Details

analyze631.0ms (3.9%)

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
12.5%	87.4%	0.1%	6
34.3%	65.5%	0.1%	7
46.8%	53%	0.1%	8
48%	51.9%	0.1%	9
63%	36.9%	0.1%	10
71.7%	28.2%	0.1%	11
72%	27.8%	0.1%	12
80.5%	19.4%	0.1%	13
85.4%	14.5%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample75.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	186×	body	128	valid
25.0ms	35×	body	1024	valid
9.0ms	29×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	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 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

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

series18.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

430×	`fma-def_binary64`
379×	`sub-neg_binary64`
339×	`distribute-rgt-neg-in_binary64`
305×	`cancel-sign-sub-inv_binary64`
292×	`distribute-lft-neg-in_binary64`

Counts

46 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	573
1	80	546
2	212	543
3	688	541
4	2534	541
5	4191	541
6	4953	541
7	4936	541

prune29.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Error

0.0b

Counts

34 → 4

Alt Table

Status	Error	Program
	32.6b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	38.9b	(cbrt.f64 (pow.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) 3))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 517 to 153 computations (70.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.5b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

series1.5s (9.2%)

Counts

3 → 108

Calls

3 calls:

1.0s

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

462.0ms

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

29.0ms

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

rewrite37.0ms (0.2%)

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:

11.0ms

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

8.0ms

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

1.0ms

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

simplify409.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-def_binary64`
652×	`times-frac_binary64`
323×	`*-commutative_binary64`
168×	`+-commutative_binary64`
127×	`sqr-pow_binary64`

Counts

201 → 254

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	772	10896
1	2612	9995
2	4999	9995
3	4962	9995

prune807.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	509	2	511
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	510	5	515

Error

0.0b

Counts

515 → 5

Alt Table

Status	Error	Program
▶	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))
	32.6b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	38.9b	(cbrt.f64 (pow.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) 3))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 31398 to 11856 computations (62.2% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.5b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

series1.9s (11.4%)

Counts

2 → 72

Calls

2 calls:

1.1s	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
773.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

5.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
2.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

simplify328.0ms (2%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
638×	`times-frac_binary64`
301×	`*-commutative_binary64`
160×	`+-commutative_binary64`
139×	`sqr-pow_binary64`

Counts

99 → 150

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	724	9015
1	2517	8301
2	4979	8301

prune1.5s (8.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	769	0	769
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	769	5	774

Error

0.0b

Counts

774 → 5

Alt Table

Status	Error	Program
✓	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))
	32.6b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	38.9b	(cbrt.f64 (pow.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) 3))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 76641 to 26942 computations (64.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.5b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))
✓	0.6b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))

series1.9s (11.7%)

Counts

1 → 36

Calls

1 calls:

1.9s

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
8×	`pow1_binary64`
6×	`pow1/3_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 36

Calls

1 calls:

9.0ms

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

simplify312.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

451×	`*-commutative_binary64`
287×	`times-frac_binary64`
230×	`associate-r_binary64`
208×	`associate-/r*_binary64`
201×	`+-commutative_binary64`

Counts

72 → 99

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	853	11226
1	3054	9729
2	5055	9729

prune2.8s (17.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1192	0	1192
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1192	5	1197

Error

0.0b

Counts

1197 → 5

Alt Table

Status	Error	Program
✓	1.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))
	32.6b	(*.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))))) (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	38.9b	(cbrt.f64 (pow.f64 (+.f64 (sin.f64 y) (fma.f64 (cos.f64 y) z x)) 3))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 150698 to 48237 computations (68% saved)

regimes971.0ms (5.9%)

Accuracy

Total 0.0b remaining (40.8%)

Threshold costs 0.0b (40.8%)

Counts

124 → 1

Compiler

Compiled 19340 to 6658 computations (65.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	12	14
2	12	14

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample3.0s (18.2%)

Algorithm

1×

intervals

Results

1.1s	1280×	body	1024	valid
823.0ms	5722×	body	128	valid
285.0ms	684×	body	512	valid
97.0ms	309×	body	256	valid
9.0ms	5×	body	2048	valid

Compiler

Compiled 204 to 72 computations (64.7% saved)

Details

analyze631.0ms (3.9%)

sample75.0ms (0.5%)

simplify7.0ms (0%)

prune3.0ms (0%)

localize7.0ms (0%)

series18.0ms (0.1%)

rewrite1.0ms (0%)

simplify107.0ms (0.7%)

prune29.0ms (0.2%)

localize13.0ms (0.1%)

series1.5s (9.2%)

rewrite37.0ms (0.2%)

simplify409.0ms (2.5%)

prune807.0ms (4.9%)

localize27.0ms (0.2%)

series1.9s (11.4%)

rewrite10.0ms (0.1%)

simplify328.0ms (2%)

prune1.5s (8.9%)

localize16.0ms (0.1%)

series1.9s (11.7%)

rewrite18.0ms (0.1%)

simplify312.0ms (1.9%)

prune2.8s (17.2%)

regimes971.0ms (5.9%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.0s (18.2%)

Profiling