Details

analyze562.0ms (7.8%)

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
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (40.4%)

Results

1.5s	2099×	body	1024	valid
742.0ms	4586×	body	128	valid
411.0ms	1001×	body	512	valid
176.0ms	566×	body	256	valid
5.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% 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 (sin.f64 y) (*.f64 z (cos.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 (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.1b	(*.f64 z (cos.f64 y))

series22.0ms (0.3%)

Counts

3 → 64

Calls

3 calls:

14.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
7.0ms	(*.f64 z (cos.f64 y))
1.0ms	(sin.f64 y)

rewrite5.0ms (0.1%)

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:

3.0ms	(*.f64 z (cos.f64 y))
1.0ms	(sin.f64 y)
0.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

simplify116.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-neg_binary64`
413×	`sub-neg_binary64`
295×	`associate-l_binary64`
259×	`unswap-sqr_binary64`
258×	`associate-r_binary64`

Counts

103 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1076
1	225	1013
2	651	994
3	1798	994
4	3982	994
5	4885	994
6	5000	994
7	4925	994

prune62.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
	4.2b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
▶	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	29.4b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 1281 to 448 computations (65% saved)

localize12.0ms (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))

series798.0ms (11.1%)

Counts

4 → 72

Calls

4 calls:

479.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
185.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
127.0ms	(cbrt.f64 (cos.f64 y))
7.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite25.0ms (0.3%)

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:

8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
6.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
5.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
1.0ms	(cbrt.f64 (cos.f64 y))

simplify156.0ms (2.2%)

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	1918
2	1218	1772
3	2345	1734
4	4484	1716
5	4900	1716
6	4962	1716

prune218.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	218	7	225

Error

0.0b

Counts

225 → 7

Alt Table

Status	Error	Program
	4.2b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	29.4b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
▶	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 5082 to 1517 computations (70.1% saved)

localize14.0ms (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)))
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))

series507.0ms (7.1%)

Counts

3 → 52

Calls

3 calls:

495.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
9.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
3.0ms	(pow.f64 (cos.f64 y) 2)

rewrite19.0ms (0.3%)

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:

8.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
6.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify95.0ms (1.3%)

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	2043
1	368	1709
2	1211	1576
3	2361	1564
4	4311	1562
5	4956	1562

prune178.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	165	7	172

Error

0.0b

Counts

172 → 7

Alt Table

Status	Error	Program
	4.2b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
▶	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	29.4b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 3882 to 1916 computations (50.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series310.0ms (4.3%)

Counts

2 → 24

Calls

2 calls:

187.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))
123.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 y)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))
1.0ms	(cbrt.f64 (cbrt.f64 (cos.f64 y)))

simplify122.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
417×	`sub-neg_binary64`
376×	`distribute-rgt-neg-in_binary64`
360×	`cancel-sign-sub-inv_binary64`
292×	`distribute-lft-neg-in_binary64`

Counts

96 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	1708
1	179	1708
2	446	1584
3	1164	1547
4	2742	1197
5	4226	1197
6	4705	1197
7	4885	1197

prune427.0ms (6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	344	7	351

Error

0.0b

Counts

351 → 7

Alt Table

Status	Error	Program
	4.2b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
✓	0.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (*.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cbrt.f64 (cos.f64 y))))) (cbrt.f64 (cbrt.f64 (cos.f64 y)))))
	0.6b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (cbrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	29.4b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.2b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y))))

Compiler

Compiled 11686 to 2486 computations (78.7% saved)

regimes446.0ms (6.2%)

Accuracy

Total 0.1b remaining (49.9%)

Threshold costs 0.1b (49.9%)

Counts

89 → 1

Compiler

Compiled 6940 to 3990 computations (42.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	13	12
2	12	12

end124.0ms (1.7%)

Compiler: Compiled 173 to 89 computations (48.6% saved)

Details

analyze562.0ms (7.8%)

sample2.9s (40.4%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series22.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify116.0ms (1.6%)

prune62.0ms (0.9%)

localize12.0ms (0.2%)

series798.0ms (11.1%)

rewrite25.0ms (0.3%)

simplify156.0ms (2.2%)

prune218.0ms (3%)

localize14.0ms (0.2%)

series507.0ms (7.1%)

rewrite19.0ms (0.3%)

simplify95.0ms (1.3%)

prune178.0ms (2.5%)

localize15.0ms (0.2%)

series310.0ms (4.3%)

rewrite13.0ms (0.2%)

simplify122.0ms (1.7%)

prune427.0ms (6%)

regimes446.0ms (6.2%)

simplify2.0ms (0%)

end124.0ms (1.7%)

Profiling