Details

analyze449.0ms (5.7%)

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
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.4s (42.6%)

Results

1.8s	2094×	body	1024	valid
808.0ms	4578×	body	128	valid
521.0ms	1082×	body	512	valid
146.0ms	497×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

prune2.0ms (0%)

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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series34.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

20.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
7.0ms	(*.f64 x (cos.f64 y))

rewrite95.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

208× egg-rr

Counts

3 → 208

Calls

2 calls:

90.0ms	((.f64 z (sin.f64 y)) (.f64 x (cos.f64 y)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	194	26
2	2475	26
3	4984	26
0	0	0
1	0	0

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

728×	`distribute-rgt-neg-in_binary64`
651×	`fma-neg_binary64`
403×	`sub-neg_binary64`
381×	`*-commutative_binary64`
370×	`neg-mul-1_binary64`

Counts

292 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	850
1	171	841
2	481	822
3	1534	819
4	3510	819
5	4870	819
6	5013	819

prune159.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	224	8	232
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	8	233

Error

0.0b

Counts

233 → 8

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	28.7b	(-.f64 (.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (sin.f64 y))) 2))
	31.6b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2)) (fma.f64 z (sin.f64 y) (*.f64 x (cos.f64 y))))
▶	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
	16.9b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	34.9b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	1.0b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))

Compiler

Compiled 5156 to 1156 computations (77.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
✓	54.6b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

series73.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

35.0ms

(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))

21.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))

16.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

rewrite56.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

68× egg-rr

Counts

3 → 68

Calls

2 calls:

54.0ms

((fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	220	51
2	2346	51
3	5191	51
0	0	0
1	0	0

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
658×	`distribute-rgt-neg-in_binary64`
566×	`distribute-lft-neg-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
408×	`fma-neg_binary64`

Counts

152 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	726
1	126	720
2	335	708
3	890	704
4	3065	704
5	4465	704
6	4937	704

prune95.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Error

0.0b

Counts

119 → 8

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	28.7b	(-.f64 (.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (sin.f64 y))) 2))
	16.9b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
▶	0.6b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
	34.9b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	1.0b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))

Compiler

Compiled 2579 to 754 computations (70.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
✓	6.4b	(cbrt.f64 (*.f64 z (sin.f64 y)))
✓	54.0b	(fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))

series1.8s (23.2%)

Counts

3 → 72

Calls

3 calls:

875.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
488.0ms	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3)
480.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

rewrite62.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

83× egg-rr

Counts

3 → 83

Calls

2 calls:

61.0ms	((fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 3)) (cbrt.f64 (.f64 z (sin.f64 y))) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	190	25
2	1888	25
3	5892	25
0	0	0
1	0	0

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

635×	`distribute-rgt-neg-in_binary64`
616×	`unswap-sqr_binary64`
426×	`associate-r_binary64`
403×	`associate-l_binary64`
293×	`fma-def_binary64`

Counts

155 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1557
1	255	1481
2	736	1213
3	2937	728
4	4949	728

prune128.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	146	8	154

Error

0.0b

Counts

154 → 8

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	28.7b	(-.f64 (.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (sin.f64 y))) 2))
▶	0.5b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z)))))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
	16.9b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	34.9b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	1.0b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))

Compiler

Compiled 4064 to 1469 computations (63.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z))
✓	0.5b	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
✓	0.6b	(cbrt.f64 (sin.f64 y))
✓	53.9b	(fma.f64 z (neg.f64 (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z)))

series376.0ms (4.7%)

Counts

4 → 72

Calls

4 calls:

176.0ms	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
172.0ms	(cbrt.f64 (sin.f64 y))
18.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z)))
10.0ms	(.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z))

rewrite57.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

4 → 82

Calls

2 calls:

56.0ms

((fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (*.f64 (cbrt.f64 (sin.f64 y)) z))) (cbrt.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (*.f64 (cbrt.f64 (sin.f64 y)) z)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	222	29
2	2204	29
3	4985	29
0	0	0
1	0	0

simplify105.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

660×	`cancel-sign-sub-inv_binary64`
634×	`distribute-rgt-neg-in_binary64`
543×	`sub-neg_binary64`
511×	`fma-neg_binary64`
327×	`neg-mul-1_binary64`

Counts

154 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	486
1	221	478
2	553	462
3	1513	462
4	3240	462
5	4329	462
6	4725	462
7	4964	462
8	4895	462

prune132.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	141	9	150

Error

0.0b

Counts

150 → 9

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	28.7b	(-.f64 (.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (.f64 z (sin.f64 y))) 2))
	19.6b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 y) z)))))
✓	0.5b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z)))))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y))) (neg.f64 (*.f64 z (sin.f64 y))))
	16.9b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	34.9b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	1.0b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))

Compiler

Compiled 4102 to 1459 computations (64.4% saved)

regimes444.0ms (5.6%)

Accuracy

Total 0.1b remaining (69.5%)

Threshold costs 0.1b (69.5%)

Counts

105 → 1

Compiler

Compiled 7252 to 4570 computations (37% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-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	10	15
1	13	15
2	15	15
3	16	15
4	16	15

end134.0ms (1.7%)

Compiler: Compiled 201 to 119 computations (40.8% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Details

analyze449.0ms (5.7%)

sample3.4s (42.6%)

simplify16.0ms (0.2%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series34.0ms (0.4%)

rewrite95.0ms (1.2%)

simplify90.0ms (1.1%)

prune159.0ms (2%)

localize13.0ms (0.2%)

series73.0ms (0.9%)

rewrite56.0ms (0.7%)

simplify89.0ms (1.1%)

prune95.0ms (1.2%)

localize15.0ms (0.2%)

series1.8s (23.2%)

rewrite62.0ms (0.8%)

simplify63.0ms (0.8%)

prune128.0ms (1.6%)

localize16.0ms (0.2%)

series376.0ms (4.7%)

rewrite57.0ms (0.7%)

simplify105.0ms (1.3%)

prune132.0ms (1.7%)

regimes444.0ms (5.6%)

simplify2.0ms (0%)

end134.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14