Details

analyze693.0ms (6.5%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.3s (21.7%)

Results

946.0ms	1315×	body	1024	valid
910.0ms	5899×	body	128	valid
320.0ms	740×	body	512	valid
88.0ms	299×	body	256	valid
4.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-def_binary64`
379×	`sub-neg_binary64`
339×	`distribute-rgt-neg-in_binary64`
305×	`cancel-sign-sub-inv_binary64`
292×	`distribute-lft-neg-in_binary64`

Counts

46 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	573
1	80	546
2	212	543
3	688	541
4	2534	541
5	4191	541
6	4953	541
7	4936	541

prune24.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Error

0.0b

Counts

35 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	29.3b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 549 to 153 computations (72.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

series966.0ms (9.1%)

Counts

3 → 108

Calls

3 calls:

560.0ms

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

392.0ms

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

13.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify205.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-def_binary64`
652×	`times-frac_binary64`
323×	`*-commutative_binary64`
168×	`+-commutative_binary64`
127×	`sqr-pow_binary64`

Counts

201 → 254

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	772	10896
1	2612	9995
2	4999	9995
3	4962	9995

prune425.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	509	2	511
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	510	5	515

Error

0.0b

Counts

515 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	29.3b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 31390 to 11864 computations (62.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))

series926.0ms (8.7%)

Counts

2 → 72

Calls

2 calls:

545.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
380.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

rewrite5.0ms (0%)

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:

2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

simplify147.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
638×	`times-frac_binary64`
301×	`*-commutative_binary64`
160×	`+-commutative_binary64`
139×	`sqr-pow_binary64`

Counts

99 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	724	9015
1	2517	8301
2	4979	8301

prune721.0ms (6.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	657	0	657
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	657	5	662

Error

0.0b

Counts

662 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	29.3b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 65675 to 23630 computations (64% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))))
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))))
✓	0.6b	(cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))
	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

series1.5s (13.8%)

Counts

3 → 108

Calls

3 calls:

575.0ms

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

509.0ms

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

376.0ms

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`cbrt-prod_binary64`
36×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 85

Calls

3 calls:

6.0ms

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

1.0ms

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

1.0ms

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

simplify241.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-/l*_binary64`
423×	`*-commutative_binary64`
224×	`+-commutative_binary64`
196×	`fma-def_binary64`
185×	`sqr-pow_binary64`

Counts

193 → 294

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1021	14551
1	3479	13593
2	5533	13593

prune1.0s (9.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	773	1	774
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	774	5	779

Error

0.0b

Counts

779 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	29.3b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	1.9b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))))) (cbrt.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x))))))) (cbrt.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 75584 to 25535 computations (66.2% saved)

regimes1.2s (11.2%)

Accuracy

Total 0.0b remaining (37.3%)

Threshold costs 0.0b (37.3%)

Counts

207 → 1

Compiler

Compiled 41728 to 13486 computations (67.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end84.0ms (0.8%)

Compiler: Compiled 241 to 73 computations (69.7% saved)

Details

analyze693.0ms (6.5%)

sample2.3s (21.7%)

simplify7.0ms (0.1%)

prune4.0ms (0%)

localize6.0ms (0.1%)

series12.0ms (0.1%)

rewrite1.0ms (0%)

simplify85.0ms (0.8%)

prune24.0ms (0.2%)

localize10.0ms (0.1%)

series966.0ms (9.1%)

rewrite22.0ms (0.2%)

simplify205.0ms (1.9%)

prune425.0ms (4%)

localize15.0ms (0.1%)

series926.0ms (8.7%)

rewrite5.0ms (0%)

simplify147.0ms (1.4%)

prune721.0ms (6.8%)

localize21.0ms (0.2%)

series1.5s (13.8%)

rewrite17.0ms (0.2%)

simplify241.0ms (2.3%)

prune1.0s (9.5%)

regimes1.2s (11.2%)

simplify2.0ms (0%)

end84.0ms (0.8%)

Profiling