Details

analyze438.0ms (5.9%)

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 (31%)

Results

952.0ms	1366×	body	1024	valid
895.0ms	5868×	body	128	valid
278.0ms	682×	body	512	valid
93.0ms	334×	body	256	valid
8.0ms	6×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify21.0ms (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 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)))
✓	0.1b	(*.f64 z (sin.f64 y))

series25.0ms (0.3%)

Counts

3 → 84

Calls

3 calls:

14.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
4.0ms	(+.f64 x (cos.f64 y))

rewrite12.0ms (0.2%)

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))
2.0ms	(+.f64 x (cos.f64 y))

simplify99.0ms (1.3%)

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

prune79.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Error

0.0b

Counts

121 → 5

Alt Table

Status	Error	Program
▶	0.4b	(-.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)))))
	16.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z (sin.f64 y)) (.f64 z (sin.f64 y))) (*.f64 z (sin.f64 y)))))
	33.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1972 to 594 computations (69.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.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))))
✓	7.7b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.3s (16.9%)

Counts

3 → 72

Calls

3 calls:

802.0ms

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

435.0ms

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

22.0ms

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

rewrite18.0ms (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:

6.0ms

(*.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)))

simplify118.0ms (1.6%)

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

prune260.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	296	6	302

Error

0.0b

Counts

302 → 6

Alt Table

Status	Error	Program
	11.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2)) (cbrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y))))))
	16.5b	(-.f64 (+.f64 x (cos.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	33.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 8365 to 2064 computations (75.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 z) (sin.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series249.0ms (3.3%)

Counts

4 → 72

Calls

4 calls:

157.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
41.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
30.0ms	(cbrt.f64 z)
21.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
720×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
496×	`*-commutative_binary64`
395×	`unswap-sqr_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1734
1	311	1507
2	1181	1430
3	2385	1407
4	4566	1395
5	4973	1395
6	4943	1395

prune164.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	195	7	202

Error

Counts

202 → 7

Alt Table

Status	Error	Program
	11.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2)) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	1.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (*.f64 z (pow.f64 (sin.f64 y) 3)))))
▶	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y))))))
	34.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (sin.f64 y))))
	33.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 4277 to 1166 computations (72.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	1.3b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))) 8)
	7.7b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.5s (20.1%)

Counts

3 → 72

Calls

3 calls:

800.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))) 8)

672.0ms

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

22.0ms

(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
18×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 80

Calls

3 calls:

6.0ms

(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))))

2.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y)))) 8)

1.0ms

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

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
487×	`cancel-sign-sub-inv_binary64`
340×	`*-commutative_binary64`
262×	`fma-def_binary64`
239×	`distribute-rgt-neg-in_binary64`

Counts

152 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	186	3057
1	440	2956
2	1230	2629
3	2613	2431
4	4530	2431
5	4999	2431
6	4876	2431

prune218.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	231	7	238

Error

Counts

238 → 7

Alt Table

Status	Error	Program
	11.1b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2)) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.4b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	1.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 (*.f64 z (pow.f64 (sin.f64 y) 3)))))
✓	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 8) (cbrt.f64 (cbrt.f64 (*.f64 z (sin.f64 y))))))
	34.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z))) (sin.f64 y))))
	33.3b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

Compiler

Compiled 6659 to 2186 computations (67.2% saved)

regimes222.0ms (3%)

Accuracy

Total 0.0b remaining (49.8%)

Threshold costs 0.0b (49.8%)

Counts

53 → 1

Compiler

Compiled 3852 to 2462 computations (36.1% saved)

simplify2.0ms (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

end114.0ms (1.5%)

Compiler: Compiled 161 to 99 computations (38.5% 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

analyze438.0ms (5.9%)

sample2.3s (31%)

simplify21.0ms (0.3%)

prune2.0ms (0%)

localize12.0ms (0.2%)

series25.0ms (0.3%)

rewrite12.0ms (0.2%)

simplify99.0ms (1.3%)

prune79.0ms (1.1%)

localize11.0ms (0.1%)

series1.3s (16.9%)

rewrite18.0ms (0.2%)

simplify118.0ms (1.6%)

prune260.0ms (3.5%)

localize11.0ms (0.1%)

series249.0ms (3.3%)

rewrite20.0ms (0.3%)

simplify115.0ms (1.5%)

prune164.0ms (2.2%)

localize13.0ms (0.2%)

series1.5s (20.1%)

rewrite17.0ms (0.2%)

simplify137.0ms (1.8%)

prune218.0ms (2.9%)

regimes222.0ms (3%)

simplify2.0ms (0%)

end114.0ms (1.5%)

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