Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample5.0s (64.2%)

Results

2.4s	3593×	body	1024	valid
1.6s	1294×	body	2048	valid
585.0ms	1459×	body	512	valid
193.0ms	1317×	body	128	valid
166.0ms	590×	body	256	valid
9.0ms	3×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Stop Event

1×

saturated

Counts

1 → 1

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

38.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.8b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	3.6b	(sin.f64 (+.f64 x eps))

series10.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

464×	`fma-def_binary64`
445×	`log-prod_binary64`
214×	`fma-neg_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	173	17
2	2692	17

Stop Event

1×	node limit

Counts

2 → 151

Calls

2 calls:

55.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
54.0ms	(sin.f64 (+.f64 x eps))

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
266×	`cancel-sign-sub-inv_binary64`
264×	`associate-+l-_binary64`
245×	`distribute-rgt-neg-in_binary64`
243×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	602
1	172	587
2	566	572
3	2209	569

Stop Event

1×	node limit

Counts

199 → 180

prune164.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	171	9	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	9	181

Error

0.1b

Counts

181 → 9

Alt Table

Status	Error	Program
	29.8b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 eps)) 3) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) 3)) (fma.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))))) (sin.f64 x))
	25.2b	(fma.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 x) (cos.f64 eps))) (cbrt.f64 (.f64 (sin.f64 x) (cos.f64 eps)))) (cbrt.f64 (.f64 (sin.f64 x) (cos.f64 eps))) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
▶	24.5b	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
	24.5b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	29.4b	(-.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (cos.f64 x))) (.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
	32.3b	(-.f64 (log.f64 (.f64 (exp.f64 (.f64 (cos.f64 x) (sin.f64 eps))) (exp.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))) (sin.f64 x))
	24.5b	(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
	43.3b	(fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
	25.1b	(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))

Compiler

Compiled 3639 to 1150 computations (68.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 x)
✓	0.1b	(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x)))
✓	2.4b	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))

series31.0ms (0.4%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
11.0ms	(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x)))
2.0ms	(cos.f64 x)

rewrite76.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
285×	`prod-diff_binary64`
197×	`egg-rr`
104×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	199	33
2	2458	33

Stop Event

1×	node limit

Counts

3 → 197

Calls

3 calls:

71.0ms	(cos.f64 x)
71.0ms	(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x)))
71.0ms	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-neg_binary64`
320×	`distribute-rgt-neg-in_binary64`
309×	`distribute-lft-neg-in_binary64`
297×	`sub-neg_binary64`
294×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	918
1	247	892
2	728	845
3	2849	834

Stop Event

1×	node limit

Counts

249 → 237

prune198.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	237	9	246

Error

0.1b

Counts

246 → 9

Alt Table

Status	Error	Program
	24.5b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	24.5b	(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 x))) 1) (sin.f64 eps) (neg.f64 (sin.f64 x))))
	29.4b	(-.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (cos.f64 x))) (.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
	27.4b	(fma.f64 (sin.f64 x) (cos.f64 eps) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (pow.f64 (sin.f64 x) 2)) (fma.f64 (cos.f64 x) (sin.f64 eps) (sin.f64 x))))
	32.3b	(-.f64 (log.f64 (.f64 (exp.f64 (.f64 (cos.f64 x) (sin.f64 eps))) (exp.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))) (sin.f64 x))
	24.5b	(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
▶	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	43.3b	(fma.f64 (sqrt.f64 (sin.f64 x)) (*.f64 (sqrt.f64 (sin.f64 x)) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))
	25.1b	(fma.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 2) (*.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps)) (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (sin.f64 x))))

Compiler

Compiled 6685 to 1964 computations (70.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 x)
✓	0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
✓	0.1b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
✓	1.3b	(+.f64 (cos.f64 eps) -1)

series32.0ms (0.4%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
13.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
3.0ms	(+.f64 (cos.f64 eps) -1)

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`prod-diff_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
189×	`fma-def_binary64`
146×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	227	36
2	2927	30

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

51.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
51.0ms	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
51.0ms	(+.f64 (cos.f64 eps) -1)

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

630×	`fma-def_binary64`
575×	`sub-neg_binary64`
424×	`cancel-sign-sub-inv_binary64`
273×	`associate-l_binary64`
257×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1102
1	327	1032
2	1070	986
3	4767	986

