Details

analyze419.0ms (9.9%)

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)

sample81.0ms (1.9%)

Algorithm

1×

intervals

Results

33.0ms	58×	body	1024	valid
13.0ms	154×	body	128	valid
8.0ms	33×	body	512	valid
2.0ms	11×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% 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

prune5.0ms (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 (0.2%)

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 (0.5%)

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)))

simplify98.0ms (2.3%)

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 (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	5	65

Error

0.0b

Counts

65 → 5

Alt Table

Status	Error	Program
	34.8b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
▶	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	24.9b	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
	30.4b	(.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)))))
	26.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1018 to 341 computations (66.5% saved)

localize8.0ms (0.2%)

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)

series22.0ms (0.5%)

Counts

2 → 40

Calls

2 calls:

14.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
7.0ms	(*.f64 (sin.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 (sin.f64 y) x)
0.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))

simplify91.0ms (2.2%)

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

prune50.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
▶	24.9b	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
	33.0b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	30.4b	(.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)))))
	36.0b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	34.8b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	26.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1078 to 374 computations (65.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 z (.f64 y y)) -1/2 z)
✓	0.0b	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
✓	6.3b	(.f64 z (.f64 y y))

series55.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

26.0ms	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
20.0ms	(fma.f64 (.f64 z (.f64 y y)) -1/2 z)
8.0ms	(.f64 z (.f64 y y))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms	(.f64 z (.f64 y y))
0.0ms	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
0.0ms	(fma.f64 (.f64 z (.f64 y y)) -1/2 z)

simplify102.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-def_binary64`
622×	`fma-neg_binary64`
422×	`cancel-sign-sub-inv_binary64`
396×	`associate-l_binary64`
327×	`associate-r_binary64`

Counts

125 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1667
1	182	1475
2	479	1473
3	1744	1471
4	4199	1471
5	4998	1471
6	4974	1471

prune54.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Error

0.0b

Counts

91 → 7

Alt Table

Status	Error	Program
✓	24.9b	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
	33.0b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	30.4b	(.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)))))
	36.0b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	34.8b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
▶	26.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1574 to 625 computations (60.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
✓	0.1b	(.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))
✓	0.1b	(.f64 (.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y)))
✓	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y))))

series65.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

28.0ms

(*.f64 (*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))

19.0ms

(*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y)))

17.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y))))

rewrite47.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

197×	`pow1_binary64`
86×	`pow-prod-down_binary64`
65×	`add-cbrt-cube_binary64`
56×	`add-exp-log_binary64`
42×	`cbrt-unprod_binary64`

Counts

3 → 126

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))

12.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y))))

5.0ms

(*.f64 (*.f64 z (cos.f64 y)) (*.f64 z (cos.f64 y)))

simplify133.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-neg_binary64`
577×	`cancel-sign-sub-inv_binary64`
418×	`*-commutative_binary64`
287×	`fma-def_binary64`
247×	`associate-l_binary64`

Counts

198 → 130

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	135	2823
1	309	1737
2	1128	1636
3	2687	1626
4	4611	1494
5	4941	1494

prune158.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	241	7	248

Error

0.0b

Counts

248 → 7

Alt Table

Status	Error	Program
✓	24.9b	(fma.f64 x (sin.f64 y) (fma.f64 (.f64 z (.f64 y y)) -1/2 z))
	33.0b	(fma.f64 (cos.f64 y) z (.f64 (.f64 (sin.f64 y) (sqrt.f64 x)) (sqrt.f64 x)))
	30.4b	(.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)))))
	36.0b	(fma.f64 (cos.f64 y) z (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) x)))
	34.8b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	26.5b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z (cos.f64 y)) (.f64 z (cos.f64 y))) (*.f64 z (cos.f64 y)))))

Compiler

Compiled 5882 to 1497 computations (74.5% saved)

regimes344.0ms (8.1%)

Accuracy

Total 0.1b remaining (41.6%)

Threshold costs 0.1b (41.6%)

Counts

67 → 1

Compiler

Compiled 4168 to 2654 computations (36.3% saved)

simplify2.0ms (0.1%)

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

end0.0ms (0%)

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

sample2.4s (56.6%)

Algorithm

1×

intervals

Results

1.1s	1991×	body	1024	valid
416.0ms	4494×	body	128	valid
280.0ms	1022×	body	512	valid
90.0ms	487×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 143 to 81 computations (43.4% saved)

Details

analyze419.0ms (9.9%)

sample81.0ms (1.9%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

series22.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify98.0ms (2.3%)

prune41.0ms (1%)

localize8.0ms (0.2%)

series22.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify91.0ms (2.2%)

prune50.0ms (1.2%)

localize9.0ms (0.2%)

series55.0ms (1.3%)

rewrite7.0ms (0.2%)

simplify102.0ms (2.4%)

prune54.0ms (1.3%)

localize10.0ms (0.2%)

series65.0ms (1.5%)

rewrite47.0ms (1.1%)

simplify133.0ms (3.1%)

prune158.0ms (3.7%)

regimes344.0ms (8.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.4s (56.6%)

Profiling