Details

analyze986.0ms (18.5%)

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 (22.1%)

Results

931.0ms	8256×	body	128	valid
201.0ms	1847×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify6.0ms (0.1%)

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%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (fma.f64 x y z) t)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)

series13.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

13.0ms

(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 (1.2%)

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

prune21.0ms (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
	34.5b	(*.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)) (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
	4.2b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
▶	1.4b	(.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)))

Compiler

Compiled 453 to 135 computations (70.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(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)))
✓	0.6b	(cbrt.f64 (fma.f64 y (fma.f64 x y z) t))

series393.0ms (7.4%)

Counts

3 → 144

Calls

3 calls:

249.0ms

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

129.0ms

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

14.0ms

(*.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)))

rewrite21.0ms (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:

10.0ms

(*.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))

simplify259.0ms (4.9%)

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

prune721.0ms (13.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

0.0b

Counts

601 → 4

Alt Table

Status	Error	Program
	34.5b	(*.f64 (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)) (sqrt.f64 (fma.f64 y (fma.f64 x y z) t)))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
▶	4.2b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
	32.5b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (fma.f64 x y z) t) (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))

Compiler

Compiled 41971 to 20312 computations (51.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (.f64 (.f64 y y) x))
✓	0.0b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
✓	10.8b	(.f64 (.f64 y y) x)

series48.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

20.0ms	(fma.f64 y z (.f64 (.f64 y y) x))
19.0ms	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
9.0ms	(.f64 (.f64 y y) x)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

4.0ms	(.f64 (.f64 y y) x)
2.0ms	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
0.0ms	(fma.f64 y z (.f64 (.f64 y y) x))

simplify92.0ms (1.7%)

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

157 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	1762
1	183	1549
2	548	1321
3	2026	1321
4	3264	1321
5	4989	1321
6	4960	1321

prune42.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	78	5	83

Error

0.0b

Counts

83 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
▶	4.4b	(+.f64 t (fma.f64 y z (.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
✓	4.2b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
	32.5b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (fma.f64 x y z) t) (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
	35.6b	(+.f64 t (fma.f64 y z (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 1307 to 343 computations (73.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.7b	(cbrt.f64 x)
✓	2.9b	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	7.9b	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

series428.0ms (8%)

Counts

4 → 72

Calls

4 calls:

333.0ms	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
41.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
31.0ms	(cbrt.f64 x)
23.0ms	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite39.0ms (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:

12.0ms	(.f64 (.f64 y y) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
11.0ms	(.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify134.0ms (2.5%)

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

prune197.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	186	6	192

Error

Counts

192 → 6

Alt Table

Status	Error	Program
✓	4.2b	(+.f64 t (fma.f64 y z (.f64 (.f64 y y) x)))
	32.5b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (fma.f64 x y z) t) (fma.f64 y (fma.f64 x y z) t))) (cbrt.f64 (fma.f64 y (fma.f64 x y z) t)))
	1.6b	(+.f64 t (fma.f64 y z (.f64 (.f64 y (.f64 y (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 x))))
	4.4b	(+.f64 t (fma.f64 y z (.f64 (.f64 (sqrt.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (sqrt.f64 (.f64 (.f64 y y) (.f64 (cbrt.f64 x) (cbrt.f64 x))))) (cbrt.f64 x))))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
	35.6b	(+.f64 t (fma.f64 y z (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x)))))

Compiler

Compiled 4070 to 1185 computations (70.9% saved)

regimes551.0ms (10.4%)

Accuracy

Total 0.0b remaining (73.4%)

Threshold costs 0.0b (73.4%)

Counts

83 → 1

Compiler

Compiled 10724 to 5890 computations (45.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end78.0ms (1.5%)

Compiler: Compiled 148 to 69 computations (53.4% saved)

Details

analyze986.0ms (18.5%)

sample1.2s (22.1%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite1.0ms (0%)

simplify64.0ms (1.2%)

prune21.0ms (0.4%)

localize8.0ms (0.2%)

series393.0ms (7.4%)

rewrite21.0ms (0.4%)

simplify259.0ms (4.9%)

prune721.0ms (13.6%)

localize6.0ms (0.1%)

series48.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify92.0ms (1.7%)

prune42.0ms (0.8%)

localize12.0ms (0.2%)

series428.0ms (8%)

rewrite39.0ms (0.7%)

simplify134.0ms (2.5%)

prune197.0ms (3.7%)

regimes551.0ms (10.4%)

simplify4.0ms (0.1%)

end78.0ms (1.5%)

Profiling