Details

analyze150.0ms (4.6%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
81.1%	18.7%	0.1%	9
81.1%	18.7%	0.1%	10
81.1%	15.6%	3.3%	11
84.3%	10.9%	4.8%	12
84.3%	10.9%	4.8%	13
84.3%	8.6%	7.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample78.0ms (2.4%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

9.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify25.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

209×	`fma-def_binary64`
157×	`fma-neg_binary64`
56×	`cancel-sign-sub-inv_binary64`
42×	`distribute-rgt-neg-in_binary64`
36×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 42 to 29 computations (31% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x y) 2)
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

series14.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
5.0ms	(/.f64 (*.f64 x y) 2)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (*.f64 x y) 2)
0.0ms	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

753×	`distribute-rgt-in_binary64`
565×	`associate-/r/_binary64`
449×	`associate-l_binary64`
391×	`associate-/r*_binary64`
388×	`associate-*r/_binary64`

Counts

93 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	74	985
1	140	863
2	382	863
3	1101	863
4	3121	863
5	5499	863

prune34.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	3	60

Error

0.0b

Counts

60 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 827 to 513 computations (38% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
✓	0.5b	(/.f64 x (/.f64 2 y))

series13.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

8.0ms	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
5.0ms	(/.f64 x (/.f64 2 y))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 82

Calls

2 calls:

4.0ms	(/.f64 x (/.f64 2 y))
0.0ms	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))

simplify153.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
506×	`*-commutative_binary64`
463×	`distribute-rgt-in_binary64`
331×	`associate-/r/_binary64`
299×	`associate-/l/_binary64`

Counts

142 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1984
1	336	1847
2	944	1846
3	2170	1846
4	2928	1846
5	4851	1846
6	4996	1846
7	5000	1846
8	4912	1846

prune79.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
▶	0.7b	(fma.f64 z -1/8 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y)))))
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 2204 to 1332 computations (39.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 x (/.f64 2 (cbrt.f64 y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y))))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series339.0ms (10.4%)

Counts

4 → 72

Calls

4 calls:

247.0ms	(/.f64 x (/.f64 2 (cbrt.f64 y)))
39.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)
19.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y))))

rewrite57.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

263×	`times-frac_binary64`
167×	`add-sqr-sqrt_binary64`
150×	`*-un-lft-identity_binary64`
150×	`add-cube-cbrt_binary64`
83×	`cbrt-prod_binary64`

Counts

4 → 264

Calls

4 calls:

18.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y))))
5.0ms	(/.f64 x (/.f64 2 (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify186.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

734×	`associate-l_binary64`
734×	`unswap-sqr_binary64`
419×	`associate-r_binary64`
301×	`*-commutative_binary64`
259×	`associate-*r/_binary64`

Counts

336 → 422

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	329	5988
1	837	4967
2	3787	4869
3	3693	4741
4	5069	4741

prune290.0ms (8.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	458	0	458
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	458	4	462

Error

Counts

462 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
✓	0.7b	(fma.f64 z -1/8 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y)))))
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 10897 to 5219 computations (52.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
✓	0.6b	(cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2)))

series118.0ms (3.6%)

Counts

3 → 108

Calls

3 calls:

59.0ms

(*.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))

50.0ms

(cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2)))

9.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))

rewrite20.0ms (0.6%)

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:

7.0ms

(*.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))

1.0ms

(cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2)))

simplify132.0ms (4%)

Algorithm

1×	egg-herbie

Rules

421×	`associate-r_binary64`
336×	`times-frac_binary64`
296×	`associate-/r*_binary64`
288×	`associate-l_binary64`
269×	`associate-/l*_binary64`

Counts

201 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	472	7363
1	1467	6929
2	5178	6929

prune513.0ms (15.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	502	0	502
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	502	4	506

Error

Counts

506 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z -1/8 (/.f64 x (/.f64 2 y)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (.f64 x y) 2)))) (cbrt.f64 (fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))))
✓	0.7b	(fma.f64 z -1/8 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 x (/.f64 2 (cbrt.f64 y)))))
✓	0.0b	(fma.f64 z -1/8 (/.f64 (*.f64 x y) 2))

Compiler

Compiled 24148 to 16010 computations (33.7% saved)

regimes278.0ms (8.6%)

Accuracy

Total 0.1b remaining (94.1%)

Threshold costs 0.1b (94.1%)

Counts

23 → 1

Compiler

Compiled 2846 to 2082 computations (26.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	13	13
2	20	13
3	24	13
4	27	13
5	28	13
6	28	13

end5.0ms (0.2%)

Remove: (sort x y)
Compiler: Compiled 36 to 27 computations (25% saved)

sample657.0ms (20.2%)

Algorithm

1×

intervals

Results

308.0ms	8000×	body	128	valid
18.0ms	466×	body	128	invalid

Compiler

Compiled 100 to 70 computations (30% saved)

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11

Details

analyze150.0ms (4.6%)

sample78.0ms (2.4%)

simplify25.0ms (0.8%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify61.0ms (1.9%)

prune34.0ms (1%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite10.0ms (0.3%)

simplify153.0ms (4.7%)

prune79.0ms (2.4%)

localize9.0ms (0.3%)

series339.0ms (10.4%)

rewrite57.0ms (1.8%)

simplify186.0ms (5.7%)

prune290.0ms (8.9%)

localize9.0ms (0.3%)

series118.0ms (3.6%)

rewrite20.0ms (0.6%)

simplify132.0ms (4%)

prune513.0ms (15.8%)

regimes278.0ms (8.6%)

simplify3.0ms (0.1%)

end5.0ms (0.2%)

sample657.0ms (20.2%)

Profiling

Iter	Nodes	Cost
0	10	13
1	15	13
2	26	13
3	39	13
4	66	11
5	109	11
6	198	11
7	307	11
8	429	11
9	522	11
10	578	11
11	593	11
12	596	11
13	513	11