Details

analyze332.0ms (6.3%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample109.0ms (2.1%)

Algorithm

1×

intervals

Results

32.0ms	65×	body	1024	valid
31.0ms	32×	body	512	valid
12.0ms	142×	body	128	valid
3.0ms	17×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 y)
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.1b	(*.f64 z (sin.f64 y))

series27.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

18.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
2.0ms	(sin.f64 y)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

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

simplify153.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
478×	`distribute-rgt-neg-in_binary64`
380×	`distribute-lft-neg-in_binary64`
321×	`*-commutative_binary64`
320×	`sub-neg_binary64`

Counts

103 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1088
1	210	1014
2	612	997
3	1656	995
4	3249	995
5	4837	995
6	4999	995
7	5000	995
8	4906	995

prune88.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Error

0.1b

Counts

83 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	16.9b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	42.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	33.0b	(fma.f64 (.f64 x (.f64 y y)) -1/2 (fma.f64 y z x))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (expm1.f64 (log1p.f64 (sin.f64 y)))))

Compiler

Compiled 1351 to 492 computations (63.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 y)
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
✓	0.1b	(*.f64 (cos.f64 y) x)

series22.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
7.0ms	(*.f64 (cos.f64 y) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

803×	`distribute-rgt-neg-in_binary64`
796×	`fma-def_binary64`
741×	`cancel-sign-sub-inv_binary64`
379×	`fma-neg_binary64`
324×	`*-commutative_binary64`

Counts

70 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	840
1	173	788
2	484	778
3	1314	771
4	3692	771
5	4945	771

prune68.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Error

0.0b

Counts

89 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	16.9b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	42.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
▶	0.1b	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
	34.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	15.7b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1429 to 523 computations (63.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
	0.1b	(*.f64 (cos.f64 y) x)
✓	0.1b	(expm1.f64 (log1p.f64 (sin.f64 y)))
✓	0.3b	(log1p.f64 (sin.f64 y))

series223.0ms (4.2%)

Counts

3 → 60

Calls

3 calls:

206.0ms	(log1p.f64 (sin.f64 y))
16.0ms	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
2.0ms	(expm1.f64 (log1p.f64 (sin.f64 y)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p.f64 (sin.f64 y))
0.0ms	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
0.0ms	(expm1.f64 (log1p.f64 (sin.f64 y)))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

640×	`cancel-sign-sub-inv_binary64`
509×	`distribute-rgt-neg-in_binary64`
500×	`sub-neg_binary64`
385×	`distribute-lft-neg-in_binary64`
373×	`fma-neg_binary64`

Counts

92 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	895
1	172	848
2	427	838
3	1224	833
4	2697	831
5	4593	831
6	4947	831

prune90.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Error

0.0b

Counts

119 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	16.9b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	42.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.1b	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
	34.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	15.7b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
▶	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1931 to 652 computations (66.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.4b	(cbrt.f64 (cos.f64 y))

series856.0ms (16.3%)

Counts

4 → 72

Calls

4 calls:

430.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
240.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
177.0ms	(cbrt.f64 (cos.f64 y))
9.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))

rewrite23.0ms (0.4%)

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 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
3.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
1.0ms	(cbrt.f64 (cos.f64 y))

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-neg_binary64`
389×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
267×	`fma-def_binary64`
221×	`associate-+l+_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1804
1	339	1606
2	1140	1555
3	2286	1535
4	4798	1409
5	4941	1409
6	4947	1409

prune164.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	204	9	213

Error

0.0b

Counts

213 → 9

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	16.9b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 y) z) 3)))
	42.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.1b	(fma.f64 (expm1.f64 (log1p.f64 (sin.f64 y))) z (*.f64 (cos.f64 y) x))
	34.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	15.7b	(fma.f64 (sin.f64 y) z (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (pow.f64 (cos.f64 y) 2/3) x)))
	1.0b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x)))))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))

Compiler

Compiled 4686 to 1241 computations (73.5% saved)

regimes427.0ms (8.1%)

Accuracy

Total 0.1b remaining (53.2%)

Threshold costs 0.1b (53.2%)

Counts

101 → 1

Compiler

Compiled 6304 to 3750 computations (40.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	13	12
2	12	12

end0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample2.4s (45%)

Algorithm

1×

intervals

Results

1.2s	2069×	body	1024	valid
442.0ms	4401×	body	128	valid
264.0ms	1037×	body	512	valid
83.0ms	490×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 236 to 114 computations (51.7% saved)

Details

analyze332.0ms (6.3%)

sample109.0ms (2.1%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series27.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify153.0ms (2.9%)

prune88.0ms (1.7%)

localize7.0ms (0.1%)

series22.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify63.0ms (1.2%)

prune68.0ms (1.3%)

localize11.0ms (0.2%)

series223.0ms (4.2%)

rewrite2.0ms (0%)

simplify81.0ms (1.5%)

prune90.0ms (1.7%)

localize12.0ms (0.2%)

series856.0ms (16.3%)

rewrite23.0ms (0.4%)

simplify111.0ms (2.1%)

prune164.0ms (3.1%)

regimes427.0ms (8.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.4s (45%)

Profiling