Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.6s (36.8%)

Infinites

0% of outputs are infinite.

Results

1.1s	1338×	body	1024	valid
985.0ms	5888×	body	128	valid
311.0ms	676×	body	512	valid
120.0ms	351×	body	256	valid
5.0ms	3×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify11.0ms (0.2%)

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

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series29.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

16.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
8.0ms	(*.f64 z (cos.f64 y))
5.0ms	(+.f64 x (sin.f64 y))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`fma-def_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 56

Calls

3 calls:

5.0ms	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
3.0ms	(*.f64 z (cos.f64 y))
3.0ms	(+.f64 x (sin.f64 y))

simplify126.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-neg_binary64`
472×	`fma-def_binary64`
359×	`associate-l_binary64`
320×	`associate-r_binary64`
247×	`distribute-rgt-neg-in_binary64`

Counts

140 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1385
1	336	1325
2	977	1308
3	3255	1308
4	4656	1308
5	4995	1308
6	4925	1308

prune73.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

0.0b

Counts

108 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
▶	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	31.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	20.7b	(+.f64 (+.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))

Compiler

Compiled 1775 to 539 computations (69.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
✓	0.2b	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
✓	0.3b	(cbrt.f64 (cos.f64 y))

series1.3s (18.1%)

Counts

4 → 72

Calls

4 calls:

780.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
278.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
214.0ms	(cbrt.f64 (cos.f64 y))
9.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

11.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
9.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
8.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify176.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
609×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
370×	`cancel-sign-sub-inv_binary64`
351×	`log-prod_binary64`

Counts

174 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	2118
1	352	1762
2	1218	1642
3	2345	1606
4	4484	1588
5	4900	1588
6	4962	1588

prune328.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	219	7	226

Error

0.0b

Counts

226 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y))))))
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	31.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	20.7b	(+.f64 (+.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 (.f64 z (cos.f64 y))) (cbrt.f64 (.f64 z (cos.f64 y)))) (cbrt.f64 (*.f64 z (cos.f64 y)))))

Compiler

Compiled 5251 to 1530 computations (70.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
✓	0.2b	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series776.0ms (11%)

Counts

3 → 52

Calls

3 calls:

761.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
11.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
5.0ms	(pow.f64 (cos.f64 y) 2)

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`unpow-prod-down_binary64`
18×	`associate-r_binary64`
16×	`prod-exp_binary64`

Counts

3 → 85

Calls

3 calls:

13.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
11.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
3.0ms	(pow.f64 (cos.f64 y) 2)

simplify144.0ms (2%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
568×	`unswap-sqr_binary64`
398×	`*-commutative_binary64`
354×	`cancel-sign-sub-inv_binary64`
289×	`log-prod_binary64`

Counts

137 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	164	1962
1	368	1687
2	1211	1550
3	2361	1550
4	4311	1548
5	4956	1548

prune444.0ms (6.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Error

0.0b

Counts

172 → 8

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
▶	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	0.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2))) 1/3)) (cbrt.f64 (cos.f64 y))))
	18.8b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (pow.f64 (cos.f64 y) 1/3)))
	31.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	20.7b	(+.f64 (+.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 4051 to 1968 computations (51.4% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 z (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) 1/3)) (cbrt.f64 (cos.f64 y)))
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 6))
✓	0.6b	(pow.f64 (cos.f64 y) 6)

series42.0ms (0.6%)

Counts

3 → 40

Calls

3 calls:

20.0ms	(pow.f64 (cos.f64 y) 6)
15.0ms	(.f64 (.f64 z (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) 1/3)) (cbrt.f64 (cos.f64 y)))
6.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 6))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64`
10×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 61

Calls

3 calls:

14.0ms	(.f64 (.f64 z (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) 1/3)) (cbrt.f64 (cos.f64 y)))
4.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 6))
3.0ms	(pow.f64 (cos.f64 y) 6)

simplify197.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
549×	`fma-def_binary64`
438×	`log-prod_binary64`
411×	`*-commutative_binary64`
380×	`exp-prod_binary64`

Counts

101 → 107

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	133	1313
1	304	1163
2	936	1115
3	1884	853
4	3681	850
5	4299	850
6	4579	841
7	4918	841
8	4899	841

prune236.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	130	9	139

Error

Counts

139 → 9

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 6)) 1/3)) (cbrt.f64 (cos.f64 y))))
✓	0.1b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
	0.3b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2))) 1/3)) (cbrt.f64 (cos.f64 y))))
	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))
	18.8b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (pow.f64 (cos.f64 y) 1/3)))
	31.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	20.7b	(+.f64 (+.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))

Compiler

Compiled 3116 to 1568 computations (49.7% saved)

regimes265.0ms (3.7%)

Accuracy

Total 0.0b remaining (69.1%)

Threshold costs 0.0b (69.1%)

Counts

36 → 1

Compiler

Compiled 2416 to 1510 computations (37.5% saved)

simplify4.0ms (0.1%)

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

end164.0ms (2.3%)

Compiler: Compiled 205 to 137 computations (33.2% saved)

Details

analyze2.0ms (0%)

sample2.6s (36.8%)

simplify11.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series29.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify126.0ms (1.8%)

prune73.0ms (1%)

localize11.0ms (0.2%)

series1.3s (18.1%)

rewrite36.0ms (0.5%)

simplify176.0ms (2.5%)

prune328.0ms (4.6%)

localize13.0ms (0.2%)

series776.0ms (11%)

rewrite37.0ms (0.5%)

simplify144.0ms (2%)

prune444.0ms (6.3%)

localize28.0ms (0.4%)

series42.0ms (0.6%)

rewrite27.0ms (0.4%)

simplify197.0ms (2.8%)

prune236.0ms (3.3%)

regimes265.0ms (3.7%)

simplify4.0ms (0.1%)

end164.0ms (2.3%)

Profiling