Details

analyze623.0ms (8.3%)

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 (38.9%)

Results

1.5s	2064×	body	1024	valid
744.0ms	4639×	body	128	valid
444.0ms	1052×	body	512	valid
144.0ms	498×	body	256	valid
4.0ms	3×	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)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series23.0ms (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)))

simplify104.0ms (1.4%)

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

prune42.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Error

0.0b

Counts

65 → 8

Alt Table

Status	Error	Program
	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)))))
	37.6b	(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)))))
	14.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
▶	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	25.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (*.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	25.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	33.8b	(.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 1167 to 400 computations (65.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.2b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series245.0ms (3.3%)

Counts

4 → 72

Calls

4 calls:

153.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
38.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
34.0ms	(cbrt.f64 z)
19.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
3.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
1.0ms	(cbrt.f64 z)

simplify141.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
458×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1636
1	297	1460
2	1128	1401
3	2242	1385
4	4280	1287
5	4570	1287
6	4884	1287
7	4872	1287

prune133.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	185	10	195

Error

0.0b

Counts

195 → 10

Alt Table

Status	Error	Program
	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)))))
	18.8b	(fma.f64 x (sin.f64 y) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	35.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (sqrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	37.6b	(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)))))
	14.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.8b	(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 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (cos.f64 y))))
	25.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	33.8b	(.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 4022 to 1132 computations (71.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.6b	(cbrt.f64 (cbrt.f64 z))
	0.6b	(cbrt.f64 z)

series578.0ms (7.7%)

Counts

2 → 24

Calls

2 calls:

295.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
283.0ms	(cbrt.f64 (cbrt.f64 z))

rewrite4.0ms (0.1%)

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:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
1.0ms	(cbrt.f64 (cbrt.f64 z))

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

693×	`sqr-pow_binary64`
622×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
318×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	474
1	78	474
2	138	474
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune174.0ms (2.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	244	10	254

Error

0.0b

Counts

254 → 10

Alt Table

Status	Error	Program
▶	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)))))
	18.8b	(fma.f64 x (sin.f64 y) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	35.5b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (sqrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	37.6b	(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)))))
	14.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.8b	(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 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (cos.f64 y))))
	25.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	33.8b	(.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 6968 to 1643 computations (76.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (cos.f64 y))
✓	0.3b	(.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)))))
✓	0.5b	(.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)))))
✓	0.6b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

series828.0ms (11.1%)

Counts

3 → 108

Calls

3 calls:

452.0ms

(*.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)))))

361.0ms

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

15.0ms

(*.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)))))

rewrite33.0ms (0.4%)

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:

6.0ms

(*.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)))))

4.0ms

(*.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)))))

1.0ms

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

simplify145.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
477×	`times-frac_binary64`
443×	`associate-l_binary64`
311×	`associate-/r*_binary64`
306×	`associate-/l*_binary64`

Counts

201 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	432	7251
1	1431	6422
2	4883	6418
3	5155	6418

prune389.0ms (5.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	520	3	523
Fresh	2	4	6
Picked	1	0	1
Done	0	3	3
Total	523	10	533

Error

0.0b

Counts

533 → 10

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
	1.8b	(.f64 (.f64 (.f64 (cbrt.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 (.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 (.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)))))
	34.3b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) (cbrt.f64 (sqrt.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)))))
	37.6b	(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)))))
	14.8b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
✓	0.9b	(fma.f64 x (sin.f64 y) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z))) (cos.f64 y))))
	25.2b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 y) z) 3)))
	27.7b	(.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (.f64 (sin.f64 y) x)) 2)) (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)))
	33.8b	(.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 24769 to 7678 computations (69% saved)

regimes766.0ms (10.2%)

Accuracy

Total 0.1b remaining (48.8%)

Threshold costs 0.1b (48.8%)

Counts

167 → 1

Compiler

Compiled 21972 to 8874 computations (59.6% 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

end161.0ms (2.2%)

Compiler: Compiled 314 to 122 computations (61.1% saved)

Details

analyze623.0ms (8.3%)

sample2.9s (38.9%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series23.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify104.0ms (1.4%)

prune42.0ms (0.6%)

localize12.0ms (0.2%)

series245.0ms (3.3%)

rewrite19.0ms (0.3%)

simplify141.0ms (1.9%)

prune133.0ms (1.8%)

localize15.0ms (0.2%)

series578.0ms (7.7%)

rewrite4.0ms (0.1%)

simplify100.0ms (1.3%)

prune174.0ms (2.3%)

localize10.0ms (0.1%)

series828.0ms (11.1%)

rewrite33.0ms (0.4%)

simplify145.0ms (1.9%)

prune389.0ms (5.2%)

regimes766.0ms (10.2%)

simplify2.0ms (0%)

end161.0ms (2.2%)

Profiling