Details

analyze450.0ms (6.2%)

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)

sample2.3s (30.9%)

Results

920.0ms	5916×	body	128	valid
886.0ms	1307×	body	1024	valid
265.0ms	681×	body	512	valid
103.0ms	348×	body	256	valid
5.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

230×	`fma-def_binary64`
171×	`fma-neg_binary64`
66×	`cancel-sign-sub-inv_binary64`
44×	`associate--r+_binary64`
44×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.3%)

Counts

4 → 88

Calls

4 calls:

11.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

rewrite127.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
460×	`fma-def_binary64`
219×	`egg-rr`
217×	`fma-neg_binary64`
194×	`expm1-udef_binary64`

Counts

4 → 219

Calls

4 calls:

123.0ms	(+.f64 x (cos.f64 y))
123.0ms	(cos.f64 y)
123.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
123.0ms	(*.f64 z (sin.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	202	29
2	2746	29
3	5522	29
0	0	0
1	0	0

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

542×	`sub-neg_binary64`
539×	`distribute-rgt-neg-in_binary64`
526×	`fma-neg_binary64`
317×	`neg-mul-1_binary64`
300×	`*-commutative_binary64`

Counts

307 → 255

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	886
1	196	874
2	516	854
3	1563	848
4	3403	848
5	4538	848
6	4979	848
7	4909	848

prune206.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	246	9	255
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	247	9	256

Error

0.0b

Counts

256 → 9

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (cos.f64 y) (*.f64 (sin.f64 y) z)) x)
	0.4b	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	27.2b	(fma.f64 (-.f64 (pow.f64 (+.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2)) (/.f64 1 (fma.f64 z (sin.f64 y) (+.f64 x (cos.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (.f64 z (sin.f64 y))))
	27.1b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	0.1b	(-.f64 (+.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))) (*.f64 z (sin.f64 y)))
	34.9b	(/.f64 1 (/.f64 (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (+.f64 x (cos.f64 y))) (pow.f64 (+.f64 x (cos.f64 y)) 2)) (-.f64 (pow.f64 (+.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3))))
	41.6b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	27.9b	(-.f64 (+.f64 x (cos.f64 y)) (-.f64 (.f64 y z) (.f64 1/6 (*.f64 (pow.f64 y 3) z))))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))

Compiler

Compiled 4790 to 1434 computations (70.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series16.0ms (0.2%)

Counts

2 → 11

Calls

2 calls:

9.0ms	(*.f64 (sin.f64 y) z)
7.0ms	(-.f64 (cos.f64 y) (*.f64 (sin.f64 y) z))

rewrite62.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

771×	`log1p-expm1-u_binary64`
771×	`expm1-log1p-u_binary64`
649×	`prod-diff_binary64`
110×	`egg-rr`
80×	`add-sqr-sqrt_binary64`

Counts

2 → 110

Calls

2 calls:

59.0ms	(-.f64 (cos.f64 y) (*.f64 (sin.f64 y) z))
59.0ms	(*.f64 (sin.f64 y) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	151	17
2	1933	17
3	5957	17
0	0	0
1	0	0

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
741×	`distribute-rgt-neg-in_binary64`
636×	`distribute-lft-neg-in_binary64`
518×	`cancel-sign-sub-inv_binary64`
465×	`associate-l_binary64`

Counts

121 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	149
1	114	139
2	321	127
3	926	119
4	3235	119
5	4622	119
6	5105	119

prune183.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

0.0b

Counts

164 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z)) x)
	0.4b	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	27.2b	(fma.f64 (-.f64 (pow.f64 (+.f64 x (cos.f64 y)) 2) (pow.f64 (.f64 z (sin.f64 y)) 2)) (/.f64 1 (fma.f64 z (sin.f64 y) (+.f64 x (cos.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (.f64 z (sin.f64 y))))
	27.1b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	41.6b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	11.1b	(+.f64 (/.f64 1 (/.f64 (+.f64 (.f64 (sin.f64 y) z) (cos.f64 y)) (-.f64 (pow.f64 (cos.f64 y) 2) (pow.f64 (.f64 (sin.f64 y) z) 2)))) x)
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))

Compiler

Compiled 3911 to 1192 computations (69.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z))
	0.1b	(*.f64 (sin.f64 y) z)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series19.0ms (0.3%)

Counts

3 → 40

Calls

3 calls:

12.0ms	(-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z))
5.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite124.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

821×	`prod-diff_binary64`
617×	`fma-udef_binary64`
246×	`fma-def_binary64`
205×	`fma-neg_binary64`
173×	`expm1-udef_binary64`

Counts

3 → 156

Calls

3 calls:

121.0ms	(-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z))
121.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
121.0ms	(pow.f64 (cos.f64 y) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	196	20
2	2350	20
3	4699	20
4	4688	20
5	4964	20
0	0	0
1	0	0

