Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample657.0ms (41.2%)

Infinites

12% of outputs are infinite.

Results

582.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
▶	0.1b	(*.f64 (fma.f64 x 3 -12/29) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 3 -12/29)
✓	0.1b	(*.f64 (fma.f64 x 3 -12/29) y)

series9.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

7.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
2.0ms	(fma.f64 x 3 -12/29)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
0.0ms	(fma.f64 x 3 -12/29)

simplify45.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
595×	`distribute-rgt-in_binary64`
593×	`distribute-lft-in_binary64`
497×	`associate-+r+_binary64`
408×	`associate-+l+_binary64`

Counts

66 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	691
1	91	531
2	246	531
3	644	531
4	2128	531
5	5282	531

prune47.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	55	7	62

Error

Counts

62 → 7

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (fma.f64 3 x -12/29) y)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	34.7b	(.f64 (.f64 (fma.f64 x 3 -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	25.5b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	24.9b	(*.f64 (log.f64 (exp.f64 (fma.f64 x 3 -12/29))) y)

Compiler

Compiled 799 to 584 computations (26.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 x -12/29)
✓	0.1b	(*.f64 (fma.f64 3 x -12/29) y)

series9.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(*.f64 (fma.f64 3 x -12/29) y)
1.0ms	(fma.f64 3 x -12/29)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(*.f64 (fma.f64 3 x -12/29) y)
0.0ms	(fma.f64 3 x -12/29)

simplify45.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-def_binary64`
595×	`distribute-rgt-in_binary64`
593×	`distribute-lft-in_binary64`
497×	`associate-+r+_binary64`
408×	`associate-+l+_binary64`

Counts

66 → 49

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	691
1	89	531
2	246	531
3	644	531
4	2128	531
5	5282	531

prune34.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	49	7	56

Error

Counts

56 → 7

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (fma.f64 3 x -12/29) y)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	34.7b	(.f64 (.f64 (fma.f64 x 3 -12/29) (sqrt.f64 y)) (sqrt.f64 y))
▶	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	25.5b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	24.9b	(*.f64 (log.f64 (exp.f64 (fma.f64 x 3 -12/29))) y)

Compiler

Compiled 674 to 499 computations (26% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series9.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

7.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite16.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`associate-l_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
7.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

simplify106.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
495×	`associate-r_binary64`
206×	`sqr-pow_binary64`
195×	`distribute-rgt-in_binary64`
194×	`distribute-lft-in_binary64`

Counts

83 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	921
1	206	672
2	611	666
3	1677	666
4	2385	666
5	3622	666
6	4778	666
7	4997	666
8	4869	666

prune56.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	86	6	92

Error

Counts

92 → 6

Alt Table

Status	Error	Program
	25.5b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	0.2b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))
	24.9b	(*.f64 (log.f64 (exp.f64 (fma.f64 x 3 -12/29))) y)

Compiler

Compiled 1337 to 1043 computations (22% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(*.f64 12/29 y)
✓	0.2b	(.f64 3 (.f64 y x))

series13.0ms (0.8%)

Counts

3 → 15

Calls

3 calls:

6.0ms	(.f64 3 (.f64 y x))
6.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
1.0ms	(*.f64 12/29 y)

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 56

Calls

3 calls:

4.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
4.0ms	(.f64 3 (.f64 y x))
3.0ms	(*.f64 12/29 y)

simplify87.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
509×	`associate-l_binary64`
472×	`fma-neg_binary64`
366×	`associate-r_binary64`
288×	`distribute-rgt-in_binary64`

Counts

71 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	701
1	230	632
2	626	623
3	1846	614
4	3688	612
5	4571	612
6	5558	612

prune69.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Error

Counts

91 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 3 (.f64 y x) (.f64 y -12/29))
✓	0.1b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
	25.5b	(*.f64 (log1p.f64 (expm1.f64 (fma.f64 x 3 -12/29))) y)
	0.3b	(-.f64 (.f64 3 (.f64 y x)) (.f64 (.f64 (cbrt.f64 12/29) (cbrt.f64 12/29)) (*.f64 (cbrt.f64 12/29) y)))
	0.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) (cbrt.f64 (fma.f64 x 3 -12/29))) (*.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) y))

Compiler

Compiled 1224 to 796 computations (35% saved)

regimes259.0ms (16.2%)

Accuracy

Total 0.1b remaining (86.5%)

Threshold costs 0.1b (86.5%)

Counts

57 → 1

Compiler

Compiled 3691 to 2807 computations (24% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8
2	8	8

end83.0ms (5.2%)

Compiler: Compiled 86 to 68 computations (20.9% saved)

Details

analyze1.0ms (0.1%)

sample657.0ms (41.2%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series9.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify45.0ms (2.8%)

prune47.0ms (2.9%)

localize4.0ms (0.2%)

series9.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify45.0ms (2.8%)

prune34.0ms (2.1%)

localize5.0ms (0.3%)

series9.0ms (0.5%)

rewrite16.0ms (1%)

simplify106.0ms (6.6%)

prune56.0ms (3.5%)

localize5.0ms (0.3%)

series13.0ms (0.8%)

rewrite12.0ms (0.7%)

simplify87.0ms (5.5%)

prune69.0ms (4.3%)

regimes259.0ms (16.2%)

simplify3.0ms (0.2%)

end83.0ms (5.2%)

Profiling