Details

analyze405.0ms (7.9%)

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)

sample79.0ms (1.5%)

Algorithm

1×

intervals

Results

28.0ms	55×	body	1024	valid
12.0ms	145×	body	128	valid
8.0ms	32×	body	512	valid
5.0ms	23×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify8.0ms (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)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series24.0ms (0.5%)

Counts

3 → 64

Calls

3 calls:

15.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
2.0ms	(cos.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	(cos.f64 y)
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
495×	`sub-neg_binary64`
289×	`associate-l_binary64`
258×	`unswap-sqr_binary64`
256×	`distribute-rgt-neg-in_binary64`

Counts

103 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1088
1	229	1018
2	653	1001
3	1805	999
4	3991	999
5	4797	999
6	4959	999

prune63.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Error

0.0b

Counts

83 → 9

Alt Table

Status	Error	Program
	48.0b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	31.2b	(.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	1.3b	(.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)))))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	34.3b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	0.2b	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1415 to 522 computations (63.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
✓	0.2b	(*.f64 (cos.f64 y) x)

series23.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
8.0ms	(*.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))

simplify62.0ms (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

prune84.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Error

0.0b

Counts

91 → 10

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
	48.0b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
	0.4b	(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)))
	28.6b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x))))
	1.3b	(.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)))))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	29.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	34.3b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1443 to 551 computations (61.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
✓	0.2b	(*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x)
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series29.0ms (0.6%)

Counts

4 → 84

Calls

4 calls:

16.0ms	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
7.0ms	(*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x)
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

3.0ms	(*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x)
0.0ms	(expm1.f64 (cos.f64 y))
0.0ms	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
342×	`distribute-rgt-neg-in_binary64`
333×	`distribute-lft-neg-in_binary64`
323×	`associate-l_binary64`
276×	`associate-r_binary64`

Counts

136 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1318
1	266	1238
2	755	1215
3	2190	1207
4	4841	1207
5	5035	1207

prune107.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Error

0.0b

Counts

123 → 10

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
	48.0b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
▶	0.4b	(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)))
	28.6b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x))))
	1.3b	(.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)))))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	29.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	34.3b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 2024 to 739 computations (63.5% 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)
✓	0.1b	(.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))

series989.0ms (19.3%)

Counts

4 → 72

Calls

4 calls:

483.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
252.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
245.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.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:

8.0ms	(.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)))
4.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
1.0ms	(cbrt.f64 (cos.f64 y))

simplify117.0ms (2.3%)

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

prune211.0ms (4.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	204	10	214

Error

0.0b

Counts

214 → 10

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (log1p.f64 (expm1.f64 (cos.f64 y))) x))
	48.0b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y))) (*.f64 (sqrt.f64 z) (sqrt.f64 (sin.f64 y)))))
✓	0.4b	(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)))
	28.6b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x))))
	1.3b	(.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)))))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	29.1b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	34.3b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 4660 to 1241 computations (73.4% saved)

regimes393.0ms (7.7%)

Accuracy

Total 0.1b remaining (60.5%)

Threshold costs 0.1b (60.5%)

Counts

99 → 1

Compiler

Compiled 6108 to 3714 computations (39.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	12	14
2	12	14

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.3s (44.3%)

Algorithm

1×

intervals

Results

1.0s	1941×	body	1024	valid
407.0ms	4490×	body	128	valid
278.0ms	1055×	body	512	valid
93.0ms	504×	body	256	valid
14.0ms	10×	body	2048	valid

Compiler

Compiled 211 to 115 computations (45.5% saved)

Details

analyze405.0ms (7.9%)

sample79.0ms (1.5%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series24.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify94.0ms (1.8%)

prune63.0ms (1.2%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify62.0ms (1.2%)

prune84.0ms (1.6%)

localize10.0ms (0.2%)

series29.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify83.0ms (1.6%)

prune107.0ms (2.1%)

localize12.0ms (0.2%)

series989.0ms (19.3%)

rewrite23.0ms (0.4%)

simplify117.0ms (2.3%)

prune211.0ms (4.1%)

regimes393.0ms (7.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.3s (44.3%)

Profiling