Details

analyze349.0ms (6%)

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)

sample66.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	61×	body	1024	valid
12.0ms	145×	body	128	valid
10.0ms	35×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify7.0ms (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

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
▶	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series26.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

19.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))

rewrite5.0ms (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 z (sin.f64 y))
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
465×	`distribute-rgt-neg-in_binary64`
379×	`distribute-lft-neg-in_binary64`
307×	`distribute-rgt-in_binary64`
280×	`*-commutative_binary64`

Counts

90 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	972
1	183	913
2	538	901
3	1443	900
4	2915	900
5	4952	900
6	5012	900

prune53.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	57	8	65
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Error

0.1b

Counts

67 → 8

Alt Table

Status	Error	Program
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	37.5b	(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)))))
	22.5b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	32.4b	(.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)))))
	1.5b	(.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)))))
	0.6b	(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))))

Compiler

Compiled 1198 to 411 computations (65.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series23.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

14.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
9.0ms	(*.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))

simplify66.0ms (1.1%)

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

prune58.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Error

0.1b

Counts

73 → 10

Alt Table

Status	Error	Program
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	32.4b	(.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)))))
	1.5b	(.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)))))
	22.5b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.9b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	16.0b	(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 z (*.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))))
	26.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)) (.f64 (*.f64 x x) x))))

Compiler

Compiled 1255 to 456 computations (63.7% saved)

localize10.0ms (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))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series876.0ms (15.1%)

Counts

4 → 72

Calls

4 calls:

435.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
243.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
190.0ms	(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))

rewrite22.0ms (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)))
4.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
1.0ms	(cbrt.f64 (cos.f64 y))

simplify140.0ms (2.4%)

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

prune239.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	202	12	214

Error

0.0b

Counts

214 → 12

Alt Table

Status	Error	Program
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	0.6b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))) (cbrt.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))))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (log.f64 (exp.f64 (cbrt.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 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) x))))
	16.0b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	32.4b	(.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)))))
	1.5b	(.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)))))
▶	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)))
	22.5b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.6b	(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))))
	26.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)) (.f64 (*.f64 x x) x))))

Compiler

Compiled 5015 to 1410 computations (71.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
✓	0.2b	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series258.0ms (4.4%)

Counts

3 → 32

Calls

3 calls:

247.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
8.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
25×	`unpow-prod-down_binary64`
15×	`prod-exp_binary64`
13×	`pow-exp_binary64`
12×	`associate-l_binary64`

Counts

3 → 84

Calls

3 calls:

9.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
3.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-neg_binary64`
666×	`fma-def_binary64`
363×	`*-commutative_binary64`
224×	`cancel-sign-sub-inv_binary64`
216×	`unswap-sqr_binary64`

Counts

116 → 135

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	1654
1	343	1348
2	1032	1202
3	2129	1194
4	4529	1192
5	4942	1192

prune235.0ms (4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	154	4	158
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	157	13	170

Error

0.0b

Counts

170 → 13

Alt Table

Status	Error	Program
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (log.f64 (exp.f64 (cbrt.f64 (cos.f64 y)))) x)))
	1.5b	(.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)))))
	0.3b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (*.f64 x (cbrt.f64 (cos.f64 y))) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/6))))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) x))))
	26.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (.f64 (pow.f64 (cos.f64 y) 2) (.f64 (cos.f64 y) (.f64 (.f64 x x) x)))))
	30.3b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	32.4b	(.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)))))
✓	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)))
	22.5b	(fma.f64 x (cos.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))))
	0.5b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))) (.f64 (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (.f64 (cbrt.f64 (cos.f64 y)) x))))
	15.9b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (sqrt.f64 (cos.f64 y)) 2) 1/3) (.f64 x (pow.f64 (cos.f64 y) 2/3))))
	0.6b	(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))))

Compiler

Compiled 3688 to 1779 computations (51.8% saved)

regimes668.0ms (11.5%)

Accuracy

Total 0.1b remaining (73.5%)

Threshold costs 0.1b (73.5%)

Counts

124 → 1

Compiler

Compiled 9180 to 5706 computations (37.8% 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

end1.0ms (0%)

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

sample2.5s (42.6%)

Algorithm

1×

intervals

Results

1.0s	2027×	body	1024	valid
472.0ms	4504×	body	128	valid
315.0ms	970×	body	512	valid
89.0ms	492×	body	256	valid
8.0ms	7×	body	2048	valid

Compiler

Compiled 332 to 190 computations (42.8% saved)

Details

analyze349.0ms (6%)

sample66.0ms (1.1%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series26.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify91.0ms (1.6%)

prune53.0ms (0.9%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify66.0ms (1.1%)

prune58.0ms (1%)

localize10.0ms (0.2%)

series876.0ms (15.1%)

rewrite22.0ms (0.4%)

simplify140.0ms (2.4%)

prune239.0ms (4.1%)

localize12.0ms (0.2%)

series258.0ms (4.4%)

rewrite17.0ms (0.3%)

simplify84.0ms (1.5%)

prune235.0ms (4%)

regimes668.0ms (11.5%)

simplify2.0ms (0%)

end1.0ms (0%)

sample2.5s (42.6%)

Profiling