Details

analyze70.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample953.0ms (41.8%)

Results

912.0ms	8256×	body	128	valid
5.0ms	61×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify7.0ms (0.3%)

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 (0.1%)

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 (-.f64 x (/.f64 16 116)) 3) y)
	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series7.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

5.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
2.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite19.0ms (0.8%)

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:

10.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
7.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

simplify98.0ms (4.3%)

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

prune64.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Error

Counts

87 → 6

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	18.0b	(/.f64 (.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 (/.f64 16 116) 3)) 3) y) (+.f64 (.f64 x x) (+.f64 (.f64 (/.f64 16 116) (/.f64 16 116)) (*.f64 x (/.f64 16 116)))))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3)) (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) y)
	42.2b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y) (.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)) (.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)))
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 1446 to 1138 computations (21.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

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)

simplify46.0ms (2%)

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

prune40.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

Counts

66 → 5

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3)) (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) (cbrt.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))
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

Compiler

Compiled 783 to 580 computations (25.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series29.0ms (1.3%)

Counts

2 → 28

Calls

2 calls:

24.0ms	(*.f64 y (-.f64 x 4/29))
5.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

7.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
5.0ms	(*.f64 y (-.f64 x 4/29))

simplify95.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
474×	`*-commutative_binary64`
412×	`unsub-neg_binary64`
391×	`neg-mul-1_binary64`
389×	`neg-sub0_binary64`

Counts

152 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	1710
1	293	1349
2	721	1349
3	1730	1347
4	3194	1347
5	4989	1347
6	4900	1347

prune125.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	166	5	171

Error

Counts

171 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3)) (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) (cbrt.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))
▶	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

Compiler

Compiled 3239 to 2508 computations (22.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.f64 (*.f64 3 y) (-.f64 x 4/29))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`prod-diff_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 50

Calls

1 calls:

6.0ms

(*.f64 (*.f64 3 y) (-.f64 x 4/29))

simplify85.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
413×	`*-commutative_binary64`
330×	`sqr-pow_binary64`
258×	`exp-prod_binary64`
219×	`neg-mul-1_binary64`

Counts

74 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	818
1	251	682
2	694	682
3	1447	680
4	2211	680
5	3814	680
6	4938	680
7	4898	680

prune49.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	68	5	73

Error

Counts

73 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3)) (cbrt.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) (cbrt.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))
✓	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

Compiler

Compiled 1276 to 1002 computations (21.5% saved)

regimes437.0ms (19.2%)

Accuracy

Total 0.2b remaining (91%)

Threshold costs 0.2b (91%)

Counts

77 → 1

Compiler

Compiled 6990 to 5539 computations (20.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end80.0ms (3.5%)

Compiler: Compiled 95 to 77 computations (18.9% saved)

Details

analyze70.0ms (3.1%)

sample953.0ms (41.8%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series7.0ms (0.3%)

rewrite19.0ms (0.8%)

simplify98.0ms (4.3%)

prune64.0ms (2.8%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify46.0ms (2%)

prune40.0ms (1.7%)

localize4.0ms (0.2%)

series29.0ms (1.3%)

rewrite23.0ms (1%)

simplify95.0ms (4.2%)

prune125.0ms (5.5%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite9.0ms (0.4%)

simplify85.0ms (3.7%)

prune49.0ms (2.1%)

regimes437.0ms (19.2%)

simplify2.0ms (0.1%)

end80.0ms (3.5%)

Profiling