Details

analyze2.0ms (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 (68.8%)

Results

2.5s	3614×	body	1024	valid
1.6s	1273×	body	2048	valid
567.0ms	1395×	body	512	valid
197.0ms	1344×	body	128	valid
167.0ms	628×	body	256	valid
6.0ms	2×	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`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

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

37.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.8b	(-.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))
✓	2.9b	(sin.f64 (+.f64 x eps))

series11.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	(sin.f64 (+.f64 x eps))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
483×	`fma-def_binary64`
351×	`cancel-sign-sub-inv_binary64`
291×	`sub-neg_binary64`
284×	`associate-+l-_binary64`

Counts

90 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1256
1	297	1180
2	960	1116
3	2426	1108
4	4776	1108
5	4953	1108
6	4839	1108

prune96.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

0.2b

Counts

93 → 3

Alt Table

Status	Error	Program
	32.5b	(fma.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) -1/2)))
▶	21.7b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	21.7b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

Compiler

Compiled 1657 to 503 computations (69.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
✓	0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
✓	0.2b	(*.f64 (cos.f64 x) (sin.f64 eps))
✓	2.6b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

series48.0ms (0.7%)

Counts

4 → 64

Calls

4 calls:

18.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
11.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
10.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
9.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
5.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
3.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-neg_binary64`
429×	`distribute-rgt-in_binary64`
243×	`associate-r_binary64`
235×	`associate-l_binary64`
225×	`distribute-rgt-neg-in_binary64`

Counts

150 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	2802
1	644	2630
2	2370	2544
3	4765	2537
4	5246	2537

prune178.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	183	9	192
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	185	10	195

Error

0.1b

Counts

195 → 10

Alt Table

Status	Error	Program
	21.8b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 x) (sin.f64 eps)))) (sin.f64 x)))
	22.1b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
	21.7b	(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
	29.0b	(log.f64 (.f64 (exp.f64 (.f64 (sin.f64 x) (cos.f64 eps))) (exp.f64 (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))))
	22.2b	(+.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	32.5b	(fma.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) -1/2)))
	22.5b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) 3)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	20.7b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
▶	0.4b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (.f64 (sin.f64 x) 1)))

Compiler

Compiled 4802 to 1385 computations (71.2% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
✓	0.2b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
✓	1.7b	(+.f64 (cos.f64 eps) -1)

series31.0ms (0.4%)

Counts

3 → 60

Calls

3 calls:

17.0ms	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
12.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.0ms	(+.f64 (cos.f64 eps) -1)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`associate-r_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 54

Calls

3 calls:

5.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
3.0ms	(+.f64 (cos.f64 eps) -1)
0.0ms	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

simplify113.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
629×	`sub-neg_binary64`
442×	`cancel-sign-sub-inv_binary64`
294×	`distribute-rgt-in_binary64`
256×	`distribute-lft-in_binary64`

Counts

114 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1922
1	473	1753
2	1508	1707
3	4579	1707
4	5293	1707

prune178.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Error

0.1b

Counts

141 → 10

Alt Table

Status	Error	Program
	28.9b	(+.f64 (log.f64 (exp.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (.f64 (sin.f64 x) 1)))
	21.8b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 x) (sin.f64 eps)))) (sin.f64 x)))
	22.1b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
	22.2b	(+.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	32.5b	(fma.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) -1/2)))
▶	0.4b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (/.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 (cos.f64 eps) 1))))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (.f64 (sin.f64 x) 1)))
	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	20.7b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	0.5b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (pow.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)) (sin.f64 x)))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (*.f64 (sin.f64 x) 1)))
	21.7b	(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))

Compiler

Compiled 4385 to 2118 computations (51.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 (cos.f64 eps) 1)))
✓	0.4b	(pow.f64 (cos.f64 eps) 3)
✓	0.4b	(+.f64 (cos.f64 eps) 1)
✓	1.4b	(+.f64 -1 (pow.f64 (cos.f64 eps) 3))

series61.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

46.0ms	(/.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 (cos.f64 eps) 1)))
7.0ms	(+.f64 -1 (pow.f64 (cos.f64 eps) 3))
6.0ms	(pow.f64 (cos.f64 eps) 3)
2.0ms	(+.f64 (cos.f64 eps) 1)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 (cos.f64 eps) 1)))
4.0ms	(+.f64 -1 (pow.f64 (cos.f64 eps) 3))
3.0ms	(+.f64 (cos.f64 eps) 1)
3.0ms	(pow.f64 (cos.f64 eps) 3)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
600×	`fma-def_binary64`
317×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-in_binary64`
267×	`distribute-lft-in_binary64`

Counts

134 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2531
1	401	2376
2	1243	2232
3	4081	2232
4	4989	2232

prune278.0ms (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	162	10	172

Error

0.1b

Counts

172 → 10

Alt Table

Status	Error	Program
	28.9b	(+.f64 (log.f64 (exp.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (.f64 (sin.f64 x) 1)))
	21.8b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 x) (sin.f64 eps)))) (sin.f64 x)))
	22.1b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
	22.2b	(+.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cos.f64 eps))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
	32.5b	(fma.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6)) (.f64 (sin.f64 x) (.f64 (.f64 eps eps) -1/2)))
✓	0.4b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (/.f64 (+.f64 -1 (pow.f64 (cos.f64 eps) 3)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 (cos.f64 eps) 1))))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (.f64 (sin.f64 x) 1)))
	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	20.7b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	0.5b	(+.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (pow.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)) (sin.f64 x)))) (fma.f64 (neg.f64 (sin.f64 x)) 1 (*.f64 (sin.f64 x) 1)))
	21.7b	(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))

Compiler

Compiled 7049 to 3566 computations (49.4% saved)

regimes657.0ms (9%)

Accuracy

Total 0.3b remaining (67.9%)

Threshold costs 0.3b (67.9%)

Counts

197 → 1

Compiler

Compiled 12810 to 8057 computations (37.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`distribute-rgt-neg-in_binary64`
1×	`distribute-lft-neg-in_binary64`
1×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	27	34
2	32	34
3	33	34
4	31	34

end200.0ms (2.7%)

Compiler: Compiled 310 to 188 computations (39.4% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze2.0ms (0%)

sample5.0s (68.8%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite11.0ms (0.1%)

simplify95.0ms (1.3%)

prune96.0ms (1.3%)

localize12.0ms (0.2%)

series48.0ms (0.7%)

rewrite23.0ms (0.3%)

simplify108.0ms (1.5%)

prune178.0ms (2.4%)

localize15.0ms (0.2%)

series31.0ms (0.4%)

rewrite10.0ms (0.1%)

simplify113.0ms (1.5%)

prune178.0ms (2.4%)

localize21.0ms (0.3%)

series61.0ms (0.8%)

rewrite19.0ms (0.3%)

simplify99.0ms (1.3%)

prune278.0ms (3.8%)

regimes657.0ms (9%)

simplify3.0ms (0%)

end200.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11