Details

analyze935.0ms (19%)

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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
18.7%	70.2%	11.1%	11
21.1%	66.7%	12.3%	12
31.6%	55.9%	12.5%	13
34.5%	52.3%	13.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (25.3%)

Results

1.0s	8256×	body	128	valid
211.0ms	1813×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

22×	`fma-def_binary64`
8×	`+-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	25	9
3	38	9
4	52	9
5	52	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 y (fma.f64 x y z) t)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (fma.f64 x y z) t)

series15.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(fma.f64 y (fma.f64 x y z) t)

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 y (fma.f64 x y z) t)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

775×	`associate-+l+_binary64`
772×	`associate-+r+_binary64`
678×	`unswap-sqr_binary64`
551×	`*-commutative_binary64`
295×	`distribute-lft-in_binary64`

Counts

58 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	697
1	47	499
2	84	499
3	257	499
4	1272	499
5	3520	499
6	4213	499
7	5348	499

prune22.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.0b	(fma.f64 y (fma.f64 x y z) t)
	3.5b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
	40.1b	(cbrt.f64 (pow.f64 (fma.f64 y (fma.f64 y x z) t) 3))

Compiler

Compiled 439 to 137 computations (68.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 y (fma.f64 x y z) t)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.5b	(cbrt.f64 (fma.f64 y (fma.f64 x y z) t))

series424.0ms (8.6%)

Counts

3 → 144

Calls

3 calls:

282.0ms

(*.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))

127.0ms

(cbrt.f64 (fma.f64 y (fma.f64 x y z) t))

15.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))

rewrite19.0ms (0.4%)

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:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))

1.0ms

(cbrt.f64 (fma.f64 y (fma.f64 x y z) t))

simplify260.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

452×	`*-commutative_binary64`
227×	`+-commutative_binary64`
192×	`fma-def_binary64`
180×	`cancel-sign-sub-inv_binary64`
180×	`sub-neg_binary64`

Counts

237 → 294

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1059	14782
1	3790	13671
2	4988	13671
3	4958	13671

prune629.0ms (12.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	595	2	597
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	597	4	601

Error

0.0b

Counts

601 → 4

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.0b	(fma.f64 y (fma.f64 x y z) t)
	32.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)))))
▶	3.5b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))

Compiler

Compiled 41983 to 20309 computations (51.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
✓	8.5b	(.f64 (.f64 y y) x)

series29.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
8.0ms	(.f64 (.f64 y y) x)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(.f64 (.f64 y y) x)
2.0ms	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
417×	`associate-l_binary64`
298×	`associate-r_binary64`
270×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

111 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	1277
1	177	1101
2	542	947
3	2018	947
4	3252	947
5	4966	947
6	4937	947

prune32.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Error

0.0b

Counts

66 → 5

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.0b	(fma.f64 y (fma.f64 x y z) t)
▶	3.8b	(+.f64 t (fma.f64 y z (.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
	32.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)))))
✓	3.5b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))

Compiler

Compiled 1068 to 285 computations (73.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	2.1b	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	6.4b	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

series412.0ms (8.4%)

Counts

4 → 72

Calls

4 calls:

318.0ms	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
36.0ms	(cbrt.f64 x)
35.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
22.0ms	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`pow1_binary64`
36×	`add-exp-log_binary64`
29×	`pow-prod-down_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`

Counts

4 → 118

Calls

4 calls:

11.0ms	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
7.0ms	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
689×	`unswap-sqr_binary64`
493×	`*-commutative_binary64`
409×	`log-prod_binary64`
408×	`sqr-pow_binary64`

Counts

190 → 151

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	118	2010
1	232	1695
2	997	1577
3	1899	1536
4	3263	1426
5	4585	1388
6	4730	1388
7	5010	1388

prune137.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	187	5	192

Error

Counts

192 → 5

Alt Table

Status	Error	Program
	1.0b	(+.f64 t (fma.f64 y z (.f64 (.f64 y (.f64 y (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 x))))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.0b	(fma.f64 y (fma.f64 x y z) t)
	39.8b	(+.f64 t (fma.f64 y z (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 6))))
✓	3.5b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))

Compiler

Compiled 4036 to 1173 computations (70.9% saved)

regimes336.0ms (6.8%)

Accuracy

Total 0.0b remaining (68.9%)

Threshold costs 0.0b (68.9%)

Counts

57 → 1

Compiler

Compiled 6764 to 3640 computations (46.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end66.0ms (1.3%)

Compiler: Compiled 114 to 57 computations (50% saved)

Details

analyze935.0ms (19%)

sample1.2s (25.3%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite1.0ms (0%)

simplify64.0ms (1.3%)

prune22.0ms (0.4%)

localize8.0ms (0.2%)

series424.0ms (8.6%)

rewrite19.0ms (0.4%)

simplify260.0ms (5.3%)

prune629.0ms (12.8%)

localize6.0ms (0.1%)

series29.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify88.0ms (1.8%)

prune32.0ms (0.7%)

localize10.0ms (0.2%)

series412.0ms (8.4%)

rewrite32.0ms (0.7%)

simplify128.0ms (2.6%)

prune137.0ms (2.8%)

regimes336.0ms (6.8%)

simplify2.0ms (0%)

end66.0ms (1.3%)

Profiling