Details

analyze491.0ms (7.4%)

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
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)

sample2.8s (42.2%)

Results

1.4s	2116×	body	1024	valid
782.0ms	4667×	body	128	valid
399.0ms	957×	body	512	valid
166.0ms	512×	body	256	valid
5.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (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)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

660×	`distribute-rgt-neg-in_binary64`
557×	`distribute-lft-neg-in_binary64`
467×	`fma-neg_binary64`
332×	`*-commutative_binary64`
297×	`neg-mul-1_binary64`

Counts

90 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	960
1	173	908
2	526	895
3	1471	895
4	3145	895
5	4780	895
6	4991	895
7	4926	895

prune44.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	9	65

Error

0.0b

Counts

65 → 9

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.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))))
	0.9b	(fma.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)))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	1.3b	(.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)))))
	30.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))

Compiler

Compiled 1213 to 414 computations (65.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))

series924.0ms (13.9%)

Counts

4 → 72

Calls

4 calls:

531.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
218.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
166.0ms	(cbrt.f64 (cos.f64 y))
8.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))

rewrite24.0ms (0.4%)

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

simplify119.0ms (1.8%)

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

prune186.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	220	9	229

Error

0.0b

Counts

229 → 9

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.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)))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	1.3b	(.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)))))
	30.5b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
▶	0.3b	(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 5130 to 1544 computations (69.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.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))

series602.0ms (9.1%)

Counts

3 → 52

Calls

3 calls:

589.0ms	(*.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)

rewrite17.0ms (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:

6.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
5.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify103.0ms (1.5%)

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

prune166.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	166	8	174

Error

0.0b

Counts

174 → 8

Alt Table

Status	Error	Program
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.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)))))
	30.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (sqrt.f64 z) (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (sqrt.f64 z))) (cbrt.f64 (cos.f64 y))))
▶	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.3b	(.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)))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (exp.f64 (log.f64 (cbrt.f64 (cos.f64 y))))))

Compiler

Compiled 3979 to 1960 computations (50.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))

series176.0ms (2.7%)

Counts

1 → 12

Calls

1 calls:

176.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

454×	`unswap-sqr_binary64`
442×	`distribute-rgt-neg-in_binary64`
380×	`distribute-lft-neg-in_binary64`
346×	`associate-l_binary64`
319×	`fma-def_binary64`

Counts

24 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	181
1	75	175
2	183	171
3	524	169
4	1910	169
5	4928	169

prune240.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

0.0b

Counts

202 → 8

Alt Table

Status	Error	Program
	36.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))) (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	0.9b	(fma.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)))))
	30.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (sqrt.f64 z) (*.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (sqrt.f64 z))) (cbrt.f64 (cos.f64 y))))
✓	0.3b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	1.3b	(.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)))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	15.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (exp.f64 (log.f64 (cbrt.f64 (cos.f64 y))))))

Compiler

Compiled 5938 to 2451 computations (58.7% saved)

regimes357.0ms (5.4%)

Accuracy

Total 0.1b remaining (46.1%)

Threshold costs 0.1b (46.1%)

Counts

68 → 1

Compiler

Compiled 5532 to 3466 computations (37.3% saved)

simplify4.0ms (0.1%)

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

end122.0ms (1.8%)

Compiler: Compiled 212 to 105 computations (50.5% saved)

Details

analyze491.0ms (7.4%)

sample2.8s (42.2%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify108.0ms (1.6%)

prune44.0ms (0.7%)

localize12.0ms (0.2%)

series924.0ms (13.9%)

rewrite24.0ms (0.4%)

simplify119.0ms (1.8%)

prune186.0ms (2.8%)

localize13.0ms (0.2%)

series602.0ms (9.1%)

rewrite17.0ms (0.3%)

simplify103.0ms (1.5%)

prune166.0ms (2.5%)

localize21.0ms (0.3%)

series176.0ms (2.7%)

rewrite5.0ms (0.1%)

simplify70.0ms (1.1%)

prune240.0ms (3.6%)

regimes357.0ms (5.4%)

simplify4.0ms (0.1%)

end122.0ms (1.8%)

Profiling