Details

analyze377.0ms (5.8%)

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
31.2%	68.6%	0.1%	6
43.7%	56.2%	0.1%	7
59.3%	40.6%	0.1%	8
59.3%	40.6%	0.1%	9
68.6%	31.2%	0.1%	10
78%	21.8%	0.1%	11
78%	21.8%	0.1%	12
83.5%	16.4%	0.1%	13
88.5%	11.3%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample113.0ms (1.7%)

Algorithm

1×

intervals

Results

18.0ms	38×	body	1024	valid
15.0ms	191×	body	128	valid
5.0ms	21×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify23.0ms (0.4%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

14.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`fma-neg_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
3.0ms	(*.f64 z (sin.f64 y))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
410×	`fma-def_binary64`
366×	`associate-l_binary64`
322×	`associate-r_binary64`
269×	`distribute-rgt-neg-in_binary64`

Counts

104 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1326
1	276	1263
2	879	1219
3	3114	1209
4	4789	1209
5	5015	1209

prune66.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Error

0.0b

Counts

90 → 5

Alt Table

Status	Error	Program
	31.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	22.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.8b	(fma.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (.f64 z (sin.f64 y))))
	25.1b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

Compiler

Compiled 1523 to 446 computations (70.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (.f64 z (sin.f64 y))))
✓	0.4b	(cbrt.f64 (+.f64 x (cos.f64 y)))
✓	0.4b	(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))

series1.9s (29.8%)

Counts

3 → 84

Calls

3 calls:

1.4s

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

291.0ms

(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))

222.0ms

(cbrt.f64 (+.f64 x (cos.f64 y)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`cbrt-div_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

8.0ms

(*.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y))))

5.0ms

(cbrt.f64 (+.f64 x (cos.f64 y)))

0.0ms

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

simplify147.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

453×	`cancel-sign-sub-inv_binary64`
446×	`unswap-sqr_binary64`
289×	`fma-neg_binary64`
266×	`associate-r_binary64`
204×	`log-prod_binary64`

Counts

165 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	309	3824
1	839	3595
2	2625	3423
3	4646	3332
4	4920	3332
5	5062	3332

prune257.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	353	5	358

Error

0.0b

Counts

358 → 5

Alt Table

Status	Error	Program
	31.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
▶	22.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.8b	(fma.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (.f64 z (sin.f64 y))))
	25.1b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

Compiler

Compiled 12123 to 4037 computations (66.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))
✓	9.3b	(sqrt.f64 (*.f64 z (sin.f64 y)))

series27.0ms (0.4%)

Counts

2 → 28

Calls

2 calls:

16.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))
11.0ms	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
30×	`sqrt-pow1_binary64`
21×	`pow-prod-down_binary64`
11×	`pow1/2_binary64`
10×	`pow-prod-up_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y))))
3.0ms	(sqrt.f64 (*.f64 z (sin.f64 y)))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-def_binary64`
613×	`cancel-sign-sub-inv_binary64`
566×	`associate-l_binary64`
554×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`

Counts

92 → 84

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	72	822
1	147	769
2	503	734
3	2067	708
4	4316	651
5	4490	651
6	4924	649
7	4898	649

prune131.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	178	5	183

Error

0.0b

Counts

183 → 5

Alt Table

Status	Error	Program
	31.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
✓	22.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.8b	(fma.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (.f64 z (sin.f64 y))))
▶	25.1b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

Compiler

Compiled 3772 to 893 computations (76.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.0b	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

series114.0ms (1.7%)

Counts

2 → 56

Calls

2 calls:

99.0ms	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))
14.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
14×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 78

Calls

2 calls:

14.0ms	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))
5.0ms	(sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))

simplify157.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
390×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
338×	`cancel-sign-sub-inv_binary64`
191×	`fma-neg_binary64`

Counts

134 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	3358
1	481	3112
2	1663	2995
3	4739	2974
4	5050	2974

prune213.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	371	0	371
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	371	5	376

Error

0.0b

Counts

376 → 5

Alt Table

Status	Error	Program
	31.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	35.9b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
✓	22.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.8b	(fma.f64 (.f64 (cbrt.f64 (+.f64 x (cos.f64 y))) (cbrt.f64 (+.f64 x (cos.f64 y)))) (cbrt.f64 (+.f64 x (cos.f64 y))) (neg.f64 (.f64 z (sin.f64 y))))
✓	25.1b	(.f64 (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) (sqrt.f64 (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))))

Compiler

Compiled 11252 to 2292 computations (79.6% saved)

regimes852.0ms (13.1%)

Accuracy

Total 0.0b remaining (47.4%)

Threshold costs 0.0b (47.4%)

Counts

180 → 1

Compiler

Compiled 13442 to 8784 computations (34.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`cancel-sign-sub-inv_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	22	14
2	32	14
3	37	14
4	42	14
5	44	14
6	42	14

end0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample1.8s (27.4%)

Algorithm

1×

intervals

Results

660.0ms	1290×	body	1024	valid
473.0ms	5703×	body	128	valid
174.0ms	664×	body	512	valid
109.0ms	336×	body	256	valid
8.0ms	7×	body	2048	valid

Compiler

Compiled 129 to 71 computations (45% 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

analyze377.0ms (5.8%)

sample113.0ms (1.7%)

simplify23.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series21.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify81.0ms (1.2%)

prune66.0ms (1%)

localize13.0ms (0.2%)

series1.9s (29.8%)

rewrite19.0ms (0.3%)

simplify147.0ms (2.3%)

prune257.0ms (3.9%)

localize11.0ms (0.2%)

series27.0ms (0.4%)

rewrite14.0ms (0.2%)

simplify96.0ms (1.5%)

prune131.0ms (2%)

localize10.0ms (0.1%)

series114.0ms (1.7%)

rewrite27.0ms (0.4%)

simplify157.0ms (2.4%)

prune213.0ms (3.3%)

regimes852.0ms (13.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (27.4%)

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