Details

analyze623.0ms (14.1%)

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
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.2s (50.1%)

Results

924.0ms	1303×	body	1024	valid
862.0ms	5911×	body	128	valid
290.0ms	716×	body	512	valid
91.0ms	318×	body	256	valid
11.0ms	8×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune3.0ms (0.1%)

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 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

12.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
4.0ms	(+.f64 x (sin.f64 y))
3.0ms	(cos.f64 y)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-def_binary64`

Counts

3 → 36

Calls

3 calls:

2.0ms	(+.f64 x (sin.f64 y))
1.0ms	(cos.f64 y)
0.0ms	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify125.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

607×	`cancel-sign-sub-inv_binary64`
443×	`distribute-rgt-neg-in_binary64`
357×	`distribute-rgt-in_binary64`
346×	`sub-neg_binary64`
340×	`distribute-lft-in_binary64`

Counts

100 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	991
1	226	940
2	515	929
3	1512	928
4	3685	928
5	4604	928
6	4967	928
7	4999	928
8	4879	928

prune49.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Error

0.0b

Counts

81 → 5

Alt Table

Status	Error	Program
	34.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	31.9b	(-.f64 (+.f64 y (+.f64 z x)) (.f64 1/2 (.f64 (pow.f64 y 2) z)))
	0.2b	(fma.f64 z (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
▶	0.1b	(fma.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))

Compiler

Compiled 1167 to 405 computations (65.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (sin.f64 y))
✓	0.1b	(fma.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.2b	(expm1.f64 (log1p.f64 (cos.f64 y)))
✓	0.3b	(log1p.f64 (cos.f64 y))

series218.0ms (5%)

Counts

3 → 60

Calls

3 calls:

200.0ms	(log1p.f64 (cos.f64 y))
16.0ms	(fma.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
2.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p.f64 (cos.f64 y))
0.0ms	(fma.f64 z (expm1.f64 (log1p.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))
0.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

543×	`distribute-rgt-neg-in_binary64`
450×	`distribute-lft-neg-in_binary64`
413×	`sub-neg_binary64`
354×	`fma-neg_binary64`
308×	`*-commutative_binary64`

Counts

92 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	86	904
1	176	855
2	442	846
3	1419	846
4	3440	846
5	4714	846
6	4998	846

prune78.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	31.9b	(fma.f64 (.f64 (.f64 y y) z) -1/2 (+.f64 y (+.f64 x z)))
	34.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	17.4b	(fma.f64 z (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (cos.f64 y))) (sqrt.f64 (log1p.f64 (cos.f64 y))))) (+.f64 x (sin.f64 y)))
▶	0.2b	(fma.f64 z (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (+.f64 x (sin.f64 y)))

Compiler

Compiled 1691 to 550 computations (67.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (+.f64 x (sin.f64 y)))
✓	0.1b	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
✓	0.3b	(*.f64 (cos.f64 y) (cos.f64 y))
✓	0.4b	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

series25.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

15.0ms	(fma.f64 z (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (+.f64 x (sin.f64 y)))
6.0ms	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
3.0ms	(*.f64 (cos.f64 y) (cos.f64 y))
2.0ms	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 84

Calls

4 calls:

5.0ms	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
4.0ms	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))
3.0ms	(*.f64 (cos.f64 y) (cos.f64 y))
0.0ms	(fma.f64 z (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))) (+.f64 x (sin.f64 y)))

simplify106.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

644×	`unswap-sqr_binary64`
637×	`fma-neg_binary64`
472×	`associate-l_binary64`
404×	`associate-r_binary64`
290×	`exp-prod_binary64`

Counts

156 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	135	1575
1	280	1321
2	766	1306
3	2544	1261
4	4085	1215
5	4693	1215
6	4936	1215

prune130.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
	17.4b	(fma.f64 z (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (cos.f64 y))) (sqrt.f64 (log1p.f64 (cos.f64 y))))) (+.f64 x (sin.f64 y)))
▶	0.2b	(fma.f64 z (log.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	31.9b	(fma.f64 (.f64 (.f64 y y) z) -1/2 (+.f64 y (+.f64 x z)))
	34.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))

Compiler

Compiled 2810 to 871 computations (69% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))
	0.3b	(*.f64 (cos.f64 y) (cos.f64 y))
✓	0.3b	(log.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))))
	0.4b	(cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y)))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

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

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`log-pow_binary64`
4×	`exp-prod_binary64`
3×	`log-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

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

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-neg_binary64`
777×	`cancel-sign-sub-inv_binary64`
308×	`distribute-rgt-neg-in_binary64`
288×	`unswap-sqr_binary64`
273×	`distribute-lft-neg-in_binary64`

Counts

30 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	460
1	89	283
2	170	199
3	403	197
4	1310	197
5	4061	197
6	4806	197
7	4976	197
8	4937	197

prune150.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	155	6	161

Error

0.0b

Counts

161 → 6

Alt Table

Status	Error	Program
	17.4b	(fma.f64 z (expm1.f64 (*.f64 (sqrt.f64 (log1p.f64 (cos.f64 y))) (sqrt.f64 (log1p.f64 (cos.f64 y))))) (+.f64 x (sin.f64 y)))
✓	0.2b	(fma.f64 z (log.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 y) (cos.f64 y)) (cos.f64 y))))) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	31.9b	(fma.f64 (.f64 (.f64 y y) z) -1/2 (+.f64 y (+.f64 x z)))
	34.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))))
	0.2b	(fma.f64 z (.f64 (cbrt.f64 (.f64 (cos.f64 y) (cos.f64 y))) (cbrt.f64 (cos.f64 y))) (+.f64 x (sin.f64 y)))

Compiler

Compiled 3247 to 1120 computations (65.5% saved)

regimes334.0ms (7.6%)

Accuracy

Total 0.0b remaining (39.1%)

Threshold costs 0.0b (39.1%)

Counts

85 → 1

Compiler

Compiled 5276 to 3618 computations (31.4% 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

end83.0ms (1.9%)

Compiler: Compiled 136 to 74 computations (45.6% saved)

Details

analyze623.0ms (14.1%)

sample2.2s (50.1%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series20.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify125.0ms (2.8%)

prune49.0ms (1.1%)

localize10.0ms (0.2%)

series218.0ms (5%)

rewrite2.0ms (0%)

simplify88.0ms (2%)

prune78.0ms (1.8%)

localize10.0ms (0.2%)

series25.0ms (0.6%)

rewrite15.0ms (0.3%)

simplify106.0ms (2.4%)

prune130.0ms (3%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite2.0ms (0.1%)

simplify90.0ms (2%)

prune150.0ms (3.4%)

regimes334.0ms (7.6%)

simplify2.0ms (0%)

end83.0ms (1.9%)

Profiling