Details

analyze724.0ms (16.6%)

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
34.3%	65.5%	0.1%	9
39%	60.8%	0.1%	10
41.3%	58.5%	0.1%	11
52.7%	47.2%	0.1%	12
54%	45.7%	0.2%	13
55.3%	43.8%	0.9%	14

Compiler

Compiled 19 to 10 computations (47.4% saved)

sample2.0s (46.1%)

Results

760.0ms	6035×	body	128	valid
268.0ms	843×	body	1024	valid
217.0ms	285×	body	512	invalid
195.0ms	510×	body	2048	valid
143.0ms	1348×	body	128	invalid
132.0ms	548×	body	512	valid
113.0ms	320×	body	256	valid
57.0ms	197×	body	1024	invalid
37.0ms	217×	body	256	invalid

Compiler

Compiled 56 to 29 computations (48.2% saved)

simplify249.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

7175×	`fma-neg_binary64`
753×	`unsub-neg_binary64`
515×	`distribute-lft-out_binary64`
498×	`distribute-lft-out--_binary64`
472×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	27	10
2	80	7
3	206	7
4	565	7
5	1825	7
6	2161	7
7	2289	7
8	2491	7
9	2604	7
10	2649	7
11	3904	7
12	3380	7
13	3584	7
14	3584	7
15	3996	7
16	4202	7
17	4202	7
18	4202	7
19	4304	7
20	4304	7
21	11032	7

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.1b	(+.f64 (-.f64 (-.f64 (.f64 x y) (.f64 y z)) (.f64 y y)) (.f64 y y))
▶	0.0b	(*.f64 y (-.f64 x z))

Compiler

Compiled 75 to 39 computations (48% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x z))

series6.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

6.0ms

(*.f64 y (-.f64 x z))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 50

Calls

1 calls:

6.0ms

(*.f64 y (-.f64 x z))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
422×	`unsub-neg_binary64`
281×	`unswap-sqr_binary64`
277×	`*-commutative_binary64`
231×	`neg-mul-1_binary64`

Counts

86 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	869
1	190	803
2	577	749
3	1458	695
4	3029	695
5	4852	695
6	5000	695
7	4766	695

prune34.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Error

0.0b

Counts

69 → 3

Alt Table

Status	Error	Program
	30.2b	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))
▶	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))

Compiler

Compiled 1059 to 292 computations (72.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

7.0ms

(-.f64 (*.f64 y x) (*.f64 y z))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`distribute-lft-out--_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`

Counts

1 → 17

Calls

1 calls:

2.0ms

(-.f64 (*.f64 y x) (*.f64 y z))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

791×	`unsub-neg_binary64`
633×	`fma-def_binary64`
541×	`distribute-rgt-in_binary64`
482×	`distribute-lft-in_binary64`
320×	`times-frac_binary64`

Counts

35 → 35

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	332
1	121	314
2	415	307
3	1268	304
4	3520	304
5	4176	304
6	4949	304
7	4865	304

prune17.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	35	3	38

Error

0.0b

Counts

38 → 3

Alt Table

Status	Error	Program
▶	30.2b	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))

Compiler

Compiled 441 to 127 computations (71.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 x z))
✓	0.1b	(*.f64 y (sqrt.f64 (-.f64 x z)))
✓	0.1b	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))

series72.0ms (1.6%)

Counts

3 → 60

Calls

3 calls:

33.0ms	(*.f64 y (sqrt.f64 (-.f64 x z)))
22.0ms	(sqrt.f64 (-.f64 x z))
16.0ms	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
16×	`sqrt-div_binary64`
15×	`*-un-lft-identity_binary64`

Counts

3 → 80

Calls

3 calls:

8.0ms	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))
7.0ms	(*.f64 y (sqrt.f64 (-.f64 x z)))
3.0ms	(sqrt.f64 (-.f64 x z))

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
373×	`fma-def_binary64`
328×	`*-commutative_binary64`
293×	`times-frac_binary64`
221×	`distribute-rgt-in_binary64`

Counts

140 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	1956
1	465	1848
2	1434	1828
3	4198	1826
4	4990	1826
5	4977	1826

prune60.0ms (1.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
▶	52.2b	(/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))) (sqrt.f64 (-.f64 x z))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z)))))
✓	30.2b	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))

Compiler

Compiled 3367 to 1038 computations (69.2% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.1b	(*.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3))))
✓	9.6b	(/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))) (sqrt.f64 (-.f64 x z))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z)))))
✓	14.9b	(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))
✓	24.3b	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))

series247.0ms (5.6%)

Counts

4 → 72

Calls

4 calls:

173.0ms	(/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))) (sqrt.f64 (-.f64 x z))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z)))))
48.0ms	(*.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3))))
17.0ms	(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))

rewrite72.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64`
60×	`sqrt-prod_binary64`
33×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
28×	`associate-r_binary64`

Counts

4 → 146

Calls

4 calls:

22.0ms	(/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))) (sqrt.f64 (-.f64 x z))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z)))))
17.0ms	(sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))
15.0ms	(*.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))

simplify158.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
386×	`cancel-sign-sub-inv_binary64`
349×	`fma-neg_binary64`
257×	`associate-r_binary64`
254×	`associate-l_binary64`

Counts

218 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	5513
1	865	5021
2	3202	4877
3	4873	4877
4	4958	4877

prune161.0ms (3.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	256	4	260

Error

Counts

260 → 4

Alt Table

Status	Error	Program
✓	52.2b	(/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)))) (sqrt.f64 (-.f64 x z))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z)))))
✓	30.2b	(.f64 (.f64 y (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z)))
✓	0.0b	(-.f64 (.f64 y x) (.f64 y z))
✓	0.0b	(*.f64 y (-.f64 x z))

Compiler

Compiled 9757 to 4115 computations (57.8% saved)

regimes147.0ms (3.4%)

Accuracy

Total 0.0b remaining (59.2%)

Threshold costs 0.0b (59.2%)

Counts

30 → 1

Compiler

Compiled 2384 to 1468 computations (38.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	24	10
3	29	10
4	31	10
5	31	10

end55.0ms (1.3%)

Compiler: Compiled 83 to 50 computations (39.8% saved)

Details

analyze724.0ms (16.6%)

sample2.0s (46.1%)

simplify249.0ms (5.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify88.0ms (2%)

prune34.0ms (0.8%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify80.0ms (1.8%)

prune17.0ms (0.4%)

localize6.0ms (0.1%)

series72.0ms (1.6%)

rewrite23.0ms (0.5%)

simplify103.0ms (2.3%)

prune60.0ms (1.4%)

localize19.0ms (0.4%)

series247.0ms (5.6%)

rewrite72.0ms (1.6%)

simplify158.0ms (3.6%)

prune161.0ms (3.7%)

regimes147.0ms (3.4%)

simplify3.0ms (0.1%)

end55.0ms (1.3%)

Profiling