Details

analyze515.0ms (9.7%)

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 (53.3%)

Results

1.5s	2046×	body	1024	valid
767.0ms	4633×	body	128	valid
391.0ms	998×	body	512	valid
161.0ms	574×	body	256	valid
7.0ms	5×	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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
▶	0.1b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.7%)

Counts

4 → 88

Calls

4 calls:

19.0ms	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cos.f64 y)))
10.0ms	(*.f64 z (cos.f64 y))
7.0ms	(*.f64 x (sin.f64 y))
1.0ms	(cos.f64 y)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
543×	`fma-def_binary64`
451×	`sub-neg_binary64`
312×	`cancel-sign-sub-inv_binary64`
285×	`distribute-rgt-neg-in_binary64`

Counts

151 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1530
1	367	1483
2	1146	1455
3	2500	1454
4	4742	1454
5	5157	1454

prune110.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Error

0.0b

Counts

124 → 12

Alt Table

Status	Error	Program
	17.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	27.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	25.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.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)))))
	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	28.4b	(+.f64 (.f64 (sqrt.f64 (.f64 x (sin.f64 y))) (sqrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
▶	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (log1p.f64 (expm1.f64 (cos.f64 y)))))
	33.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.6b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	32.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))

Compiler

Compiled 2304 to 824 computations (64.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
✓	0.1b	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series12.0ms (0.2%)

Counts

3 → 48

Calls

3 calls:

7.0ms	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite4.0ms (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 → 42

Calls

3 calls:

2.0ms	(*.f64 z (log1p.f64 (expm1.f64 (cos.f64 y))))
0.0ms	(expm1.f64 (cos.f64 y))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
482×	`distribute-rgt-neg-in_binary64`
480×	`sub-neg_binary64`
311×	`*-commutative_binary64`
296×	`neg-mul-1_binary64`

Counts

90 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	746
1	217	691
2	641	670
3	1699	664
4	3624	664
5	4669	664
6	5003	664

prune143.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Error

0.0b

Counts

135 → 12

Alt Table

Status	Error	Program
	17.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y))))
	27.3b	(+.f64 (.f64 x (sin.f64 y)) (cbrt.f64 (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	25.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.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)))))
▶	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	28.4b	(+.f64 (.f64 (sqrt.f64 (.f64 x (sin.f64 y))) (sqrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3)))))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	33.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.6b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	32.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))

Compiler

Compiled 2478 to 928 computations (62.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 x (sin.f64 y))
✓	0.1b	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 3))
✓	0.3b	(pow.f64 (cos.f64 y) 3)

series15.0ms (0.3%)

Counts

3 → 40

Calls

3 calls:

7.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
6.0ms	(pow.f64 (cos.f64 y) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 84

Calls

3 calls:

7.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3)))
2.0ms	(pow.f64 (cos.f64 y) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 3))

simplify110.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-neg_binary64`
633×	`fma-def_binary64`
330×	`sqr-pow_binary64`
298×	`*-commutative_binary64`
259×	`log-prod_binary64`

Counts

124 → 126

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	124	1089
1	250	1015
2	839	981
3	1720	975
4	3552	972
5	4768	972
6	4999	972
7	4919	972

prune197.0ms (3.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	163	12	175

Error

0.0b

Counts

175 → 12

Alt Table

Status	Error	Program
	25.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.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)))))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	17.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 y)) 3))))
	33.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	28.4b	(+.f64 (.f64 (sqrt.f64 (.f64 x (sin.f64 y))) (sqrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
▶	0.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3)))))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	0.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 z (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))
	0.6b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	32.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))

Compiler

Compiled 3270 to 1605 computations (50.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3)))
✓	0.3b	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3))
	0.6b	(expm1.f64 (cos.f64 y))
✓	0.8b	(pow.f64 (expm1.f64 (cos.f64 y)) 3)

series23.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

18.0ms	(pow.f64 (expm1.f64 (cos.f64 y)) 3)
3.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3))
2.0ms	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.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 → 59

Calls

3 calls:

1.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3))
1.0ms	(pow.f64 (expm1.f64 (cos.f64 y)) 3)
0.0ms	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (cos.f64 y)) 3)))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-neg_binary64`
528×	`associate--r+_binary64`
417×	`associate--l+_binary64`
222×	`unswap-sqr_binary64`
209×	`fma-def_binary64`

Counts

95 → 98

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	1430
1	483	1247
2	1789	1181
3	4958	1175
4	5767	1175

prune151.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	119	11	130

Error

0.0b

Counts

130 → 11

Alt Table

Status	Error	Program
	25.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (sin.f64 y) (sin.f64 y)) (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.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)))))
✓	0.2b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x (sin.f64 y))) (cbrt.f64 (.f64 x (sin.f64 y)))) (cbrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	17.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 y)) 3))))
	33.9b	(+.f64 (.f64 (.f64 x (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y))) (*.f64 z (cos.f64 y)))
	0.3b	(+.f64 (.f64 x (sin.f64 y)) (.f64 z (log1p.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (cos.f64 y)) 1) 3)))))
	28.4b	(+.f64 (.f64 (sqrt.f64 (.f64 x (sin.f64 y))) (sqrt.f64 (.f64 x (sin.f64 y)))) (.f64 z (cos.f64 y)))
	0.9b	(+.f64 (.f64 x (sin.f64 y)) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cos.f64 y))))
	0.6b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y)))) (cbrt.f64 (sin.f64 y))) (.f64 z (cos.f64 y)))
	32.4b	(+.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sin.f64 y))) (*.f64 z (cos.f64 y)))

Compiler

Compiled 3004 to 1670 computations (44.4% saved)

regimes625.0ms (11.8%)

Accuracy

Total 0.1b remaining (61.8%)

Threshold costs 0.1b (61.8%)

Counts

134 → 1

Compiler

Compiled 8920 to 6102 computations (31.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	17	14
2	16	14

end199.0ms (3.8%)

Compiler: Compiled 243 to 142 computations (41.6% saved)

Details

analyze515.0ms (9.7%)

sample2.8s (53.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series37.0ms (0.7%)

rewrite11.0ms (0.2%)

simplify87.0ms (1.6%)

prune110.0ms (2.1%)

localize13.0ms (0.2%)

series12.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify84.0ms (1.6%)

prune143.0ms (2.7%)

localize10.0ms (0.2%)

series15.0ms (0.3%)

rewrite14.0ms (0.3%)

simplify110.0ms (2.1%)

prune197.0ms (3.7%)

localize13.0ms (0.2%)

series23.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify75.0ms (1.4%)

prune151.0ms (2.9%)

regimes625.0ms (11.8%)

simplify2.0ms (0%)

end199.0ms (3.8%)

Profiling