Details

analyze1.2s (14.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample3.5s (43.2%)

Results

1.9s	2038×	body	1024	valid
855.0ms	4635×	body	128	valid
542.0ms	1060×	body	512	valid
185.0ms	518×	body	256	valid
11.0ms	5×	body	2048	valid

Compiler

Compiled 53 to 44 computations (17% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
9×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	20	22
2	31	22
3	41	22
4	49	22
5	51	22
6	50	22

prune3.0ms (0%)

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

14.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

Compiler

Compiled 61 to 48 computations (21.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
✓	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
✓	13.9b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

series27.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

14.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
3.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
2.0ms	(sin.f64 (*.f64 x 1/2))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

6.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
3.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
1.0ms	(sin.f64 (*.f64 x 1/2))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

672×	`times-frac_binary64`
637×	`associate-/l*_binary64`
499×	`fma-def_binary64`
421×	`associate-l_binary64`
300×	`cancel-sign-sub-inv_binary64`

Counts

122 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2170
1	382	1712
2	1149	1695
3	4046	1688
4	4931	1688

prune171.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	141	16	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	16	158

Error

0.1b

Counts

158 → 16

Alt Table

Status	Error	Program
	14.1b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (/.f64 1 (sin.f64 x)))
	14.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	14.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	14.1b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))))
	34.4b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
	14.1b	(/.f64 (.f64 (log1p.f64 (expm1.f64 (sin.f64 (.f64 x 1/2)))) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
	19.6b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 (.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))
▶	1.4b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	14.1b	(/.f64 (log1p.f64 (expm1.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	39.1b	(.f64 (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))) (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
	14.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	25.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))) (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))) (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (sin.f64 x))))
	37.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sqrt.f64 (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (sin.f64 (.f64 x 1/2))))) (sin.f64 x))
	27.2b	(log.f64 (exp.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))))
	31.6b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
	26.9b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (expm1.f64 (log1p.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2)))))) (sin.f64 x))

Compiler

Compiled 3740 to 2794 computations (25.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))
✓	0.4b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))
✓	0.6b	(cbrt.f64 (sin.f64 x))

series647.0ms (7.9%)

Counts

4 → 48

Calls

4 calls:

235.0ms	(*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))
208.0ms	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))
189.0ms	(cbrt.f64 (sin.f64 x))
14.0ms	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64`
34×	`add-sqr-sqrt_binary64`
31×	`add-cbrt-cube_binary64`
28×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`

Counts

4 → 135

Calls

4 calls:

11.0ms	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
6.0ms	(/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))
5.0ms	(*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))
1.0ms	(cbrt.f64 (sin.f64 x))

simplify160.0ms (2%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
396×	`associate-/r/_binary64`
275×	`fma-neg_binary64`
221×	`log-prod_binary64`
176×	`times-frac_binary64`

Counts

183 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4783
1	599	3033
2	2271	2959
3	3791	2946
4	4890	2946
5	4900	2946

prune221.0ms (2.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	268	7	275
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	271	20	291

Error

0.0b

Counts

291 → 20

Alt Table

Status	Error	Program
	14.1b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (/.f64 1 (sin.f64 x)))
	14.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	1.5b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (cbrt.f64 (sin.f64 x))))))
	14.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	14.1b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))))
	27.2b	(log.f64 (exp.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))))
	14.1b	(pow.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x))) 1)
	34.4b	(+.f64 (.f64 1/18 (pow.f64 x 3)) (.f64 2/3 x))
	14.1b	(/.f64 (.f64 (log1p.f64 (expm1.f64 (sin.f64 (.f64 x 1/2)))) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
✓	1.4b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
▶	0.6b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
	14.1b	(/.f64 (log1p.f64 (expm1.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	39.1b	(.f64 (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))) (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
	14.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	37.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 8/3 (sqrt.f64 (sin.f64 (.f64 x 1/2)))) (sqrt.f64 (sin.f64 (.f64 x 1/2))))) (sin.f64 x))
	1.7b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (sin.f64 x))) (cbrt.f64 (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (cbrt.f64 (sin.f64 x))))))
	1.1b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (.f64 8/3 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (/.f64 1 (sin.f64 x))))))
	2.1b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 x))) 5) (cbrt.f64 (cbrt.f64 (sin.f64 x))))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	31.6b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) (.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (sin.f64 x))) 8/3))
	1.4b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))))

