Details

analyze735.0ms (6.4%)

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
37.4%	62.4%	0.1%	6
49.9%	49.9%	0.1%	7
62.4%	37.4%	0.1%	8
62.4%	37.4%	0.1%	9
71.8%	28.1%	0.1%	10
79.6%	20.3%	0.1%	11
79.6%	20.3%	0.1%	12
85%	14.8%	0.1%	13
89.3%	10.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample103.0ms (0.9%)

Algorithm

1×

intervals

Results

51.0ms	66×	body	1024	valid
21.0ms	144×	body	128	valid
10.0ms	26×	body	512	valid
5.0ms	19×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify12.0ms (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

prune6.0ms (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 (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize13.0ms (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))

series42.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

28.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
14.0ms	(*.f64 z (sin.f64 y))

rewrite8.0ms (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:

6.0ms	(*.f64 z (sin.f64 y))
1.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify143.0ms (1.2%)

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

prune82.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

0.1b

Counts

66 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.2b	(.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)))))
	40.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	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))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y)))))

Compiler

Compiled 1029 to 342 computations (66.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
✓	8.2b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.9s (16.8%)

Counts

3 → 72

Calls

3 calls:

1.1s

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

787.0ms

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

35.0ms

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

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

11.0ms

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

8.0ms

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

3.0ms

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

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
445×	`cancel-sign-sub-inv_binary64`
352×	`*-commutative_binary64`
346×	`fma-def_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

151 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2495
1	410	2016
2	1169	1679
3	2733	1438
4	4659	1438
5	4981	1438
6	4891	1438

prune424.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	296	6	302

Error

0.1b

Counts

302 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.2b	(.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)))))
	40.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	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))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1))))

Compiler

Compiled 8097 to 2064 computations (74.5% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))
✓	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (sin.f64 y))
	8.2b	(cbrt.f64 (*.f64 z (sin.f64 y)))

series1.4s (12.6%)

Counts

3 → 48

Calls

3 calls:

1.1s	(.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))
277.0ms	(cbrt.f64 (sin.f64 y))
66.0ms	(cbrt.f64 z)

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))
1.0ms	(cbrt.f64 (sin.f64 y))
1.0ms	(cbrt.f64 z)

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
531×	`associate-l_binary64`
527×	`cancel-sign-sub-inv_binary64`
496×	`associate-r_binary64`
299×	`log-prod_binary64`

Counts

100 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	1321
1	301	1242
2	815	1165
3	2879	1143
4	4573	1139
5	4975	1139
6	4897	1139

prune150.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	150	7	157

Error

0.1b

Counts

157 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.2b	(.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)))))
	40.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	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))))
	0.7b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1))))

Compiler

Compiled 4747 to 1353 computations (71.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1)))
	0.5b	(.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (*.f64 z (sin.f64 y))))
	8.2b	(cbrt.f64 (*.f64 z (sin.f64 y)))
✓	8.2b	(cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z)))

series1.1s (9.8%)

Counts

2 → 48

Calls

2 calls:

956.0ms	(cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z)))
171.0ms	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1)))

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
44×	`cbrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

29.0ms	(.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1)))
11.0ms	(cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z)))

simplify218.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
333×	`fma-neg_binary64`
322×	`associate-*l/_binary64`
281×	`associate-*r/_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

129 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	3534
1	631	3042
2	1870	2909
3	4553	2903
4	5198	2903

prune533.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	254	7	261

Error

0.1b

Counts

261 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	29.2b	(.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)))))
	40.0b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x)) 3))
	12.4b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 2)) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1))))
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))))) (cbrt.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))))) (cbrt.f64 -1))))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (.f64 z (sin.f64 y))))) (cbrt.f64 (*.f64 z (sin.f64 y)))))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 (.f64 z (sin.f64 y))) (cbrt.f64 (.f64 z (sin.f64 y)))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 y) (/.f64 -1 z))) (cbrt.f64 -1))))

Compiler

Compiled 8893 to 3968 computations (55.4% saved)

regimes498.0ms (4.3%)

Accuracy

Total 0.0b remaining (33.4%)

Threshold costs 0.0b (33.4%)

Counts

77 → 1

Compiler

Compiled 7324 to 4002 computations (45.4% saved)

simplify4.0ms (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

end1.0ms (0%)

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

sample3.6s (31.3%)

Algorithm

1×

intervals

Results

1.7s	1993×	body	1024	valid
733.0ms	4512×	body	128	valid
453.0ms	1007×	body	512	valid
139.0ms	484×	body	256	valid
7.0ms	4×	body	2048	valid

Compiler

Compiled 200 to 122 computations (39% saved)

Details

analyze735.0ms (6.4%)

sample103.0ms (0.9%)

simplify12.0ms (0.1%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

series42.0ms (0.4%)

rewrite8.0ms (0.1%)

simplify143.0ms (1.2%)

prune82.0ms (0.7%)

localize23.0ms (0.2%)

series1.9s (16.8%)

rewrite27.0ms (0.2%)

simplify141.0ms (1.2%)

prune424.0ms (3.7%)

localize30.0ms (0.3%)

series1.4s (12.6%)

rewrite9.0ms (0.1%)

simplify117.0ms (1%)

prune150.0ms (1.3%)

localize18.0ms (0.2%)

series1.1s (9.8%)

rewrite58.0ms (0.5%)

simplify218.0ms (1.9%)

prune533.0ms (4.6%)

regimes498.0ms (4.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample3.6s (31.3%)

Profiling