Details

analyze520.0ms (9.2%)

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
49.9%	49.9%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
71.8%	28.1%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
85%	14.8%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample87.0ms (1.5%)

Algorithm

1×

intervals

Results

34.0ms	71×	body	1024	valid
12.0ms	139×	body	128	valid
7.0ms	31×	body	512	valid
2.0ms	15×	body	256	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 (sin.f64 y) (*.f64 z (cos.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 (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series23.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

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

simplify114.0ms (2%)

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

prune60.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	8	65

Error

0.1b

Counts

65 → 8

Alt Table

Status	Error	Program
	32.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	32.8b	(-.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 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	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))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	35.6b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.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)))))
	42.9b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))

Compiler

Compiled 1154 to 409 computations (64.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series24.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

15.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
9.0ms	(*.f64 (sin.f64 y) x)

rewrite7.0ms (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:

5.0ms	(*.f64 (sin.f64 y) x)
0.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

410×	`fma-neg_binary64`
405×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
293×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	852
1	184	793
2	507	781
3	1282	780
4	2630	780
5	4874	780
6	4926	780

prune65.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	61	5	66
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	65	9	74

Error

0.0b

Counts

74 → 9

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
	32.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
	30.0b	(fma.f64 (cos.f64 y) z (-.f64 (.f64 y x) (.f64 1/6 (*.f64 (pow.f64 y 3) x))))
▶	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))))
	23.3b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	35.6b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1211 to 441 computations (63.6% saved)

localize12.0ms (0.2%)

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))))
✓	0.2b	(.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)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series985.0ms (17.3%)

Counts

4 → 72

Calls

4 calls:

568.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
240.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
169.0ms	(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)))

rewrite40.0ms (0.7%)

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:

24.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
5.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
5.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify123.0ms (2.2%)

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

prune261.0ms (4.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	219	10	229

Error

0.0b

Counts

229 → 10

Alt Table

Status	Error	Program
	17.7b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (*.f64 (pow.f64 (cos.f64 y) 2/3) z) (cbrt.f64 (pow.f64 (cos.f64 y) 2/3))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
	32.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
	30.0b	(fma.f64 (cos.f64 y) z (-.f64 (.f64 y x) (.f64 1/6 (*.f64 (pow.f64 y 3) x))))
	23.3b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	1.0b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	35.6b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 5165 to 1597 computations (69.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series253.0ms (4.5%)

Counts

3 → 40

Calls

3 calls:

239.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
8.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
5.0ms	(pow.f64 (cos.f64 y) 2)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 61

Calls

3 calls:

6.0ms	(.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)))
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

667×	`unswap-sqr_binary64`
626×	`fma-def_binary64`
343×	`fma-neg_binary64`
324×	`exp-prod_binary64`
322×	`log-prod_binary64`

Counts

101 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1345
1	282	1135
2	923	1093
3	1865	1081
4	4189	1081
5	4716	1081
6	4899	1081

prune153.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	126	10	136

Error

0.0b

Counts

136 → 10

Alt Table

Status	Error	Program
	30.0b	(fma.f64 (cos.f64 y) z (-.f64 (.f64 y x) (.f64 1/6 (*.f64 (pow.f64 y 3) x))))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (pow.f64 (pow.f64 (cos.f64 y) 2) 1/6) (pow.f64 (pow.f64 (cos.f64 y) 2) 1/6))) (cbrt.f64 (cos.f64 y))))
	0.5b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
	32.3b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (*.f64 (cbrt.f64 (sin.f64 y)) x)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 y))))))
	23.3b	(fma.f64 (cos.f64 y) z (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)) (.f64 (*.f64 x x) x))))
	35.6b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 2782 to 1355 computations (51.3% saved)

regimes394.0ms (6.9%)

Accuracy

Total 0.1b remaining (59%)

Threshold costs 0.1b (59%)

Counts

96 → 1

Compiler

Compiled 6048 to 3726 computations (38.4% 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

end2.0ms (0%)

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

sample2.3s (40.7%)

Algorithm

1×

intervals

Results

1.1s	2048×	body	1024	valid
392.0ms	4415×	body	128	valid
263.0ms	1028×	body	512	valid
93.0ms	504×	body	256	valid
5.0ms	5×	body	2048	valid

Compiler

Compiled 230 to 135 computations (41.3% saved)

Details

analyze520.0ms (9.2%)

sample87.0ms (1.5%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series23.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify114.0ms (2%)

prune60.0ms (1.1%)

localize8.0ms (0.1%)

series24.0ms (0.4%)

rewrite7.0ms (0.1%)

simplify83.0ms (1.5%)

prune65.0ms (1.1%)

localize12.0ms (0.2%)

series985.0ms (17.3%)

rewrite40.0ms (0.7%)

simplify123.0ms (2.2%)

prune261.0ms (4.6%)

localize12.0ms (0.2%)

series253.0ms (4.5%)

rewrite13.0ms (0.2%)

simplify105.0ms (1.9%)

prune153.0ms (2.7%)

regimes394.0ms (6.9%)

simplify2.0ms (0%)

end2.0ms (0%)

sample2.3s (40.7%)

Profiling