Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.6s (30.4%)

Infinites

0% of outputs are infinite.

Results

1.4s	2070×	body	1024	valid
640.0ms	4600×	body	128	valid
363.0ms	1046×	body	512	valid
131.0ms	537×	body	256	valid
4.0ms	3×	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

0.1b

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)

localize9.0ms (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))

series31.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(-.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))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 56

Calls

3 calls:

3.0ms	(-.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))

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary64`
513×	`fma-def_binary64`
401×	`sub-neg_binary64`
272×	`distribute-rgt-neg-in_binary64`
257×	`*-commutative_binary64`

Counts

140 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	1548
1	342	1505
2	1070	1476
3	2342	1476
4	4338	1476
5	4932	1476

prune113.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Error

0.0b

Counts

111 → 7

Alt Table

Status	Error	Program
	32.5b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	23.4b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.6b	(-.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 1934 to 622 computations (67.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series281.0ms (3.3%)

Counts

4 → 72

Calls

4 calls:

174.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
43.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
38.0ms	(cbrt.f64 z)
25.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite24.0ms (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:

7.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify123.0ms (1.4%)

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

prune191.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	195	8	203

Error

0.0b

Counts

203 → 8

Alt Table

Status	Error	Program
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	23.4b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	32.5b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
▶	0.6b	(-.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 4378 to 1211 computations (72.3% saved)

localize13.0ms (0.2%)

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))))
✓	8.5b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.6s (18.2%)

Counts

3 → 72

Calls

3 calls:

1.1s

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

473.0ms

(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))))

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))))

5.0ms

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

2.0ms

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

simplify134.0ms (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

prune414.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	296	9	305

Error

0.0b

Counts

305 → 9

Alt Table

Status	Error	Program
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	23.4b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y))))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))))) (.f64 (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)))))
	32.5b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.6b	(-.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 8592 to 2149 computations (75% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series954.0ms (11.2%)

Counts

2 → 24

Calls

2 calls:

505.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
449.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
2.0ms	(cbrt.f64 (cbrt.f64 z))

simplify158.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

692×	`sqr-pow_binary64`
622×	`fma-def_binary64`
551×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
313×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	468
1	78	468
2	138	468
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune330.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	196	9	205

Error

0.0b

Counts

205 → 9

Alt Table

Status	Error	Program
	18.8b	(-.f64 (.f64 (.f64 x (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.8b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (pow.f64 (cbrt.f64 (cbrt.f64 z)) 4)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.6b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (.f64 (cbrt.f64 z) (sin.f64 y))))
	0.8b	(-.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (cos.f64 y))) (.f64 z (sin.f64 y)))
	23.4b	(-.f64 (.f64 x (cos.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	33.2b	(-.f64 (.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 x (cos.f64 y)))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 x (cos.f64 y)) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y))))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))))) (.f64 (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)))))
	32.5b	(-.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y))) (*.f64 z (sin.f64 y)))
✓	0.6b	(-.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 5774 to 1464 computations (74.6% saved)

regimes1.3s (14.7%)

Accuracy

Total 0.1b remaining (49.2%)

Threshold costs 0.1b (49.2%)

Counts

176 → 1

Compiler

Compiled 14352 to 8906 computations (37.9% 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	16	14
1	22	14
2	32	14
3	38	14
4	43	14
5	45	14
6	42	14

end148.0ms (1.7%)

Compiler: Compiled 251 to 126 computations (49.8% 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

analyze2.0ms (0%)

sample2.6s (30.4%)

simplify16.0ms (0.2%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series31.0ms (0.4%)

rewrite11.0ms (0.1%)

simplify114.0ms (1.3%)

prune113.0ms (1.3%)

localize12.0ms (0.1%)

series281.0ms (3.3%)

rewrite24.0ms (0.3%)

simplify123.0ms (1.4%)

prune191.0ms (2.2%)

localize13.0ms (0.2%)

series1.6s (18.2%)

rewrite19.0ms (0.2%)

simplify134.0ms (1.6%)

prune414.0ms (4.8%)

localize32.0ms (0.4%)

series954.0ms (11.2%)

rewrite8.0ms (0.1%)

simplify158.0ms (1.8%)

prune330.0ms (3.9%)

regimes1.3s (14.7%)

simplify3.0ms (0%)

end148.0ms (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