Details

analyze1.3s (27%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (29.3%)

Results

942.0ms	8256×	body	128	valid
325.0ms	2786×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

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
▶	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	7.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	4.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series31.0ms (0.7%)

Counts

2 → 88

Calls

2 calls:

22.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
9.0ms	(/.f64 (-.f64 t z) a)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune91.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Error

0.0b

Counts

80 → 7

Alt Table

Status	Error	Program
	24.3b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 t z) a) (/.f64 (-.f64 t z) a)) (/.f64 (-.f64 t z) a))) x)
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	6.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)))
	5.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
	38.3b	(/.f64 (-.f64 (.f64 y t) (.f64 y z)) a)
	5.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
▶	1.5b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 1309 to 385 computations (70.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series21.0ms (0.4%)

Counts

1 → 60

Calls

1 calls:

21.0ms

(fma.f64 (/.f64 y a) (-.f64 t z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y a) (-.f64 t z) x)

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-lft-neg-out_binary64`
425×	`distribute-rgt-neg-out_binary64`
378×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

70 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	863
1	76	750
2	164	733
3	450	733
4	2142	733
5	4579	733
6	5069	733

prune16.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	27	7	34

Error

0.0b

Counts

34 → 7

Alt Table

Status	Error	Program
	24.3b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 t z) a) (/.f64 (-.f64 t z) a)) (/.f64 (-.f64 t z) a))) x)
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	6.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)))
▶	5.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
	38.3b	(/.f64 (-.f64 (.f64 y t) (.f64 y z)) a)
	5.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (cbrt.f64 (-.f64 t z)) a)) x)
✓	1.5b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 541 to 180 computations (66.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (-.f64 t z) (/.f64 1 a))
✓	4.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)

series34.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

24.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
10.0ms	(*.f64 (-.f64 t z) (/.f64 1 a))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 54

Calls

2 calls:

8.0ms	(*.f64 (-.f64 t z) (/.f64 1 a))
0.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
427×	`times-frac_binary64`
324×	`distribute-rgt-neg-out_binary64`
320×	`distribute-lft-neg-out_binary64`
254×	`distribute-rgt-in_binary64`

Counts

150 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1617
1	260	1438
2	729	1436
3	2014	1436
4	4433	1436
5	5099	1436

prune60.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	105	6	111

Error

0.0b

Counts

111 → 6

Alt Table

Status	Error	Program
	24.3b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 t z) a) (/.f64 (-.f64 t z) a)) (/.f64 (-.f64 t z) a))) x)
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	5.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
	38.3b	(/.f64 (-.f64 (.f64 y t) (.f64 y z)) a)
▶	5.8b	(fma.f64 y (.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a))) x)
✓	1.5b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 1714 to 694 computations (59.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
✓	0.6b	(cbrt.f64 (/.f64 1 a))
✓	4.9b	(fma.f64 y (.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a))) x)

series124.0ms (2.7%)

Counts

4 → 120

Calls

4 calls:

35.0ms	(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
33.0ms	(fma.f64 y (.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a))) x)
32.0ms	(cbrt.f64 (/.f64 1 a))
23.0ms	(.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`cbrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 182

Calls

4 calls:

14.0ms	(.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a)))
13.0ms	(*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))
2.0ms	(cbrt.f64 (/.f64 1 a))
0.0ms	(fma.f64 y (.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a))) x)

simplify143.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

497×	`times-frac_binary64`
445×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
287×	`associate-l_binary64`
233×	`associate-r_binary64`

Counts

302 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	4651
1	410	4023
2	1486	3925
3	4523	3904
4	5064	3904

prune272.0ms (5.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	336	6	342

Error

0.0b

Counts

342 → 6

Alt Table

Status	Error	Program
	24.3b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 t z) a) (/.f64 (-.f64 t z) a)) (/.f64 (-.f64 t z) a))) x)
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	5.3b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 a)) x)
	38.3b	(/.f64 (-.f64 (.f64 y t) (.f64 y z)) a)
✓	5.8b	(fma.f64 y (.f64 (.f64 (-.f64 t z) (*.f64 (cbrt.f64 (/.f64 1 a)) (cbrt.f64 (/.f64 1 a)))) (cbrt.f64 (/.f64 1 a))) x)
✓	1.5b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

Compiler

Compiled 8986 to 5471 computations (39.1% saved)

regimes675.0ms (14.5%)

Accuracy

Total 1.2b remaining (98.2%)

Threshold costs 0b (0%)

Counts

42 → 3

Compiler

Compiled 7459 to 4469 computations (40.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	27	59
2	39	59
3	53	59
4	65	59
5	79	59
6	85	59
7	81	59

end111.0ms (2.4%)

Compiler: Compiled 199 to 101 computations (49.2% saved)

Details

analyze1.3s (27%)

sample1.4s (29.3%)

simplify65.0ms (1.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series31.0ms (0.7%)

rewrite7.0ms (0.1%)

simplify114.0ms (2.4%)

prune91.0ms (1.9%)

localize6.0ms (0.1%)

series21.0ms (0.4%)

rewrite1.0ms (0%)

simplify65.0ms (1.4%)

prune16.0ms (0.4%)

localize7.0ms (0.2%)

series34.0ms (0.7%)

rewrite11.0ms (0.2%)

simplify113.0ms (2.4%)

prune60.0ms (1.3%)

localize12.0ms (0.3%)

series124.0ms (2.7%)

rewrite46.0ms (1%)

simplify143.0ms (3.1%)

prune272.0ms (5.8%)

regimes675.0ms (14.5%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end111.0ms (2.4%)

Profiling