Details

analyze391.0ms (15.7%)

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
25%	74.9%	0.1%	8
31.2%	62.4%	6.4%	9
46.8%	46.8%	6.4%	10
53.8%	39.8%	6.4%	11
57.3%	33.2%	9.5%	12
66.9%	23.6%	9.5%	13
70.3%	20.2%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.3s (51.6%)

Symmetry

(sort x y)

Results

1.2s	8256×	body	128	valid
29.0ms	315×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

192×	`fma-def_binary64`
125×	`fma-neg_binary64`
44×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
27×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 (.f64 x 3) y) z)

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) y) z)
✓	0.2b	(.f64 (.f64 x 3) y)

series14.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

7.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
7.0ms	(.f64 (.f64 x 3) y)

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

4.0ms	(-.f64 (.f64 (.f64 x 3) y) z)
4.0ms	(.f64 (.f64 x 3) y)

simplify84.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
637×	`fma-neg_binary64`
284×	`*-commutative_binary64`
255×	`unswap-sqr_binary64`
206×	`cancel-sign-sub-inv_binary64`

Counts

100 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	949
1	197	920
2	673	908
3	1389	908
4	2926	908
5	4712	908
6	4917	908

prune52.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Error

0.0b

Counts

64 → 8

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
	29.2b	(+.f64 (fma.f64 (.f64 x 3) y (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z))))
	37.8b	(/.f64 (-.f64 (.f64 x (.f64 (.f64 y y) (.f64 x 9))) (.f64 z z)) (fma.f64 3 (.f64 y x) z))
	0.7b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) (cbrt.f64 (.f64 (.f64 x 3) y))) (cbrt.f64 (.f64 (.f64 x 3) y))) z)
	27.3b	(-.f64 (exp.f64 (log.f64 (.f64 3 (.f64 y x)))) z)

Compiler

Compiled 1090 to 638 computations (41.5% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))

series7.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(fma.f64 (*.f64 x 3) y (neg.f64 z))

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 (*.f64 x 3) y (neg.f64 z))

simplify49.0ms (2%)

Algorithm

1×	egg-herbie

Rules

908×	`unsub-neg_binary64`
729×	`distribute-rgt-in_binary64`
682×	`distribute-lft-in_binary64`
574×	`distribute-neg-out_binary64`
533×	`fma-neg_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	468
1	37	447
2	61	447
3	210	447
4	863	447
5	2572	447
6	5078	447

prune20.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	22	8	30

Error

0.0b

Counts

30 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
	29.2b	(+.f64 (fma.f64 (.f64 x 3) y (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z))))
	37.8b	(/.f64 (-.f64 (.f64 x (.f64 (.f64 y y) (.f64 x 9))) (.f64 z z)) (fma.f64 3 (.f64 y x) z))
	0.7b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
▶	0.1b	(-.f64 (.f64 x (.f64 3 y)) z)
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) (cbrt.f64 (.f64 (.f64 x 3) y))) (cbrt.f64 (.f64 (.f64 x 3) y))) z)
	27.3b	(-.f64 (exp.f64 (log.f64 (.f64 3 (.f64 y x)))) z)

Compiler

Compiled 502 to 294 computations (41.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (.f64 3 y)) z)
✓	0.3b	(.f64 x (.f64 3 y))

series12.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

7.0ms	(-.f64 (.f64 x (.f64 3 y)) z)
5.0ms	(.f64 x (.f64 3 y))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

5.0ms	(.f64 x (.f64 3 y))
4.0ms	(-.f64 (.f64 x (.f64 3 y)) z)

simplify83.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
648×	`fma-neg_binary64`
275×	`*-commutative_binary64`
217×	`unswap-sqr_binary64`
215×	`times-frac_binary64`

Counts

100 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	947
1	188	918
2	650	906
3	1354	906
4	2928	906
5	4688	906
6	4904	906

prune49.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
▶	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
	29.2b	(+.f64 (fma.f64 (.f64 x 3) y (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z))))
	0.7b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) (cbrt.f64 (.f64 (.f64 x 3) y))) (cbrt.f64 (.f64 (.f64 x 3) y))) z)
	27.3b	(-.f64 (exp.f64 (log.f64 (.f64 3 (.f64 y x)))) z)

Compiler

Compiled 1034 to 601 computations (41.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(fma.f64 x (*.f64 3 y) (neg.f64 z))

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 x (*.f64 3 y) (neg.f64 z))

simplify51.0ms (2%)

Algorithm

1×	egg-herbie

Rules

907×	`unsub-neg_binary64`
729×	`distribute-rgt-in_binary64`
682×	`distribute-lft-in_binary64`
574×	`distribute-neg-out_binary64`
535×	`fma-neg_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	468
1	35	447
2	62	447
3	210	447
4	863	447
5	2572	447
6	5078	447

prune14.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	22	7	29

Error

0.0b

Counts

29 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 x 3) y (neg.f64 z))
	0.1b	(-.f64 (.f64 3 (.f64 y x)) z)
✓	0.1b	(fma.f64 x (*.f64 3 y) (neg.f64 z))
	29.2b	(+.f64 (fma.f64 (.f64 x 3) y (neg.f64 (.f64 (sqrt.f64 z) (sqrt.f64 z)))) (fma.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z) (*.f64 (sqrt.f64 z) (sqrt.f64 z))))
	0.7b	(-.f64 (.f64 (.f64 (.f64 x 3) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) z)
	0.6b	(-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 x 3) y)) (cbrt.f64 (.f64 (.f64 x 3) y))) (cbrt.f64 (.f64 (.f64 x 3) y))) z)
	27.3b	(-.f64 (exp.f64 (log.f64 (.f64 3 (.f64 y x)))) z)

Compiler

Compiled 356 to 203 computations (43% saved)

regimes202.0ms (8.1%)

Accuracy

Total 0.2b remaining (94%)

Threshold costs 0.2b (94%)

Counts

27 → 1

Compiler

Compiled 2688 to 1863 computations (30.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	15	10
3	16	10
4	16	10

end95.0ms (3.8%)

Remove: (sort x y)
Compiler: Compiled 150 to 98 computations (34.7% saved)

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10

Details

analyze391.0ms (15.7%)

sample1.3s (51.6%)

simplify24.0ms (1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.6%)

rewrite10.0ms (0.4%)

simplify84.0ms (3.4%)

prune52.0ms (2.1%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite1.0ms (0%)

simplify49.0ms (2%)

prune20.0ms (0.8%)

localize6.0ms (0.3%)

series12.0ms (0.5%)

rewrite11.0ms (0.4%)

simplify83.0ms (3.3%)

prune49.0ms (2%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite1.0ms (0%)

simplify51.0ms (2%)

prune14.0ms (0.6%)

regimes202.0ms (8.1%)

simplify3.0ms (0.1%)

end95.0ms (3.8%)

Profiling

Iter	Nodes	Cost
0	8	10
1	15	10
2	28	10
3	38	10
4	70	10
5	109	10
6	193	10
7	311	10
8	363	10
9	420	10
10	424	10
11	426	10
12	381	10