Details

analyze608.0ms (2.4%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.2s (8.9%)

Results

931.0ms	1362×	body	1024	valid
884.0ms	5852×	body	128	valid
270.0ms	685×	body	512	valid
103.0ms	352×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify10.0ms (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)

localize6.0ms (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)))

series11.0ms (0%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(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:

0.0ms

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

simplify81.0ms (0.3%)

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

prune22.0ms (0.1%)

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
	48.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.1b	(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)))))
	37.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

Compiler

Compiled 531 to 153 computations (71.2% saved)

localize9.0ms (0%)

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)))))
✓	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

series684.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

400.0ms

(*.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)))))

272.0ms

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

12.0ms

(*.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)))))

rewrite21.0ms (0.1%)

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:

9.0ms

(*.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)))))

4.0ms

(*.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))))

simplify201.0ms (0.8%)

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

prune476.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	508	3	511
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	509	6	515

Error

0.0b

Counts

515 → 6

Alt Table

Status	Error	Program
	48.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	35.7b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3))
	37.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)
	1.6b	(.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)))))))

Compiler

Compiled 31346 to 11878 computations (62.1% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

series18.1s (72.5%)

Counts

1 → 36

Calls

1 calls:

18.1s

(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

634×	`times-frac_binary64`
517×	`fma-def_binary64`
223×	`unswap-sqr_binary64`
152×	`associate-/r/_binary64`
128×	`distribute-rgt-in_binary64`

Counts

68 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2117
1	484	1892
2	1761	1676
3	4832	1676
4	5008	1676

prune133.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	177	7	184

Error

0.0b

Counts

184 → 7

Alt Table

Status	Error	Program
	48.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	35.7b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3))
	37.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)
	2.0b	(.f64 (pow.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)))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 3))
▶	1.6b	(.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)))))))

Compiler

Compiled 6906 to 3563 computations (48.4% saved)

localize13.0ms (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)))))
	0.6b	(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)))))

series718.0ms (2.9%)

Counts

2 → 72

Calls

2 calls:

429.0ms	(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))))))
289.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

rewrite6.0ms (0%)

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:

4.0ms	(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))))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))

simplify133.0ms (0.5%)

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

prune883.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	767	2	769
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	768	8	776

Error

0.0b

Counts

776 → 8

Alt Table

Status	Error	Program
	48.3b	(log1p.f64 (expm1.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	1.6b	(.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)))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	35.7b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (cos.f64 y) z (+.f64 (sin.f64 y) x)))) 3))
	37.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)
✓	1.6b	(.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)))))))
	35.7b	(.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)))))) (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))) (cbrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))))))

Compiler

Compiled 76649 to 26953 computations (64.8% saved)

regimes415.0ms (1.7%)

Accuracy

Total 0.0b remaining (43.3%)

Threshold costs 0.0b (43.3%)

Counts

86 → 1

Compiler

Compiled 11440 to 4278 computations (62.6% saved)

simplify2.0ms (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

end119.0ms (0.5%)

Compiler: Compiled 317 to 109 computations (65.6% saved)

Details

analyze608.0ms (2.4%)

sample2.2s (8.9%)

simplify10.0ms (0%)

prune3.0ms (0%)

localize6.0ms (0%)

series11.0ms (0%)

rewrite1.0ms (0%)

simplify81.0ms (0.3%)

prune22.0ms (0.1%)

localize9.0ms (0%)

series684.0ms (2.7%)

rewrite21.0ms (0.1%)

simplify201.0ms (0.8%)

prune476.0ms (1.9%)

localize9.0ms (0%)

series18.1s (72.5%)

rewrite4.0ms (0%)

simplify79.0ms (0.3%)

prune133.0ms (0.5%)

localize13.0ms (0.1%)

series718.0ms (2.9%)

rewrite6.0ms (0%)

simplify133.0ms (0.5%)

prune883.0ms (3.5%)

regimes415.0ms (1.7%)

simplify2.0ms (0%)

end119.0ms (0.5%)

Profiling