Details

analyze587.0ms (7.9%)

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 (37.6%)

Results

1.4s	2016×	body	1024	valid
718.0ms	4671×	body	128	valid
489.0ms	1034×	body	512	valid
150.0ms	526×	body	256	valid
12.0ms	9×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (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 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))

series24.0ms (0.3%)

Counts

3 → 64

Calls

3 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
7.0ms	(*.f64 z (cos.f64 y))
2.0ms	(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)))

simplify112.0ms (1.5%)

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

prune55.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Error

0.0b

Counts

82 → 8

Alt Table

Status	Error	Program
	29.4b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	6.7b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
	31.2b	(.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)))))
	37.0b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.0b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 1348 to 489 computations (63.7% 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))))

series820.0ms (11%)

Counts

3 → 108

Calls

3 calls:

444.0ms

(*.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)))))

360.0ms

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

16.0ms

(*.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)))))

rewrite20.0ms (0.3%)

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))))

simplify148.0ms (2%)

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

prune332.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	522	1	523
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	522	9	531

Error

0.0b

Counts

531 → 9

Alt Table

Status	Error	Program
	31.2b	(.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)))))
	22.9b	(.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)))))
	29.4b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
▶	6.7b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.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)))))
	37.0b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.0b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 24762 to 7727 computations (68.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
	0.1b	(*.f64 z (cos.f64 y))
✓	0.4b	(pow.f64 (sin.f64 y) 3)
✓	21.4b	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

series22.0ms (0.3%)

Counts

3 → 52

Calls

3 calls:

15.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
6.0ms	(pow.f64 (sin.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

2.0ms	(pow.f64 (sin.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 y) 3))
0.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

614×	`cancel-sign-sub-inv_binary64`
539×	`fma-neg_binary64`
421×	`associate-l_binary64`
361×	`associate-r_binary64`
341×	`exp-prod_binary64`

Counts

110 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1112
1	229	1052
2	674	1025
3	2388	1023
4	4241	1020
5	4960	1020
6	4922	1020

prune104.0ms (1.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	135	9	144

Error

0.0b

Counts

144 → 9

Alt Table

Status	Error	Program
	31.2b	(.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)))))
	22.9b	(.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)))))
	29.4b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
✓	6.7b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
▶	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))))
	37.0b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.0b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 2421 to 1113 computations (54% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (sin.f64 y) 3)
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))))
✓	0.6b	(cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y))))
	21.4b	(cbrt.f64 (pow.f64 (sin.f64 y) 3))

series844.0ms (11.3%)

Counts

2 → 72

Calls

2 calls:

482.0ms

(*.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))))

361.0ms

(cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

6.0ms

(*.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))))

1.0ms

(cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y))))

simplify151.0ms (2%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-r_binary64`
477×	`times-frac_binary64`
400×	`associate-l_binary64`
311×	`associate-/r*_binary64`
306×	`associate-/l*_binary64`

Counts

127 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	405	6103
1	1366	5491
2	5504	5491

prune592.0ms (8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	559	1	560
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	559	10	569

Error

0.0b

Counts

569 → 10

Alt Table

Status	Error	Program
	31.2b	(.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)))))
	22.9b	(.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)))))
	29.4b	(fma.f64 x (.f64 (sqrt.f64 (sin.f64 y)) (sqrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
✓	6.7b	(fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))
✓	7.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (*.f64 z (cos.f64 y)))))
	37.0b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x)) 3))
	17.1b	(fma.f64 x (sin.f64 y) (.f64 (.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	30.0b	(fma.f64 x (sin.f64 y) (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (cos.f64 y))))
	7.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y)))) (cbrt.f64 (fma.f64 x (cbrt.f64 (pow.f64 (sin.f64 y) 3)) (.f64 z (cos.f64 y))))) (cbrt.f64 (fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 30500 to 15151 computations (50.3% saved)

regimes490.0ms (6.6%)

Accuracy

Total 0.1b remaining (57.4%)

Threshold costs 0.1b (57.4%)

Counts

88 → 1

Compiler

Compiled 9472 to 5362 computations (43.4% saved)

simplify3.0ms (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

end171.0ms (2.3%)

Compiler: Compiled 233 to 135 computations (42.1% saved)

Details

analyze587.0ms (7.9%)

sample2.8s (37.6%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series24.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify112.0ms (1.5%)

prune55.0ms (0.7%)

localize10.0ms (0.1%)

series820.0ms (11%)

rewrite20.0ms (0.3%)

simplify148.0ms (2%)

prune332.0ms (4.5%)

localize9.0ms (0.1%)

series22.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify102.0ms (1.4%)

prune104.0ms (1.4%)

localize12.0ms (0.2%)

series844.0ms (11.3%)

rewrite11.0ms (0.2%)

simplify151.0ms (2%)

prune592.0ms (8%)

regimes490.0ms (6.6%)

simplify3.0ms (0%)

end171.0ms (2.3%)

Profiling