Details

analyze524.0ms (8.9%)

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
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)

sample78.0ms (1.3%)

Algorithm

1×

intervals

Results

29.0ms	57×	body	1024	valid
14.0ms	154×	body	128	valid
7.0ms	27×	body	512	valid
3.0ms	18×	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

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

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series23.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

14.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
2.0ms	(sin.f64 y)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 39

Calls

3 calls:

8.0ms	(*.f64 z (sin.f64 y))
1.0ms	(sin.f64 y)
0.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
478×	`distribute-rgt-neg-in_binary64`
380×	`distribute-lft-neg-in_binary64`
321×	`*-commutative_binary64`
320×	`sub-neg_binary64`

Counts

103 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1088
1	210	1014
2	612	997
3	1656	995
4	3249	995
5	4837	995
6	4999	995
7	5000	995
8	4906	995

prune80.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Error

0.1b

Counts

83 → 6

Alt Table

Status	Error	Program
	31.2b	(.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)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	42.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
▶	0.1b	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
	4.2b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 1345 to 480 computations (64.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 y)
✓	0.1b	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
✓	0.1b	(.f64 z (.f64 1 (sin.f64 y)))

series24.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
7.0ms	(.f64 z (.f64 1 (sin.f64 y)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
7×	`pow1_binary64`
5×	`prod-exp_binary64`
3×	`associate-l_binary64`

Counts

2 → 31

Calls

2 calls:

4.0ms	(.f64 z (.f64 1 (sin.f64 y)))
0.0ms	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))

simplify85.0ms (1.4%)

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`
279×	`*-commutative_binary64`

Counts

91 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	973
1	191	901
2	524	889
3	1416	888
4	2907	888
5	4946	888
6	5007	888

prune61.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

0.1b

Counts

89 → 6

Alt Table

Status	Error	Program
	31.2b	(.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)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	42.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
▶	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.1b	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
	4.2b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 1456 to 644 computations (55.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
✓	0.3b	(*.f64 (cbrt.f64 z) (sin.f64 y))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series316.0ms (5.4%)

Counts

4 → 72

Calls

4 calls:

221.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
39.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
34.0ms	(cbrt.f64 z)
23.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y)))
5.0ms	(*.f64 (cbrt.f64 z) (sin.f64 y))
5.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify119.0ms (2%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
720×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
496×	`*-commutative_binary64`
395×	`unswap-sqr_binary64`

Counts

175 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1734
1	311	1507
2	1181	1430
3	2385	1407
4	4566	1395
5	4973	1395
6	4943	1395

prune127.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	196	6	202

Error

0.1b

Counts

202 → 6

Alt Table

Status	Error	Program
	31.2b	(.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)))))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	42.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
✓	0.1b	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
	4.2b	(fma.f64 x (cos.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (sin.f64 y) 3))))

Compiler

Compiled 4065 to 1115 computations (72.6% saved)

localize11.0ms (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 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.5b	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

series847.0ms (14.3%)

Counts

3 → 108

Calls

3 calls:

462.0ms

(*.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

367.0ms

(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))

17.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

1.0ms

(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))

simplify205.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
487×	`times-frac_binary64`
458×	`associate-l_binary64`
314×	`associate-/l*_binary64`
312×	`associate-/r*_binary64`

Counts

201 → 256

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	438	7239
1	1455	6431
2	4955	6431
3	5234	6431

prune384.0ms (6.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	517	6	523
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	519	10	529

Error

0.0b

Counts

529 → 10

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	31.2b	(.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)))))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.5b	(fma.f64 x (cos.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	31.6b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)))) 3)) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	31.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
	42.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))
✓	0.1b	(fma.f64 x (cos.f64 y) (.f64 z (.f64 1 (sin.f64 y))))
	1.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))))) (cbrt.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))) (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))))

Compiler

Compiled 24884 to 7734 computations (68.9% saved)

regimes554.0ms (9.4%)

Accuracy

Total 0.1b remaining (54.2%)

Threshold costs 0.1b (54.2%)

Counts

111 → 1

Compiler

Compiled 13092 to 5378 computations (58.9% 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

end0.0ms (0%)

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

sample2.2s (37.9%)

Algorithm

1×

intervals

Results

1.1s	2022×	body	1024	valid
408.0ms	4435×	body	128	valid
257.0ms	1030×	body	512	valid
87.0ms	510×	body	256	valid
3.0ms	3×	body	2048	valid

Compiler

Compiled 387 to 137 computations (64.6% saved)

Details

analyze524.0ms (8.9%)

sample78.0ms (1.3%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series23.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify130.0ms (2.2%)

prune80.0ms (1.4%)

localize10.0ms (0.2%)

series24.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify85.0ms (1.4%)

prune61.0ms (1%)

localize10.0ms (0.2%)

series316.0ms (5.4%)

rewrite23.0ms (0.4%)

simplify119.0ms (2%)

prune127.0ms (2.1%)

localize11.0ms (0.2%)

series847.0ms (14.3%)

rewrite20.0ms (0.3%)

simplify205.0ms (3.5%)

prune384.0ms (6.5%)

regimes554.0ms (9.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (37.9%)

Profiling