Details

analyze416.0ms (7.1%)

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)

sample80.0ms (1.4%)

Algorithm

1×

intervals

Results

31.0ms	60×	body	1024	valid
13.0ms	149×	body	128	valid
8.0ms	31×	body	512	valid
3.0ms	16×	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%)

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))

series26.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(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)))

simplify106.0ms (1.8%)

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

prune55.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	55	9	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	9	65

Error

0.0b

Counts

65 → 9

Alt Table

Status	Error	Program
	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)))))
▶	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	27.6b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (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)))))
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	34.0b	(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 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1220 to 425 computations (65.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series25.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

16.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
9.0ms	(*.f64 (sin.f64 y) x)

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

simplify78.0ms (1.3%)

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

prune61.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	63	12	75

Error

0.0b

Counts

75 → 12

Alt Table

Status	Error	Program
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	34.0b	(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 (cbrt.f64 (.f64 (sin.f64 y) x)) (cbrt.f64 (.f64 (sin.f64 y) x))) (cbrt.f64 (*.f64 (sin.f64 y) x))))
▶	0.3b	(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))))
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.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)))
	30.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	31.8b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) 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)))
	27.6b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	31.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 1321 to 491 computations (62.8% 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))))
✓	0.1b	(.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)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series1.1s (18.4%)

Counts

4 → 72

Calls

4 calls:

656.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
233.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
182.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite27.0ms (0.5%)

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:

8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
7.0ms	(.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)))
2.0ms	(cbrt.f64 (cos.f64 y))

simplify125.0ms (2.1%)

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

prune231.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	220	12	232

Error

0.0b

Counts

232 → 12

Alt Table

Status	Error	Program
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	0.6b	(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))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	30.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	31.8b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) 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)))
	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y))))
	27.6b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	0.8b	(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))))
	31.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 5235 to 1623 computations (69% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (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	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series635.0ms (10.8%)

Counts

3 → 52

Calls

3 calls:

624.0ms	(*.f64 z (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)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`unpow-prod-down_binary64`
18×	`associate-r_binary64`
16×	`prod-exp_binary64`

Counts

3 → 85

Calls

3 calls:

8.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
6.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
568×	`unswap-sqr_binary64`
398×	`*-commutative_binary64`
354×	`cancel-sign-sub-inv_binary64`
289×	`log-prod_binary64`

Counts

137 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	164	1962
1	368	1687
2	1211	1550
3	2361	1550
4	4311	1548
5	4956	1548

prune191.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	166	11	177

Error

0.0b

Counts

177 → 11

Alt Table

Status	Error	Program
	18.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	0.6b	(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))))
	0.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
	30.2b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (.f64 (sin.f64 y) x)) (sqrt.f64 (*.f64 (sin.f64 y) x))))
	27.6b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	31.8b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) 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)))
	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y))))))
	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	31.6b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))

Compiler

Compiled 3822 to 1898 computations (50.3% saved)

regimes293.0ms (5%)

Accuracy

Total 0.1b remaining (65.3%)

Threshold costs 0.1b (65.3%)

Counts

77 → 1

Compiler

Compiled 4932 to 2962 computations (39.9% 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

end0.0ms (0%)

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

sample2.3s (38.6%)

Algorithm

1×

intervals

Results

1.1s	1982×	body	1024	valid
388.0ms	4470×	body	128	valid
271.0ms	1042×	body	512	valid
91.0ms	501×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 239 to 132 computations (44.8% saved)

Details

analyze416.0ms (7.1%)

sample80.0ms (1.4%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series26.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify106.0ms (1.8%)

prune55.0ms (0.9%)

localize7.0ms (0.1%)

series25.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify78.0ms (1.3%)

prune61.0ms (1%)

localize12.0ms (0.2%)

series1.1s (18.4%)

rewrite27.0ms (0.5%)

simplify125.0ms (2.1%)

prune231.0ms (3.9%)

localize14.0ms (0.2%)

series635.0ms (10.8%)

rewrite20.0ms (0.3%)

simplify94.0ms (1.6%)

prune191.0ms (3.2%)

regimes293.0ms (5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (38.6%)

Profiling