Details

analyze434.0ms (7.2%)

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
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (48.7%)

Results

1.5s	2034×	body	1024	valid
868.0ms	4720×	body	128	valid
412.0ms	1024×	body	512	valid
136.0ms	476×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% 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%)

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)

localize7.0ms (0.1%)

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))

series28.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(*.f64 z (sin.f64 y))
13.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

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

simplify82.0ms (1.4%)

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

prune48.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Error

0.1b

Counts

66 → 7

Alt Table

Status	Error	Program
	30.3b	(.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)))))
	24.4b	(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))))
▶	0.1b	(fma.f64 (sin.f64 y) z (*.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)))))
	31.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	28.2b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))

Compiler

Compiled 1134 to 389 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)

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))

simplify68.0ms (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

prune55.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Error

0.0b

Counts

72 → 10

Alt Table

Status	Error	Program
	16.8b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	31.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (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)))
	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))))
	24.4b	(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)))))
	27.2b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	28.2b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	29.9b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (.f64 (cos.f64 y) x)) (sqrt.f64 (*.f64 (cos.f64 y) x))))
	25.2b	(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 1209 to 452 computations (62.6% 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))

series856.0ms (14.2%)

Counts

4 → 72

Calls

4 calls:

458.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)
222.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
167.0ms	(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:

7.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) x))
7.0ms	(*.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))

simplify114.0ms (1.9%)

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

prune189.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	204	10	214

Error

0.0b

Counts

214 → 10

Alt Table

Status	Error	Program
	16.8b	(fma.f64 (sin.f64 y) z (.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x)))
	31.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))))
	24.4b	(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)))))
▶	0.2b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x)))
	0.4b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))) x))
	27.2b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	0.8b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 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))))
	28.2b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (sin.f64 y))))
	16.9b	(fma.f64 (sin.f64 y) z (.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2/3))) (.f64 (cbrt.f64 (cos.f64 y)) x)))

Compiler

Compiled 4837 to 1354 computations (72% 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))

series230.0ms (3.8%)

Counts

3 → 32

Calls

3 calls:

218.0ms	(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)

rewrite14.0ms (0.2%)

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:

7.0ms	(.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3) (.f64 (cbrt.f64 (cos.f64 y)) x))
2.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify86.0ms (1.4%)

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

prune213.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	160	8	168

Error

0.0b

Counts

168 → 8

Alt Table

Status	Error	Program
	0.2b	(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))))
	24.4b	(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)))))
	16.8b	(fma.f64 (sin.f64 y) z (.f64 (pow.f64 (cos.f64 y) 1/3) (.f64 x (pow.f64 (cos.f64 y) 2/3))))
	27.2b	(fma.f64 (sin.f64 y) z (.f64 (.f64 (cos.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	31.1b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (sqrt.f64 (sin.f64 y))) (sqrt.f64 (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))))
	28.2b	(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 (log.f64 (exp.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))) (.f64 (cbrt.f64 (cos.f64 y)) x)))

Compiler

Compiled 3537 to 1703 computations (51.9% saved)

regimes460.0ms (7.6%)

Accuracy

Total 0.1b remaining (58.3%)

Threshold costs 0.1b (58.3%)

Counts

104 → 1

Compiler

Compiled 6960 to 4498 computations (35.4% saved)

simplify2.0ms (0%)

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

end124.0ms (2.1%)

Compiler: Compiled 176 to 109 computations (38.1% saved)

Details

analyze434.0ms (7.2%)

sample2.9s (48.7%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series28.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify82.0ms (1.4%)

prune48.0ms (0.8%)

localize7.0ms (0.1%)

series22.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify68.0ms (1.1%)

prune55.0ms (0.9%)

localize10.0ms (0.2%)

series856.0ms (14.2%)

rewrite23.0ms (0.4%)

simplify114.0ms (1.9%)

prune189.0ms (3.1%)

localize12.0ms (0.2%)

series230.0ms (3.8%)

rewrite14.0ms (0.2%)

simplify86.0ms (1.4%)

prune213.0ms (3.5%)

regimes460.0ms (7.6%)

simplify2.0ms (0%)

end124.0ms (2.1%)

Profiling