Details

analyze1.4s (15.4%)

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)

sample1.5s (17.4%)

Results

1.1s	8256×	body	128	valid
338.0ms	2697×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify62.0ms (0.7%)

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%)

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
▶	5.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	5.6b	(-.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)

series39.0ms (0.4%)

Counts

2 → 88

Calls

2 calls:

29.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
10.0ms	(/.f64 (-.f64 t z) a)

rewrite8.0ms (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:

5.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify120.0ms (1.4%)

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

prune50.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Error

0.0b

Counts

80 → 5

Alt Table

Status	Error	Program
	27.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) a) 3)) x)
	4.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
▶	3.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	5.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

Compiler

Compiled 1236 to 359 computations (71% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series23.0ms (0.3%)

Counts

1 → 60

Calls

1 calls:

23.0ms

(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)

simplify69.0ms (0.8%)

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 (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
	27.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) a) 3)) x)
▶	4.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	3.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	5.6b	(-.f64 (+.f64 (/.f64 (.f64 y t) a) x) (/.f64 (.f64 y z) a))
	5.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

Compiler

Compiled 468 to 154 computations (67.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))
	3.2b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series721.0ms (8.2%)

Counts

3 → 180

Calls

3 calls:

490.0ms

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

204.0ms

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

26.0ms

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

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

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

6.0ms

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

1.0ms

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

simplify310.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

617×	`*-commutative_binary64`
272×	`associate-r_binary64`
255×	`+-commutative_binary64`
227×	`fma-def_binary64`
174×	`associate-/l*_binary64`

Counts

273 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1376	22614
1	4931	22614
2	4986	22614

prune669.0ms (7.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	588	3	591
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	589	7	596

Error

0.0b

Counts

596 → 7

Alt Table

Status	Error	Program
▶	4.8b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	4.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	27.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) a) 3)) x)
✓	3.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	35.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))))
	5.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 t z)) a))
	5.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

Compiler

Compiled 51698 to 21140 computations (59.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))))
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	0.6b	(cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))
	3.2b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series677.0ms (7.7%)

Counts

2 → 120

Calls

2 calls:

477.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))))
199.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

8.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))

simplify240.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

616×	`*-commutative_binary64`
274×	`associate-r_binary64`
262×	`+-commutative_binary64`
229×	`fma-def_binary64`
175×	`associate-+r+_binary64`

Counts

192 → 252

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1379	22849
1	4981	22849

prune1.5s (17.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1125	0	1125
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1125	7	1132

Error

0.0b

Counts

1132 → 7

Alt Table

Status	Error	Program
✓	4.8b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
✓	4.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))
	27.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 t z) a) 3)) x)
✓	3.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
	35.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)) (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (/.f64 y a) (-.f64 t z) x)))))
	5.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 t z)) a))
	5.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

Compiler

Compiled 128567 to 44170 computations (65.6% saved)

regimes1.2s (13.5%)

Accuracy

Total 0.5b remaining (96.1%)

Threshold costs 0.5b (96.1%)

Counts

74 → 3

Compiler

Compiled 20752 to 8915 computations (57% saved)

bsearch3.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	68
1	41	68
2	53	68
3	66	68
4	73	68
5	76	68
6	77	68
7	76	68

end96.0ms (1.1%)

Compiler: Compiled 299 to 129 computations (56.9% saved)

Details

analyze1.4s (15.4%)

sample1.5s (17.4%)

simplify62.0ms (0.7%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series39.0ms (0.4%)

rewrite8.0ms (0.1%)

simplify120.0ms (1.4%)

prune50.0ms (0.6%)

localize6.0ms (0.1%)

series23.0ms (0.3%)

rewrite1.0ms (0%)

simplify69.0ms (0.8%)

prune16.0ms (0.2%)

localize9.0ms (0.1%)

series721.0ms (8.2%)

rewrite25.0ms (0.3%)

simplify310.0ms (3.5%)

prune669.0ms (7.7%)

localize14.0ms (0.2%)

series677.0ms (7.7%)

rewrite16.0ms (0.2%)

simplify240.0ms (2.7%)

prune1.5s (17.2%)

regimes1.2s (13.5%)

bsearch3.0ms (0%)

simplify6.0ms (0.1%)

end96.0ms (1.1%)

Profiling