4%	0
49.6%	0%	50.4%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.1s (84.8%)

Results

2.9s	4377×	body	2048	valid
738.0ms	2039×	body	1024	valid
279.0ms	1083×	body	512	valid
96.0ms	497×	body	256	valid
31.0ms	260×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
4×	`+-commutative_binary64`
3×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	13	6
3	19	6
4	26	6
5	36	6
6	47	6
7	59	6
8	62	6

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.2b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 15 to 12 computations (20% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(-.f64 1 (cos.f64 x))

series2.0ms (0%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(-.f64 1 (cos.f64 x))

rewrite30.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

481×	`log1p-expm1-u_binary64`
481×	`expm1-log1p-u_binary64`
276×	`unpow-prod-down_binary64`
213×	`log-prod_binary64`
157×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	103	6
2	1245	6

Stop Event

1×	node limit

Counts

1 → 51

Calls

1 calls:

30.0ms

(-.f64 1 (cos.f64 x))

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

606×	`distribute-rgt-neg-in_binary64`
463×	`associate-l_binary64`
413×	`unswap-sqr_binary64`
360×	`associate-r_binary64`
317×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	76
1	59	72
2	157	70
3	573	70
4	3301	70

Stop Event

1×	node limit

Counts

55 → 59

prune41.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	2	60

Error

0.0b

Counts

60 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
	0.1b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))

Compiler

Compiled 723 to 474 computations (34.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
✓	0.0b	(*.f64 1/720 (pow.f64 x 6))

series7.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
3.0ms	(*.f64 1/720 (pow.f64 x 6))

rewrite41.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
136×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
103×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	230	28
2	2461	28

Stop Event

1×	node limit

Counts

2 → 36

Calls

2 calls:

41.0ms	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
41.0ms	(*.f64 1/720 (pow.f64 x 6))

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

679×	`distribute-rgt-neg-in_binary64`
340×	`cancel-sign-sub-inv_binary64`
285×	`unswap-sqr_binary64`
275×	`fma-neg_binary64`
254×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	207
1	47	189
2	103	189
3	314	189
4	1453	189
5	4374	189

Stop Event

1×	node limit

Counts

48 → 45

prune31.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	45	2	47

Error

0.0b

Counts

47 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
▶	0.1b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))

Compiler

Compiled 888 to 553 computations (37.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (fma.f64 (.f64 x x) -1/24 1/2))
✓	0.0b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))
3.0ms	(.f64 x (fma.f64 (.f64 x x) -1/24 1/2))

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

672×	`log1p-expm1-u_binary64`
672×	`expm1-log1p-u_binary64`
355×	`log-prod_binary64`
136×	`expm1-udef_binary64`
136×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	163	25
2	1860	25

Stop Event

1×	node limit

Counts

2 → 45

Calls

2 calls:

39.0ms	(.f64 x (fma.f64 (.f64 x x) -1/24 1/2))
39.0ms	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1014×	`fma-def_binary64`
803×	`unswap-sqr_binary64`
397×	`fma-neg_binary64`
227×	`associate-l_binary64`
225×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	300
1	48	264
2	114	264
3	365	264
4	1265	264
5	3247	264

Stop Event

1×	node limit

Counts

69 → 55

prune41.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Error

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
✓	0.1b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))
▶	20.0b	(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))

Compiler

Compiled 803 to 507 computations (36.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)
✓	0.1b	(pow.f64 (*.f64 x x) 3)
✓	0.3b	(*.f64 x -1/24)
✓	20.0b	(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))

series12.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 x x) 3)
4.0ms	(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))
3.0ms	(pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)
1.0ms	(*.f64 x -1/24)

rewrite51.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

500×	`log-prod_binary64`
270×	`pow2_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
183×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	250	33
2	2741	33

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

49.0ms	(pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)
49.0ms	(pow.f64 (*.f64 x x) 3)
49.0ms	(*.f64 x -1/24)
49.0ms	(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

511×	`distribute-rgt-neg-in_binary64`
436×	`distribute-lft-neg-in_binary64`
389×	`associate-l_binary64`
325×	`fma-def_binary64`
323×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	453
1	83	431
2	201	423
3	653	417
4	2973	417

Stop Event

1×	node limit

Counts

146 → 120

prune88.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	120	3	123

Error

Counts

123 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) -1/24 1/2) (*.f64 1/720 (pow.f64 x 6)))
✓	0.1b	(.f64 x (.f64 x (fma.f64 (*.f64 x x) -1/24 1/2)))
✓	20.0b	(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (fma.f64 x (*.f64 x -1/24) 1/2) 3)))

Compiler

Compiled 2182 to 1535 computations (29.7% saved)

regimes126.0ms (2.6%)

Accuracy

Total 0.0b remaining (77.3%)

Threshold costs 0.0b (77.3%)

Counts

59 → 1

Compiler

Compiled 2133 to 1633 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	12	21

Stop Event

1×

saturated

end59.0ms (1.2%)

Compiler: Compiled 75 to 49 computations (34.7% saved)

Details

analyze1.0ms (0%)

sample4.1s (84.8%)

simplify10.0ms (0.2%)

prune1.0ms (0%)

localize2.0ms (0%)

series2.0ms (0%)

rewrite30.0ms (0.6%)

simplify24.0ms (0.5%)

prune41.0ms (0.9%)

localize7.0ms (0.1%)

series7.0ms (0.1%)

rewrite41.0ms (0.9%)

simplify32.0ms (0.7%)

prune31.0ms (0.7%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite40.0ms (0.8%)

simplify29.0ms (0.6%)

prune41.0ms (0.8%)

localize8.0ms (0.2%)

series12.0ms (0.2%)

rewrite51.0ms (1.1%)

simplify34.0ms (0.7%)

prune88.0ms (1.8%)

regimes126.0ms (2.6%)

simplify2.0ms (0%)

end59.0ms (1.2%)

Profiling