Details

analyze461.0ms (4.7%)

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)

sample2.4s (24.8%)

Results

1.0s	1416×	body	1024	valid
923.0ms	5819×	body	128	valid
314.0ms	684×	body	512	valid
92.0ms	336×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify23.0ms (0.2%)

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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series26.0ms (0.3%)

Counts

3 → 84

Calls

3 calls:

12.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))
5.0ms	(+.f64 x (cos.f64 y))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 61

Calls

3 calls:

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

simplify142.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
503×	`fma-def_binary64`
418×	`associate-l_binary64`
386×	`associate-r_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

145 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1641
1	369	1578
2	1084	1530
3	3795	1520
4	4687	1520
5	4866	1520

prune95.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	6	121

Error

0.0b

Counts

121 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	35.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	23.3b	(.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)))))
	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	28.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 2010 to 612 computations (69.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 z (sin.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	8.8b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.2s (12.6%)

Counts

3 → 72

Calls

3 calls:

756.0ms

(*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))

464.0ms

(cbrt.f64 (*.f64 z (sin.f64 y)))

20.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))

6.0ms

(*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))

2.0ms

(cbrt.f64 (*.f64 z (sin.f64 y)))

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
445×	`cancel-sign-sub-inv_binary64`
352×	`*-commutative_binary64`
346×	`fma-def_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

151 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2495
1	410	2016
2	1169	1679
3	2733	1438
4	4659	1438
5	4981	1438
6	4891	1438

prune358.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	297	6	303

Error

0.0b

Counts

303 → 6

Alt Table

Status	Error	Program
	28.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 8474 to 2063 computations (75.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (*.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y))))
✓	0.5b	(cbrt.f64 z)
✓	0.7b	(cbrt.f64 (sin.f64 y))
	8.8b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.1s (10.8%)

Counts

3 → 48

Calls

3 calls:

792.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (*.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y))))
229.0ms	(cbrt.f64 (sin.f64 y))
36.0ms	(cbrt.f64 z)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1/3_binary64`
8×	`cbrt-prod_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`pow-prod-down_binary64`

Counts

3 → 51

Calls

3 calls:

5.0ms	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (*.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y))))
1.0ms	(cbrt.f64 (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-neg_binary64`
324×	`*-commutative_binary64`
323×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
249×	`log-prod_binary64`

Counts

99 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	1489
1	343	1360
2	994	1221
3	2373	1042
4	4524	1022
5	4949	1022
6	4899	1022

prune166.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

0.0b

Counts

152 → 6

Alt Table

Status	Error	Program
	28.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 4594 to 1359 computations (70.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))))
✓	2.3b	(cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	8.8b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series2.2s (22.4%)

Counts

2 → 48

Calls

2 calls:

1.1s

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))) (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))))

1.1s

(cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`
9×	`pow1_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 47

Calls

2 calls:

7.0ms

(*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))) (cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))))

4.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Rules

591×	`unswap-sqr_binary64`
585×	`fma-neg_binary64`
424×	`associate-l_binary64`
386×	`associate-r_binary64`
276×	`fma-def_binary64`

Counts

95 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2996
1	347	2646
2	884	2132
3	2947	1980
4	5081	1980

prune754.0ms (7.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	497	1	498
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	497	7	504

Error

0.0b

Counts

504 → 7

Alt Table

Status	Error	Program
	28.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (sqrt.f64 (.f64 z (sin.f64 y))) (sqrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	0.5b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y))))))) (cbrt.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (.f64 (cbrt.f64 z) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 28256 to 5217 computations (81.5% saved)

regimes328.0ms (3.3%)

Accuracy

Total 0.0b remaining (50.5%)

Threshold costs 0.0b (50.5%)

Counts

74 → 1

Compiler

Compiled 9760 to 4198 computations (57% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	16	14
2	26	14
3	32	14
4	36	14
5	37	14
6	37	14

end111.0ms (1.1%)

Compiler: Compiled 279 to 104 computations (62.7% 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

analyze461.0ms (4.7%)

sample2.4s (24.8%)

simplify23.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series26.0ms (0.3%)

rewrite13.0ms (0.1%)

simplify142.0ms (1.4%)

prune95.0ms (1%)

localize11.0ms (0.1%)

series1.2s (12.6%)

rewrite19.0ms (0.2%)

simplify122.0ms (1.2%)

prune358.0ms (3.6%)

localize14.0ms (0.1%)

series1.1s (10.8%)

rewrite9.0ms (0.1%)

simplify102.0ms (1%)

prune166.0ms (1.7%)

localize16.0ms (0.2%)

series2.2s (22.4%)

rewrite14.0ms (0.1%)

simplify94.0ms (1%)

prune754.0ms (7.7%)

regimes328.0ms (3.3%)

simplify3.0ms (0%)

end111.0ms (1.1%)

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