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)

sample5.4s (67.2%)

Results

2.6s	3661×	body	1024	valid
1.7s	1287×	body	2048	valid
651.0ms	1426×	body	512	valid
224.0ms	1285×	body	128	valid
160.0ms	595×	body	256	valid
6.0ms	2×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify13.0ms (0.2%)

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

40.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	40.0b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 x)
✓	1.4b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	4.1b	(sin.f64 (+.f64 x eps))

series15.0ms (0.2%)

Counts

3 → 52

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))
2.0ms	(sin.f64 x)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 51

Calls

3 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	(sin.f64 (+.f64 x eps))
1.0ms	(sin.f64 x)

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1023×	`fma-neg_binary64`
545×	`fma-def_binary64`
414×	`cancel-sign-sub-inv_binary64`
330×	`sub-neg_binary64`
259×	`distribute-rgt-neg-in_binary64`

Counts

103 → 110

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1361
1	342	1285
2	1084	1214
3	2734	1207
4	4586	1200
5	4987	1200
6	4830	1200

prune98.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Error

0.3b

Counts

111 → 3

Alt Table

Status	Error	Program
▶	25.6b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	29.2b	(fma.f64 eps (cos.f64 x) (fma.f64 (sin.f64 x) (fma.f64 1/24 (pow.f64 eps 4) (.f64 (.f64 eps eps) -1/2)) (.f64 (.f64 (cos.f64 x) (pow.f64 eps 3)) -1/6)))
	25.6b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

Compiler

Compiled 1898 to 598 computations (68.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
✓	0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
✓	0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
✓	3.0b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series55.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

20.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
15.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
10.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
9×	`prod-diff_binary64`

Counts

4 → 87

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
4.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
3.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
3.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

simplify155.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

418×	`fma-neg_binary64`
276×	`distribute-rgt-in_binary64`
249×	`distribute-rgt-neg-in_binary64`
245×	`distribute-lft-in_binary64`
226×	`associate-r_binary64`

Counts

159 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3009
1	616	2802
2	2190	2695
3	4798	2695
4	4972	2695
5	4911	2695

prune208.0ms (2.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	175	14	189
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	177	15	192

Error

0.1b

Counts

192 → 15

Alt Table

Status	Error	Program
	26.0b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) 3)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	53.9b	(.f64 (+.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))))) (-.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))) (sqrt.f64 (sin.f64 x))))
	25.6b	(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
	25.8b	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
	26.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	28.1b	(/.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))))
	29.2b	(fma.f64 eps (cos.f64 x) (fma.f64 (sin.f64 x) (fma.f64 1/24 (pow.f64 eps 4) (.f64 (.f64 eps eps) -1/2)) (.f64 (.f64 (cos.f64 x) (pow.f64 eps 3)) -1/6)))
	26.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
	26.3b	(+.f64 (fma.f64 1 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (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))))))
	26.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (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))))))
	4.1b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
▶	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	28.1b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))))
	1.8b	(.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)))))
	23.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))

Compiler

Compiled 5509 to 1566 computations (71.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
✓	0.2b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.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)))
✓	1.9b	(+.f64 (cos.f64 eps) -1)

series52.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

18.0ms	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
18.0ms	(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))
2.0ms	(+.f64 (cos.f64 eps) -1)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`

Counts

4 → 65

Calls

4 calls:

7.0ms	(*.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)))
0.0ms	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

simplify103.0ms (1.3%)

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

149 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2724
1	476	2470
2	1511	2415
3	4582	2415
4	5296	2415

prune219.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	136	7	143
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	145	13	158

Error

0.1b

Counts

158 → 13

Alt Table

Status	Error	Program
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))))))
	26.0b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) 3)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	53.9b	(.f64 (+.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))))) (-.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))) (sqrt.f64 (sin.f64 x))))
	26.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	28.1b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 -1/2 (.f64 eps eps) (*.f64 1/24 (pow.f64 eps 4)))))))
▶	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	28.1b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))))
	23.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	4.1b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	1.8b	(log1p.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3))))))

Compiler

Compiled 3822 to 1923 computations (49.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
✓	0.2b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
✓	0.2b	(fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	1.9b	(+.f64 (cos.f64 eps) -1)

series36.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

18.0ms

(fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

18.0ms

(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

0.0ms

(fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

0.0ms

(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-neg_binary64`
353×	`distribute-rgt-in_binary64`
339×	`distribute-lft-in_binary64`
246×	`distribute-rgt-neg-in_binary64`
237×	`distribute-lft-neg-in_binary64`

Counts

69 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1588
1	176	1418
2	493	1406
3	1728	1400
4	4812	1400
5	5058	1400

prune218.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	143	13	156

Error

0.1b

Counts

156 → 13

Alt Table

Status	Error	Program
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1)))))))
	26.0b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) 3)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	53.9b	(.f64 (+.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))))) (-.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))) (sqrt.f64 (sin.f64 x))))
	26.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	28.1b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (fma.f64 -1/2 (.f64 eps eps) (*.f64 1/24 (pow.f64 eps 4)))))))
✓	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	28.1b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))))
	23.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	4.1b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))))
	1.8b	(log1p.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))))))
	0.6b	(log1p.f64 (expm1.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3))))))

Compiler

Compiled 3702 to 2002 computations (45.9% saved)

regimes916.0ms (11.4%)

Accuracy

Total 0.3b remaining (71.8%)

Threshold costs 0.3b (71.8%)

Counts

214 → 1

Compiler

Compiled 13302 to 7862 computations (40.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	18	19
2	17	19

end244.0ms (3.1%)

Compiler: Compiled 403 to 214 computations (46.9% 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

analyze1.0ms (0%)

sample5.4s (67.2%)

simplify13.0ms (0.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series15.0ms (0.2%)

rewrite11.0ms (0.1%)

simplify104.0ms (1.3%)

prune98.0ms (1.2%)

localize12.0ms (0.2%)

series55.0ms (0.7%)

rewrite24.0ms (0.3%)

simplify155.0ms (1.9%)

prune208.0ms (2.6%)

localize13.0ms (0.2%)

series52.0ms (0.7%)

rewrite13.0ms (0.2%)

simplify103.0ms (1.3%)

prune219.0ms (2.7%)

localize17.0ms (0.2%)

series36.0ms (0.5%)

rewrite2.0ms (0%)

simplify84.0ms (1%)

prune218.0ms (2.7%)

regimes916.0ms (11.4%)

simplify2.0ms (0%)

end244.0ms (3.1%)

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