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)

sample2.7s (59.3%)

Results

1.1s	1306×	body	1024	valid
1.1s	5888×	body	128	valid
330.0ms	717×	body	512	valid
105.0ms	342×	body	256	valid
7.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.2%)

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series32.0ms (0.7%)

Counts

3 → 64

Calls

3 calls:

19.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
11.0ms	(+.f64 x (sin.f64 y))
2.0ms	(cos.f64 y)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-def_binary64`

Counts

3 → 36

Calls

3 calls:

3.0ms	(+.f64 x (sin.f64 y))
1.0ms	(cos.f64 y)
0.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify137.0ms (3%)

Algorithm

1×	egg-herbie

Rules

607×	`cancel-sign-sub-inv_binary64`
443×	`distribute-rgt-neg-in_binary64`
357×	`distribute-rgt-in_binary64`
346×	`sub-neg_binary64`
340×	`distribute-lft-in_binary64`

Counts

100 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	991
1	226	940
2	515	929
3	1512	928
4	3685	928
5	4604	928
6	4967	928
7	4999	928
8	4879	928

prune62.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Error

0.0b

Counts

81 → 6

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	42.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	19.8b	(fma.f64 z (cos.f64 y) (cbrt.f64 (.f64 (.f64 (+.f64 x (sin.f64 y)) (+.f64 x (sin.f64 y))) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
▶	0.0b	(fma.f64 z (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	14.7b	(fma.f64 z (cos.f64 y) (/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 y) (sin.f64 y))) (-.f64 x (sin.f64 y))))

Compiler

Compiled 1208 to 436 computations (63.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
	0.0b	(+.f64 x (sin.f64 y))
✓	0.0b	(fma.f64 z (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))

series17.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

17.0ms

(fma.f64 z (*.f64 1 (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 (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-def_binary64`
382×	`sub-neg_binary64`
349×	`distribute-rgt-neg-in_binary64`
316×	`distribute-rgt-in_binary64`
314×	`distribute-lft-in_binary64`

Counts

46 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	573
1	86	546
2	219	543
3	763	541
4	2794	541
5	4412	541
6	4906	541
7	4940	541

prune78.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	80	6	86

Error

0.0b

Counts

86 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	42.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	19.8b	(fma.f64 z (cos.f64 y) (cbrt.f64 (.f64 (.f64 (+.f64 x (sin.f64 y)) (+.f64 x (sin.f64 y))) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.0b	(fma.f64 z (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	14.7b	(fma.f64 z (cos.f64 y) (/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 y) (sin.f64 y))) (-.f64 x (sin.f64 y))))

Compiler

Compiled 1318 to 564 computations (57.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (sin.f64 y))
✓	0.0b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
✓	0.4b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.4b	(pow.f64 (cos.f64 y) 3)

series25.0ms (0.5%)

Counts

3 → 52

Calls

3 calls:

14.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
9.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
0.0ms	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-rgt-in_binary64`
424×	`associate-l_binary64`
368×	`associate-r_binary64`
368×	`fma-neg_binary64`
226×	`exp-prod_binary64`

Counts

110 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1101
1	218	1039
2	639	1012
3	2501	1012
4	5156	1012

prune154.0ms (3.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	42.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	19.8b	(fma.f64 z (cos.f64 y) (cbrt.f64 (.f64 (.f64 (+.f64 x (sin.f64 y)) (+.f64 x (sin.f64 y))) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
▶	0.1b	(fma.f64 z (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3))) (+.f64 x (sin.f64 y)))
✓	0.0b	(fma.f64 z (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	14.7b	(fma.f64 z (cos.f64 y) (/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 y) (sin.f64 y))) (-.f64 x (sin.f64 y))))

Compiler

Compiled 2191 to 990 computations (54.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3))
✓	0.4b	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3)))
	0.4b	(pow.f64 (cos.f64 y) 3)
✓	0.4b	(pow.f64 (pow.f64 (cos.f64 y) 3) 3)

series36.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

22.0ms	(pow.f64 (pow.f64 (cos.f64 y) 3) 3)
11.0ms	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3))
3.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3)))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`cbrt-prod_binary64`
54×	`cube-prod_binary64`
54×	`unpow-prod-down_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`

Counts

3 → 129

Calls

3 calls:

8.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3)))
6.0ms	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3))
5.0ms	(pow.f64 (pow.f64 (cos.f64 y) 3) 3)

simplify160.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
531×	`fma-neg_binary64`
368×	`log-prod_binary64`
295×	`associate-+l+_binary64`
250×	`associate-+r+_binary64`

Counts

165 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1812
1	244	1642
2	734	1630
3	1605	1540
4	4390	1540
5	4998	1540
6	4971	1540

prune361.0ms (7.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	159	7	166

Error

0.0b

Counts

166 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)) (+.f64 x (sin.f64 y)))
	42.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	19.8b	(fma.f64 z (cos.f64 y) (cbrt.f64 (.f64 (.f64 (+.f64 x (sin.f64 y)) (+.f64 x (sin.f64 y))) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cbrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 3) 3))) (+.f64 x (sin.f64 y)))
✓	0.0b	(fma.f64 z (*.f64 1 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	14.7b	(fma.f64 z (cos.f64 y) (/.f64 (-.f64 (.f64 x x) (.f64 (sin.f64 y) (sin.f64 y))) (-.f64 x (sin.f64 y))))

Compiler

Compiled 3225 to 1812 computations (43.8% saved)

regimes324.0ms (7.1%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Counts

50 → 1

Compiler

Compiled 2796 to 1838 computations (34.3% saved)

simplify3.0ms (0.1%)

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

end166.0ms (3.6%)

Compiler: Compiled 142 to 86 computations (39.4% saved)

Details

analyze2.0ms (0%)

sample2.7s (59.3%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize12.0ms (0.3%)

series32.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify137.0ms (3%)

prune62.0ms (1.3%)

localize9.0ms (0.2%)

series17.0ms (0.4%)

rewrite1.0ms (0%)

simplify111.0ms (2.4%)

prune78.0ms (1.7%)

localize10.0ms (0.2%)

series25.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify99.0ms (2.1%)

prune154.0ms (3.4%)

localize12.0ms (0.3%)

series36.0ms (0.8%)

rewrite32.0ms (0.7%)

simplify160.0ms (3.5%)

prune361.0ms (7.9%)

regimes324.0ms (7.1%)

simplify3.0ms (0.1%)

end166.0ms (3.6%)

Profiling