Details

analyze586.0ms (9.1%)

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 (43.7%)

Results

1.4s	2060×	body	1024	valid
743.0ms	4603×	body	128	valid
458.0ms	1043×	body	512	valid
164.0ms	544×	body	256	valid
8.0ms	6×	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 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))

series22.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(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)))

simplify105.0ms (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

prune43.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	7	65

Error

0.1b

Counts

65 → 7

Alt Table

Status	Error	Program
	17.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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))))
	31.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.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))))
	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)))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.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)))))

Compiler

Compiled 1089 to 374 computations (65.7% 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))))
✓	0.1b	(.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))

series958.0ms (14.8%)

Counts

4 → 72

Calls

4 calls:

555.0ms	(.f64 z (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
226.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
167.0ms	(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)))

rewrite25.0ms (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:

7.0ms	(.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))

simplify118.0ms (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

prune203.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	220	7	227

Error

0.1b

Counts

227 → 7

Alt Table

Status	Error	Program
	0.4b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))))
	31.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	17.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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))))
✓	0.1b	(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)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (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)))))

Compiler

Compiled 5018 to 1512 computations (69.9% saved)

localize12.0ms (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))
✓	0.1b	(.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))

series557.0ms (8.6%)

Counts

3 → 52

Calls

3 calls:

545.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
7.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
4.0ms	(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:

7.0ms	(*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3))
6.0ms	(.f64 (.f64 z (pow.f64 (pow.f64 (cos.f64 y) 2) 1/3)) (cbrt.f64 (cos.f64 y)))
2.0ms	(pow.f64 (cos.f64 y) 2)

simplify90.0ms (1.4%)

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

prune168.0ms (2.6%)

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

0.1b

Counts

172 → 7

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))))
	31.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	17.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (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))))
✓	0.1b	(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)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2) (cbrt.f64 (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)))))

Compiler

Compiled 3842 to 1907 computations (50.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(.f64 z (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))
2.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
16×	`add-exp-log_binary64`
11×	`pow-prod-down_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 61

Calls

2 calls:

9.0ms	(.f64 z (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y))))
6.0ms	(.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-def_binary64`
497×	`associate-l_binary64`
405×	`cancel-sign-sub-inv_binary64`
393×	`unswap-sqr_binary64`
367×	`associate-r_binary64`

Counts

97 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	103	828
1	214	741
2	598	727
3	1536	723
4	3217	683
5	4631	683
6	4939	683

prune224.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	225	8	233

Error

0.1b

Counts

233 → 8

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 x (sin.f64 y) (.f64 z (.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (cbrt.f64 (cos.f64 y)))))
	31.7b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	17.6b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
✓	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))))
	17.5b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 3) 1/3)))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.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)))))

Compiler

Compiled 4883 to 1470 computations (69.9% saved)

regimes256.0ms (4%)

Accuracy

Total 0.0b remaining (41.4%)

Threshold costs 0.0b (41.4%)

Counts

65 → 1

Compiler

Compiled 4824 to 3002 computations (37.8% 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

end108.0ms (1.7%)

Compiler: Compiled 154 to 92 computations (40.3% saved)

Details

analyze586.0ms (9.1%)

sample2.8s (43.7%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series22.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify105.0ms (1.6%)

prune43.0ms (0.7%)

localize11.0ms (0.2%)

series958.0ms (14.8%)

rewrite25.0ms (0.4%)

simplify118.0ms (1.8%)

prune203.0ms (3.1%)

localize12.0ms (0.2%)

series557.0ms (8.6%)

rewrite19.0ms (0.3%)

simplify90.0ms (1.4%)

prune168.0ms (2.6%)

localize10.0ms (0.2%)

series10.0ms (0.2%)

rewrite19.0ms (0.3%)

simplify76.0ms (1.2%)

prune224.0ms (3.5%)

regimes256.0ms (4%)

simplify4.0ms (0.1%)

end108.0ms (1.7%)

Profiling