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
518×	`cancel-sign-sub-inv_binary64`
516×	`sub-neg_binary64`
449×	`distribute-rgt-neg-in_binary64`
414×	`fma-neg_binary64`

Counts

196 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	390
1	136	380
2	346	370
3	1039	362
4	2867	362
5	4341	362
6	4702	362
7	4905	362

prune264.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	198	7	205

Error

0.0b

Counts

205 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z)) x)
	0.4b	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	41.6b	(fma.f64 (+.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (+.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (fma.f64 (neg.f64 z) (sin.f64 y) (*.f64 z (sin.f64 y))))
	27.1b	(-.f64 (+.f64 x (cos.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))
	11.1b	(+.f64 (/.f64 1 (/.f64 (fma.f64 (sin.f64 y) z (cos.f64 y)) (-.f64 (pow.f64 (cos.f64 y) 2) (pow.f64 (*.f64 (sin.f64 y) z) 2)))) x)
▶	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
	11.1b	(+.f64 (fma.f64 (-.f64 (pow.f64 (cos.f64 y) 2) (pow.f64 (.f64 (sin.f64 y) z) 2)) (/.f64 1 (fma.f64 (sin.f64 y) z (cos.f64 y))) (fma.f64 (neg.f64 (sin.f64 y)) z (.f64 (sin.f64 y) z))) x)

Compiler

Compiled 4031 to 1512 computations (62.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
✓	6.0b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.7s (23.4%)

Counts

3 → 84

Calls

3 calls:

982.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
393.0ms	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
333.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

rewrite175.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

739×	`prod-diff_binary64`
520×	`fma-udef_binary64`
322×	`fma-def_binary64`
249×	`fma-neg_binary64`
218×	`expm1-udef_binary64`

Counts

3 → 91

Calls

3 calls:

173.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
173.0ms	(pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 2)
173.0ms	(cbrt.f64 (*.f64 z (sin.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	271	33
2	2900	33
3	4735	33
4	4695	31
5	4905	31
0	0	0
1	0	0

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-def_binary64`
503×	`associate-r_binary64`
461×	`associate-l_binary64`
310×	`cancel-sign-sub-inv_binary64`
242×	`associate--l+_binary64`

Counts

175 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	2175
1	373	2083
2	1112	1888
3	4697	1257
4	4966	1257
5	4960	1257

prune234.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	241	6	247

Error

Counts

247 → 6

Alt Table

Status	Error	Program
	0.4b	(fma.f64 (pow.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
	0.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y)))) (+.f64 x (cos.f64 y)))
✓	0.1b	(+.f64 (-.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (*.f64 (sin.f64 y) z)) x)
	0.1b	(+.f64 (cos.f64 y) (+.f64 x (/.f64 (sin.f64 y) (/.f64 -1 z))))
	11.1b	(+.f64 (/.f64 1 (/.f64 (fma.f64 (sin.f64 y) z (cos.f64 y)) (-.f64 (pow.f64 (cos.f64 y) 2) (pow.f64 (*.f64 (sin.f64 y) z) 2)))) x)
	11.1b	(+.f64 (fma.f64 (-.f64 (pow.f64 (cos.f64 y) 2) (pow.f64 (.f64 (sin.f64 y) z) 2)) (/.f64 1 (fma.f64 (sin.f64 y) z (cos.f64 y))) (fma.f64 (neg.f64 (sin.f64 y)) z (.f64 (sin.f64 y) z))) x)

Compiler

Compiled 5758 to 2003 computations (65.2% saved)

regimes918.0ms (12.6%)

Accuracy

Total 0.0b remaining (61.3%)

Threshold costs 0.0b (61.3%)

Counts

151 → 1

Compiler

Compiled 10787 to 6829 computations (36.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`*-rgt-identity_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	20	14
2	23	14
3	24	14
4	22	14

end118.0ms (1.6%)

Compiler: Compiled 156 to 101 computations (35.3% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14

Details

analyze450.0ms (6.2%)

sample2.3s (30.9%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize12.0ms (0.2%)

series23.0ms (0.3%)

rewrite127.0ms (1.7%)

simplify103.0ms (1.4%)

prune206.0ms (2.8%)

localize7.0ms (0.1%)

series16.0ms (0.2%)

rewrite62.0ms (0.9%)

simplify65.0ms (0.9%)

prune183.0ms (2.5%)

localize10.0ms (0.1%)

series19.0ms (0.3%)

rewrite124.0ms (1.7%)

simplify90.0ms (1.2%)

prune264.0ms (3.6%)

localize13.0ms (0.2%)

series1.7s (23.4%)

rewrite175.0ms (2.4%)

simplify98.0ms (1.3%)

prune234.0ms (3.2%)

regimes918.0ms (12.6%)

simplify2.0ms (0%)

end118.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	34	14
3	59	14
4	99	14
5	155	14
6	247	14
7	292	14
8	378	14
9	410	14
10	444	14
11	454	14
12	431	14