Details

analyze487.0ms (7.4%)

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
0%	99.9%	0.1%	6
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (44.3%)

Results

1.5s	2089×	body	1024	valid
753.0ms	4600×	body	128	valid
478.0ms	1037×	body	512	valid
144.0ms	526×	body	256	valid
5.0ms	4×	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 (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series22.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

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

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-rgt-neg-in_binary64`
557×	`distribute-lft-neg-in_binary64`
467×	`fma-neg_binary64`
332×	`*-commutative_binary64`
297×	`neg-mul-1_binary64`

Counts

90 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	960
1	173	908
2	526	895
3	1471	895
4	3145	895
5	4780	895
6	4991	895
7	4926	895

prune41.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Error

0.1b

Counts

65 → 6

Alt Table

Status	Error	Program
	29.1b	(-.f64 (fma.f64 y x z) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 y 1/6)) (*.f64 z 1/2))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	37.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
▶	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1069 to 366 computations (65.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(cbrt.f64 (cos.f64 y))

series1.1s (16.2%)

Counts

4 → 72

Calls

4 calls:

660.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
227.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
176.0ms	(cbrt.f64 (cos.f64 y))
7.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
6.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
6.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
609×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
370×	`cancel-sign-sub-inv_binary64`
351×	`log-prod_binary64`

Counts

174 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	2118
1	352	1762
2	1218	1642
3	2345	1606
4	4484	1588
5	4900	1588
6	4962	1588

prune201.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	218	8	226

Error

0.0b

Counts

226 → 8

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	29.1b	(-.f64 (fma.f64 y x z) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 y 1/6)) (*.f64 z 1/2))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	37.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
▶	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 5062 to 1534 computations (69.7% saved)

localize13.0ms (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)
✓	0.1b	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
	0.2b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(pow.f64 (cos.f64 y) 2)

series240.0ms (3.6%)

Counts

3 → 32

Calls

3 calls:

229.0ms	(pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)
8.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
4.0ms	(pow.f64 (cos.f64 y) 2)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
14×	`unpow-prod-down_binary64`
11×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 74

Calls

3 calls:

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

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
702×	`fma-def_binary64`
340×	`*-commutative_binary64`
207×	`cancel-sign-sub-inv_binary64`
206×	`associate-+l+_binary64`

Counts

106 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1427
1	340	1221
2	1046	1093
3	2083	1083
4	4495	1083
5	4934	1083

prune173.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	144	8	152

Error

0.0b

Counts

152 → 8

Alt Table

Status	Error	Program
	29.1b	(-.f64 (fma.f64 y x z) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 y 1/6)) (*.f64 z 1/2))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	37.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))) (cbrt.f64 (cos.f64 y))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y))))
	14.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (*.f64 (pow.f64 (cos.f64 y) 1/6) (pow.f64 (cos.f64 y) 1/6))))
✓	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 3343 to 1696 computations (49.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(cbrt.f64 (cos.f64 y))
	0.3b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

series455.0ms (6.9%)

Counts

2 → 24

Calls

2 calls:

229.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
226.0ms	(log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cbrt-prod_binary64`
12×	`log-pow_binary64`
11×	`exp-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 43

Calls

2 calls:

3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
3.0ms	(log.f64 (exp.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2))))

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

734×	`log-prod_binary64`
482×	`associate-l_binary64`
409×	`distribute-rgt-neg-in_binary64`
390×	`associate-r_binary64`
360×	`distribute-lft-neg-in_binary64`

Counts

67 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	760
1	130	652
2	266	648
3	670	636
4	2414	636
5	4279	636
6	4845	636
7	5104	636

prune141.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	117	7	124

Error

0.0b

Counts

124 → 7

Alt Table

Status	Error	Program
	29.1b	(-.f64 (fma.f64 y x z) (.f64 (.f64 y y) (+.f64 (.f64 x (.f64 y 1/6)) (*.f64 z 1/2))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	37.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	14.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (*.f64 (pow.f64 (cos.f64 y) 1/6) (pow.f64 (cos.f64 y) 1/6))))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (log.f64 (exp.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)))))) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 2779 to 1499 computations (46.1% saved)

regimes231.0ms (3.5%)

Accuracy

Total 0.1b remaining (43.6%)

Threshold costs 0.1b (43.6%)

Counts

52 → 1

Compiler

Compiled 4376 to 2694 computations (38.4% saved)

simplify3.0ms (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

end110.0ms (1.7%)

Compiler: Compiled 165 to 99 computations (40% saved)

Details

analyze487.0ms (7.4%)

sample2.9s (44.3%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series22.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify105.0ms (1.6%)

prune41.0ms (0.6%)

localize10.0ms (0.1%)

series1.1s (16.2%)

rewrite25.0ms (0.4%)

simplify120.0ms (1.8%)

prune201.0ms (3%)

localize13.0ms (0.2%)

series240.0ms (3.6%)

rewrite15.0ms (0.2%)

simplify76.0ms (1.2%)

prune173.0ms (2.6%)

localize16.0ms (0.2%)

series455.0ms (6.9%)

rewrite7.0ms (0.1%)

simplify92.0ms (1.4%)

prune141.0ms (2.1%)

regimes231.0ms (3.5%)

simplify3.0ms (0%)

end110.0ms (1.7%)

Profiling