Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.6%	50.4%	0
49.6%	0%	50.4%	1

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.4s (85.3%)

Results

3.1s	4432×	body	2048	valid
831.0ms	2055×	body	1024	valid
300.0ms	1025×	body	512	valid
133.0ms	513×	body	256	valid
29.0ms	231×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
4×	`+-commutative_binary64`
3×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	13	6
3	19	6
4	26	6
5	36	6
6	44	6
7	53	6
8	56	6
9	39	6

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

27.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.0b	(-.f64 1 (cos.f64 x))

Compiler

Compiled 15 to 12 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.2b	(-.f64 1 (cos.f64 x))

series2.0ms (0%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(-.f64 1 (cos.f64 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

3.0ms

(-.f64 1 (cos.f64 x))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
792×	`fma-def_binary64`
476×	`unsub-neg_binary64`
319×	`cancel-sign-sub-inv_binary64`
265×	`*-commutative_binary64`

Counts

35 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	434
1	152	378
2	411	331
3	1316	331
4	3243	331
5	4306	331
6	4860	331
7	4996	331
8	4792	331

prune36.0ms (0.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	2	44

Error

0.0b

Counts

44 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
▶	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))

Compiler

Compiled 685 to 352 computations (48.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
✓	0.0b	(*.f64 1/720 (pow.f64 x 6))
✓	0.1b	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))

series19.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

10.0ms	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))
5.0ms	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))
4.0ms	(*.f64 1/720 (pow.f64 x 6))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 1/720 (pow.f64 x 6))
0.0ms	(fma.f64 (pow.f64 x 4) -1/24 (*.f64 1/720 (pow.f64 x 6)))
0.0ms	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-def_binary64`
413×	`distribute-rgt-in_binary64`
412×	`distribute-lft-in_binary64`
392×	`unswap-sqr_binary64`
361×	`associate-l_binary64`

Counts

71 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1144
1	160	1024
2	363	992
3	1581	992
4	5000	992

prune74.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	2	81

Error

0.0b

Counts

81 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.0b	(fma.f64 1/2 (.f64 x x) (fma.f64 (pow.f64 x 4) -1/24 (.f64 1/720 (pow.f64 x 6))))

Compiler

Compiled 1679 to 1201 computations (28.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (cos.f64 x))
✓	0.0b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))

series19.0ms (0.4%)

Counts

3 → 28

Calls

3 calls:

14.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-neg_binary64`
453×	`associate-/l*_binary64`
313×	`div-sub_binary64`
309×	`associate-l_binary64`
273×	`associate-r_binary64`

Counts

103 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1344
1	324	1079
2	1002	1055
3	3863	1044
4	5375	1044

prune77.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
▶	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 1997 to 994 computations (50.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

series11.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-neg_binary64`
657×	`distribute-rgt-neg-in_binary64`
651×	`cancel-sign-sub-inv_binary64`
509×	`distribute-lft-neg-in_binary64`
348×	`neg-mul-1_binary64`

Counts

33 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	562
1	132	512
2	332	510
3	709	510
4	1612	510
5	3534	510
6	4559	510
7	5035	510

prune20.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	32	2	34

Error

Counts

34 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.0b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 447 to 292 computations (34.7% saved)

regimes87.0ms (1.7%)

Accuracy

Total 0.0b remaining (28.3%)

Threshold costs 0.0b (28.3%)

Counts

30 → 1

Compiler

Compiled 1083 to 863 computations (20.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end43.0ms (0.8%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

Details

analyze1.0ms (0%)

sample4.4s (85.3%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite5.0ms (0.1%)

simplify97.0ms (1.9%)

prune36.0ms (0.7%)

localize9.0ms (0.2%)

series19.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify56.0ms (1.1%)

prune74.0ms (1.4%)

localize6.0ms (0.1%)

series19.0ms (0.4%)

rewrite17.0ms (0.3%)

simplify78.0ms (1.5%)

prune77.0ms (1.5%)

localize5.0ms (0.1%)

series11.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify79.0ms (1.5%)

prune20.0ms (0.4%)

regimes87.0ms (1.7%)

simplify2.0ms (0%)

end43.0ms (0.8%)

Profiling