Stop Event

1×	node limit

Counts

173 → 157

prune240.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	171	11	182
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	178	13	191

Error

0.0b

Counts

191 → 13

Alt Table

Status	Error	Program
	13.9b	(fma.f64 (sin.f64 eps) (pow.f64 (sqrt.f64 (cos.f64 x)) 2) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (cbrt.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 3)))
	24.5b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	0.4b	(fma.f64 (sin.f64 eps) (log.f64 (exp.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	29.4b	(-.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (cos.f64 x))) (.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
	0.4b	(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
▶	0.3b	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
	0.4b	(fma.f64 (sin.f64 eps) (.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (cbrt.f64 (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 eps) -1) 3))))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (/.f64 1 (+.f64 (cos.f64 eps) 1)))))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 eps) 2) (-.f64 1 (*.f64 (cos.f64 eps) -1)))))))

Compiler

Compiled 3808 to 1723 computations (54.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 x)
✓	0.1b	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
✓	0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
	1.3b	(+.f64 (cos.f64 eps) -1)

series28.0ms (0.4%)

Counts

2 → 40

Calls

2 calls:

16.0ms	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
12.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
323×	`prod-diff_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
182×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	221	27
2	2718	27

Stop Event

1×	node limit

Counts

2 → 48

Calls

2 calls:

52.0ms	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
52.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

370×	`distribute-rgt-neg-in_binary64`
363×	`distribute-lft-neg-in_binary64`
332×	`fma-def_binary64`
293×	`sub-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	782
1	245	752
2	788	692
3	3188	686

Stop Event

1×	node limit

Counts

88 → 78

prune213.0ms (2.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	147	14	161

Error

0.0b

Counts

161 → 14

Alt Table

Status	Error	Program
	13.9b	(fma.f64 (sin.f64 eps) (pow.f64 (sqrt.f64 (cos.f64 x)) 2) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (cbrt.f64 (pow.f64 (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)) 3)))
	1.4b	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) 3))
	29.4b	(-.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (cos.f64 x))) (.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
	0.4b	(fma.f64 (sin.f64 eps) (cbrt.f64 (pow.f64 (cos.f64 x) 3)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
✓	0.3b	(fma.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
	0.4b	(fma.f64 (sin.f64 eps) (.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 2)) (cbrt.f64 (cos.f64 x))) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.4b	(fma.f64 (sin.f64 eps) (log.f64 (exp.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	0.3b	(fma.f64 (sin.f64 eps) (expm1.f64 (log1p.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
	18.0b	(.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x)))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (+.f64 (cos.f64 eps) -1) (sin.f64 x))) 2)))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 eps) -1) 3))))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (/.f64 1 (+.f64 (cos.f64 eps) 1)))))
	0.3b	(fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 eps) 2) (-.f64 1 (*.f64 (cos.f64 eps) -1)))))))

Compiler

Compiled 3029 to 1438 computations (52.5% saved)

regimes1.2s (15.3%)

Accuracy

Total 0.3b remaining (82.7%)

Threshold costs 0.3b (82.7%)

Counts

205 → 1

Compiler

Compiled 10276 to 7023 computations (31.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	15	23

Stop Event

1×

saturated

end240.0ms (3.1%)

Compiler: Compiled 307 to 222 computations (27.7% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Details

analyze1.0ms (0%)

sample5.0s (64.2%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series10.0ms (0.1%)

rewrite58.0ms (0.7%)

simplify33.0ms (0.4%)

prune164.0ms (2.1%)

localize10.0ms (0.1%)

series31.0ms (0.4%)

rewrite76.0ms (1%)

simplify42.0ms (0.5%)

prune198.0ms (2.5%)

localize10.0ms (0.1%)

series32.0ms (0.4%)

rewrite53.0ms (0.7%)

simplify52.0ms (0.7%)

prune240.0ms (3.1%)

localize10.0ms (0.1%)

series28.0ms (0.4%)

rewrite53.0ms (0.7%)

simplify40.0ms (0.5%)

prune213.0ms (2.7%)

regimes1.2s (15.3%)

simplify2.0ms (0%)

end240.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11