Details

analyze146.0ms (4.7%)

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)

sample31.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 21 computations (16% saved)

simplify17.0ms (0.5%)

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

prune6.0ms (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
	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
▶	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize12.0ms (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)

series14.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
3.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

rewrite34.0ms (1.1%)

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:

15.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
14.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)

simplify139.0ms (4.5%)

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

prune121.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Error

0.0b

Counts

87 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
▶	0.2b	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
	15.4b	(.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) y)
	30.9b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))
	12.9b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))

Compiler

Compiled 1342 to 1044 computations (22.2% saved)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3 x -12/29)
✓	0.2b	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)

series14.0ms (0.5%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
3.0ms	(fma.f64 3 x -12/29)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

8.0ms	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
1.0ms	(fma.f64 3 x -12/29)

simplify128.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
570×	`unswap-sqr_binary64`
442×	`associate-l_binary64`
331×	`associate-r_binary64`
307×	`exp-prod_binary64`

Counts

74 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	69	790
1	110	631
2	361	631
3	1626	631
4	2592	631
5	4408	631
6	4830	631
7	4941	631

prune83.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Error

Counts

72 → 7

Alt Table

Status	Error	Program
	50.1b	(.f64 (pow.f64 (sqrt.f64 (fma.f64 3 x -12/29)) 1) (.f64 y (sqrt.f64 (fma.f64 3 x -12/29))))
	12.9b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
	15.4b	(.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) y)
	30.9b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))
	0.3b	(.f64 (-.f64 x (/.f64 16 116)) (.f64 3 y))

Compiler

Compiled 1035 to 795 computations (23.2% saved)

localize9.0ms (0.3%)

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)))

series20.0ms (0.7%)

Counts

2 → 28

Calls

2 calls:

11.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
9.0ms	(*.f64 y (-.f64 x 4/29))

rewrite44.0ms (1.4%)

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:

12.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
12.0ms	(*.f64 y (-.f64 x 4/29))

simplify163.0ms (5.3%)

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

prune221.0ms (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
	50.1b	(.f64 (pow.f64 (sqrt.f64 (fma.f64 3 x -12/29)) 1) (.f64 y (sqrt.f64 (fma.f64 3 x -12/29))))
▶	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))
	12.9b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
	15.4b	(.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) y)
	30.9b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))

Compiler

Compiled 3255 to 2514 computations (22.8% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

12.0ms

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

rewrite21.0ms (0.7%)

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:

14.0ms

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

simplify117.0ms (3.8%)

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

prune86.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	68	7	75

Error

Counts

75 → 7

Alt Table

Status	Error	Program
	50.1b	(.f64 (pow.f64 (sqrt.f64 (fma.f64 3 x -12/29)) 1) (.f64 y (sqrt.f64 (fma.f64 3 x -12/29))))
✓	0.3b	(.f64 (.f64 3 y) (-.f64 x 4/29))
	12.9b	(/.f64 (.f64 y (.f64 3 (fma.f64 x x -16/841))) (+.f64 x (/.f64 16 116)))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (pow.f64 (fma.f64 3 x -12/29) 1) y)
	15.4b	(.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 x (/.f64 16 116)) 3))) y)
	30.9b	(.f64 (.f64 (fma.f64 3 x -12/29) (sqrt.f64 y)) (sqrt.f64 y))

Compiler

Compiled 1285 to 1006 computations (21.7% saved)

regimes445.0ms (14.5%)

Accuracy

Total 0.2b remaining (93.3%)

Threshold costs 0.2b (93.3%)

Counts

45 → 1

Compiler

Compiled 3679 to 2953 computations (19.7% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	26	13
3	30	13
4	33	13
5	34	13
6	33	13

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample1.1s (37.4%)

Algorithm

1×

intervals

Results

583.0ms	8000×	body	128	valid
7.0ms	81×	body	128	invalid

Compiler

Compiled 111 to 87 computations (21.6% saved)

Details

analyze146.0ms (4.7%)

sample31.0ms (1%)

simplify17.0ms (0.5%)

prune6.0ms (0.2%)

localize12.0ms (0.4%)

series14.0ms (0.5%)

rewrite34.0ms (1.1%)

simplify139.0ms (4.5%)

prune121.0ms (3.9%)

localize11.0ms (0.4%)

series14.0ms (0.5%)

rewrite11.0ms (0.4%)

simplify128.0ms (4.2%)

prune83.0ms (2.7%)

localize9.0ms (0.3%)

series20.0ms (0.7%)

rewrite44.0ms (1.4%)

simplify163.0ms (5.3%)

prune221.0ms (7.2%)

localize9.0ms (0.3%)

series12.0ms (0.4%)

rewrite21.0ms (0.7%)

simplify117.0ms (3.8%)

prune86.0ms (2.8%)

regimes445.0ms (14.5%)

simplify8.0ms (0.3%)

end1.0ms (0%)

sample1.1s (37.4%)

Profiling