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)

sample2.2s (29.1%)

Infinites

0% of outputs are infinite.

Results

894.0ms	1340×	body	1024	valid
848.0ms	5880×	body	128	valid
232.0ms	677×	body	512	valid
100.0ms	356×	body	256	valid
5.0ms	3×	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)

localize11.0ms (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)))
7.0ms	(*.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))

simplify88.0ms (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

prune61.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Error

0.0b

Counts

90 → 4

Alt Table

Status	Error	Program
	20.2b	(-.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)))))
	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)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.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))))

Compiler

Compiled 1467 to 422 computations (71.2% saved)

localize13.0ms (0.2%)

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)

series450.0ms (6%)

Counts

4 → 72

Calls

4 calls:

247.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
105.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
62.0ms	(cbrt.f64 z)
36.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite21.0ms (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))
4.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify121.0ms (1.6%)

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

prune375.0ms (5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	194	6	200

Error

0.0b

Counts

200 → 6

Alt Table

Status	Error	Program
	15.2b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.4b	(-.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))))
	20.2b	(-.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)))))
▶	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)))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.5b	(-.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))))

Compiler

Compiled 4284 to 1161 computations (72.9% saved)

localize14.0ms (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)))

series1.7s (23.2%)

Counts

3 → 72

Calls

3 calls:

1.1s

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

626.0ms

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

28.0ms

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

rewrite21.0ms (0.3%)

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))))

4.0ms

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

2.0ms

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

simplify124.0ms (1.7%)

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

prune356.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	297	6	303

Error

Counts

303 → 6

Alt Table

Status	Error	Program
	20.2b	(-.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)))))
✓	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)))))
▶	0.4b	(-.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))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 4) (.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)))))
	0.5b	(-.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))))

Compiler

Compiled 8424 to 2077 computations (75.3% saved)

localize21.0ms (0.3%)

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)))

series694.0ms (9.3%)

Counts

2 → 24

Calls

2 calls:

386.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
307.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite4.0ms (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:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify107.0ms (1.4%)

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

prune321.0ms (4.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	196	6	202

Error

Counts

202 → 6

Alt Table

Status	Error	Program
	20.2b	(-.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)))))
✓	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)))))
✓	0.4b	(-.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))))
✓	0.1b	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
	0.6b	(-.f64 (+.f64 x (cos.f64 y)) (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) 4) (.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)))))
	0.5b	(-.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))))

Compiler

Compiled 5696 to 1432 computations (74.9% saved)

regimes557.0ms (7.5%)

Accuracy

Total 0.0b remaining (44.2%)

Threshold costs 0.0b (44.2%)

Counts

92 → 1

Compiler

Compiled 7820 to 4650 computations (40.5% 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

end130.0ms (1.7%)

Compiler: Compiled 173 to 94 computations (45.7% 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

analyze2.0ms (0%)

sample2.2s (29.1%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series21.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify88.0ms (1.2%)

prune61.0ms (0.8%)

localize13.0ms (0.2%)

series450.0ms (6%)

rewrite21.0ms (0.3%)

simplify121.0ms (1.6%)

prune375.0ms (5%)

localize14.0ms (0.2%)

series1.7s (23.2%)

rewrite21.0ms (0.3%)

simplify124.0ms (1.7%)

prune356.0ms (4.8%)

localize21.0ms (0.3%)

series694.0ms (9.3%)

rewrite4.0ms (0.1%)

simplify107.0ms (1.4%)

prune321.0ms (4.3%)

regimes557.0ms (7.5%)

simplify3.0ms (0%)

end130.0ms (1.7%)

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