Details

analyze570.0ms (12.7%)

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
23.4%	71%	5.6%	9
35.1%	56.2%	8.7%	10
41%	49.9%	9.1%	11
45.1%	41.2%	13.7%	12
52.6%	31.2%	16.2%	13
56.3%	27.3%	16.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.0s (22.6%)

Results

823.0ms	8256×	body	128	valid
140.0ms	913×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.9b	(+.f64 x (/.f64 (*.f64 y y) z))
▶	0.1b	(fma.f64 y (/.f64 y z) x)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

11.0ms

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

rewrite2.0ms (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:

1.0ms

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

simplify47.0ms (1%)

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

prune11.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	15	4	19

Error

0.0b

Counts

19 → 4

Alt Table

Status	Error	Program
	6.9b	(+.f64 x (/.f64 (*.f64 y y) z))
	28.8b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) (sqrt.f64 (fma.f64 y (/.f64 y z) x)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)

Compiler

Compiled 274 to 87 computations (68.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (/.f64 y z) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.5b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))

series198.0ms (4.4%)

Counts

3 → 108

Calls

3 calls:

126.0ms

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

59.0ms

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

13.0ms

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

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:

8.0ms

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

4.0ms

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

1.0ms

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

simplify178.0ms (4%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
298×	`associate-r_binary64`
276×	`cancel-sign-sub-inv_binary64`
257×	`unswap-sqr_binary64`
188×	`*-commutative_binary64`

Counts

201 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	316	6172
1	905	5625
2	2738	5166
3	4604	4783
4	4960	4783
5	4920	4783

prune257.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	364	2	366
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	365	5	370

Error

0.0b

Counts

370 → 5

Alt Table

Status	Error	Program
	6.9b	(+.f64 x (/.f64 (*.f64 y y) z))
	46.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) (cbrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 -1 y) -2) z)))
▶	1.4b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
	28.8b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)) (sqrt.f64 (fma.f64 y (/.f64 y z) x)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)

Compiler

Compiled 14301 to 5267 computations (63.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (/.f64 y z) x)
	0.5b	(cbrt.f64 (fma.f64 y (/.f64 y z) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

series1.6s (36.6%)

Counts

1 → 36

Calls

1 calls:

1.6s	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
495×	`associate-l_binary64`
404×	`associate-r_binary64`
280×	`exp-prod_binary64`
214×	`log-prod_binary64`

Counts

68 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1448
1	225	1269
2	649	1149
3	3121	865
4	4719	865
5	4995	865
6	4934	865

prune69.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Error

0.0b

Counts

132 → 5

Alt Table

Status	Error	Program
▶	6.9b	(+.f64 x (/.f64 (*.f64 y y) z))
	29.6b	(pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 y z) x)))) 3)
	46.5b	(/.f64 (pow.f64 (/.f64 -1 y) -2) z)
✓	1.4b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
✓	0.1b	(fma.f64 y (/.f64 y z) x)

Compiler

Compiled 3068 to 1738 computations (43.4% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y y) z))
✓	10.8b	(/.f64 (*.f64 y y) z)

series25.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

13.0ms	(/.f64 (*.f64 y y) z)
12.0ms	(+.f64 x (/.f64 (*.f64 y y) z))

rewrite8.0ms (0.2%)

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)

simplify85.0ms (1.9%)

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

prune25.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	58	5	63

Error

Counts

63 → 5

Alt Table

Status	Error	Program
✓	6.9b	(+.f64 x (/.f64 (*.f64 y y) z))
	46.5b	(/.f64 (pow.f64 (/.f64 -1 y) -2) z)
✓	1.4b	(pow.f64 (cbrt.f64 (fma.f64 y (/.f64 y z) x)) 3)
	0.1b	(+.f64 x (/.f64 y (/.f64 z y)))
✓	0.1b	(fma.f64 y (/.f64 y z) x)

Compiler

Compiled 759 to 228 computations (70% saved)

regimes128.0ms (2.9%)

Accuracy

Total 0.1b remaining (89.9%)

Threshold costs 0.1b (89.9%)

Counts

20 → 1

Compiler

Compiled 2016 to 1088 computations (46% saved)

simplify2.0ms (0%)

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

end58.0ms (1.3%)

Compiler: Compiled 71 to 45 computations (36.6% saved)

Details

analyze570.0ms (12.7%)

sample1.0s (22.6%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series11.0ms (0.3%)

rewrite2.0ms (0%)

simplify47.0ms (1%)

prune11.0ms (0.2%)

localize9.0ms (0.2%)

series198.0ms (4.4%)

rewrite19.0ms (0.4%)

simplify178.0ms (4%)

prune257.0ms (5.7%)

localize6.0ms (0.1%)

series1.6s (36.6%)

rewrite3.0ms (0.1%)

simplify103.0ms (2.3%)

prune69.0ms (1.5%)

localize4.0ms (0.1%)

series25.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify85.0ms (1.9%)

prune25.0ms (0.6%)

regimes128.0ms (2.9%)

simplify2.0ms (0%)

end58.0ms (1.3%)

Profiling