Details

analyze418.0ms (16.3%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
27.3%	67.1%	5.6%	9
41%	50.3%	8.7%	10
43.9%	47%	9.1%	11
48.3%	38%	13.7%	12
56.3%	27.4%	16.2%	13
58.2%	25.4%	16.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample76.0ms (3%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`
1×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10
2	12	8
3	14	8
4	15	8
5	15	8

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
▶	0.1b	(fma.f64 y (/.f64 y z) x)
	6.8b	(+.f64 x (/.f64 (*.f64 y y) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

16.0ms

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

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
604×	`associate-+l+_binary64`
543×	`associate-l_binary64`
462×	`fma-def_binary64`
424×	`associate-/r*_binary64`

Counts

46 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	376
1	28	359
2	59	359
3	151	359
4	551	359
5	2861	359
6	5394	359

prune9.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (/.f64 y z) x)
▶	6.8b	(+.f64 x (/.f64 (*.f64 y y) z))
	32.9b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) (sqrt.f64 (fma.f64 y (/.f64 y z) x)))

Compiler

Compiled 222 to 71 computations (68% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	9.0b	(/.f64 (*.f64 y y) z)

series46.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

32.0ms	(/.f64 (*.f64 y y) z)
14.0ms	(+.f64 x (/.f64 (*.f64 y y) z))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

3.0ms	(+.f64 x (/.f64 (*.f64 y y) z))
3.0ms	(/.f64 (*.f64 y y) z)

simplify81.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-neg_binary64`
567×	`fma-def_binary64`
363×	`cancel-sign-sub-inv_binary64`
282×	`distribute-rgt-out_binary64`
269×	`*-commutative_binary64`

Counts

100 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	924
1	177	897
2	469	819
3	1624	819
4	3220	819
5	4792	819
6	5203	819

prune33.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	55	6	61

Error

0.0b

Counts

61 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	6.8b	(+.f64 x (.f64 (.f64 y y) (/.f64 1 z)))
✓	6.8b	(+.f64 x (/.f64 (*.f64 y y) z))
	34.5b	(+.f64 x (/.f64 (*.f64 y (/.f64 y (sqrt.f64 z))) (sqrt.f64 z)))
	7.1b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y y) z)) (cbrt.f64 (/.f64 (.f64 y y) z))) (cbrt.f64 (/.f64 (*.f64 y y) z))))

Compiler

Compiled 849 to 268 computations (68.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.1b	(/.f64 y (/.f64 z y))

series25.0ms (1%)

Counts

2 → 60

Calls

2 calls:

13.0ms	(+.f64 x (/.f64 y (/.f64 z y)))
11.0ms	(/.f64 y (/.f64 z y))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

2 → 89

Calls

2 calls:

12.0ms	(+.f64 x (/.f64 y (/.f64 z y)))
4.0ms	(/.f64 y (/.f64 z y))

simplify113.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary64`
532×	`associate-/l*_binary64`
507×	`associate-/r/_binary64`
346×	`associate-l_binary64`
308×	`fma-neg_binary64`

Counts

149 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	167	1992
1	373	1799
2	1160	1727
3	3066	1703
4	4514	1688
5	4960	1688
6	4955	1688

prune92.0ms (3.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	34.5b	(+.f64 x (/.f64 (*.f64 y (/.f64 y (sqrt.f64 z))) (sqrt.f64 z)))
	0.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 y (/.f64 z (cbrt.f64 y)))))
✓	6.8b	(+.f64 x (/.f64 (*.f64 y y) z))
▶	0.1b	(+.f64 x (/.f64 1 (/.f64 (/.f64 z y) y)))

Compiler

Compiled 2251 to 660 computations (70.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 (/.f64 z y) y)))
✓	0.2b	(/.f64 (/.f64 z y) y)
✓	0.5b	(/.f64 1 (/.f64 (/.f64 z y) y))

series50.0ms (2%)

Counts

3 → 84

Calls

3 calls:

26.0ms	(/.f64 (/.f64 z y) y)
14.0ms	(+.f64 x (/.f64 1 (/.f64 (/.f64 z y) y)))
10.0ms	(/.f64 1 (/.f64 (/.f64 z y) y))

rewrite72.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

468×	`times-frac_binary64`
233×	`*-un-lft-identity_binary64`
230×	`add-sqr-sqrt_binary64`
230×	`add-cube-cbrt_binary64`
46×	`associate-/r*_binary64`

Counts

3 → 292

Calls

3 calls:

27.0ms	(+.f64 x (/.f64 1 (/.f64 (/.f64 z y) y)))
9.0ms	(/.f64 1 (/.f64 (/.f64 z y) y))
4.0ms	(/.f64 (/.f64 z y) y)

simplify281.0ms (11%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
580×	`fma-neg_binary64`
428×	`associate-/l*_binary64`
374×	`*-commutative_binary64`
276×	`associate-/r/_binary64`

Counts

376 → 426

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	266	6762
1	533	5657
2	1379	5302
3	2451	5230
4	4254	5225
5	4724	5223
6	4995	5223
7	4868	5223

prune320.0ms (12.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	424	2	426
Fresh	2	0	2
Picked	1	0	1
Done	1	2	3
Total	428	4	432

Error

Counts

432 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)
	0.1b	(+.f64 x (/.f64 1 (*.f64 (/.f64 z y) (/.f64 1 y))))
	6.3b	(+.f64 x (/.f64 1 (*.f64 (/.f64 z 1) (/.f64 (/.f64 1 y) y))))

Compiler

Compiled 8256 to 2963 computations (64.1% saved)

regimes189.0ms (7.4%)

Accuracy

Total 0.1b remaining (84.3%)

Threshold costs 0.1b (84.3%)

Counts

33 → 1

Compiler

Compiled 3307 to 1899 computations (42.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

end0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

sample631.0ms (24.7%)

Algorithm

1×

intervals

Results

250.0ms	8000×	body	128	valid
29.0ms	971×	body	128	invalid

Compiler

Compiled 73 to 49 computations (32.9% saved)

Details

analyze418.0ms (16.3%)

sample76.0ms (3%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series16.0ms (0.6%)

rewrite1.0ms (0%)

simplify47.0ms (1.8%)

prune9.0ms (0.3%)

localize4.0ms (0.2%)

series46.0ms (1.8%)

rewrite8.0ms (0.3%)

simplify81.0ms (3.2%)

prune33.0ms (1.3%)

localize4.0ms (0.2%)

series25.0ms (1%)

rewrite21.0ms (0.8%)

simplify113.0ms (4.4%)

prune92.0ms (3.6%)

localize6.0ms (0.2%)

series50.0ms (2%)

rewrite72.0ms (2.8%)

simplify281.0ms (11%)

prune320.0ms (12.5%)

regimes189.0ms (7.4%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample631.0ms (24.7%)

Profiling