Compiler

Compiled 8945 to 5032 computations (43.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sin.f64 x))
	0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
✓	0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
✓	0.4b	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2))))

series29.0ms (0.4%)

Counts

3 → 28

Calls

3 calls:

15.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
8.0ms	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2))))
6.0ms	(/.f64 1 (sin.f64 x))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log_binary64`
35×	`add-cbrt-cube_binary64`
33×	`prod-exp_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`

Counts

3 → 104

Calls

3 calls:

9.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))
7.0ms	(.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2))))
3.0ms	(/.f64 1 (sin.f64 x))

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/r*_binary64`
543×	`associate-/l/_binary64`
454×	`associate-/r/_binary64`
429×	`fma-def_binary64`
351×	`*-commutative_binary64`

Counts

132 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2438
1	360	1915
2	1113	1909
3	2473	1902
4	4763	1902
5	4975	1902
6	4936	1902

prune235.0ms (2.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	8	10	18
Picked	1	0	1
Done	1	0	1
Total	195	16	211

Error

0.0b

Counts

211 → 16

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))
	0.8b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))))))
	14.1b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (/.f64 1 (sin.f64 x)))
	14.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	1.5b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (cbrt.f64 (sin.f64 x))))))
	14.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	14.1b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) (.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))))
	2.1b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 x))) 5) (cbrt.f64 (cbrt.f64 (sin.f64 x))))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	14.1b	(/.f64 (log1p.f64 (expm1.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	39.1b	(.f64 (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))) (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
	14.2b	(/.f64 (expm1.f64 (log1p.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	0.5b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) 3)))
	29.7b	(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 1 (sin.f64 x)) (.f64 8/3 (sin.f64 (*.f64 x 1/2))))))
	1.4b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))))
	1.3b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (cbrt.f64 (/.f64 1 (sin.f64 x)))) (.f64 (cbrt.f64 (/.f64 1 (sin.f64 x))) (.f64 8/3 (sin.f64 (*.f64 x 1/2))))))

Compiler

Compiled 4978 to 3731 computations (25.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 (*.f64 x 1/2))
✓	0.3b	(.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
✓	0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))
✓	0.4b	(/.f64 8/3 (sin.f64 x))

series38.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

24.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))
8.0ms	(.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
6.0ms	(/.f64 8/3 (sin.f64 x))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 86

Calls

3 calls:

6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))
5.0ms	(.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))
4.0ms	(/.f64 8/3 (sin.f64 x))

simplify127.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-/r*_binary64`
550×	`fma-def_binary64`
448×	`*-commutative_binary64`
417×	`associate-/l/_binary64`
300×	`associate-*l/_binary64`

Counts

114 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2098
1	370	1766
2	963	1760
3	2275	1753
4	3899	1753
5	4756	1753
6	4975	1753
7	4915	1753

prune180.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	181	4	185
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	187	14	201

Error

0.0b

Counts

201 → 14

Alt Table

Status	Error	Program
	14.1b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (*.f64 x 1/2)))) (/.f64 1 (sin.f64 x)))
	14.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x)))) (cbrt.f64 (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))))
	14.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sqrt.f64 8/3) (.f64 (sqrt.f64 8/3) (sin.f64 (*.f64 x 1/2))))) (sin.f64 x))
	31.6b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (.f64 (/.f64 (sqrt.f64 8/3) (sqrt.f64 (sin.f64 x))) (sin.f64 (*.f64 x 1/2)))))
	14.1b	(/.f64 1 (/.f64 (sin.f64 x) (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2))))
	1.7b	(.f64 (sin.f64 (.f64 x 1/2)) (log1p.f64 (expm1.f64 (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))))
	1.4b	(.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))) (.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) (cbrt.f64 (sin.f64 (.f64 x 1/2)))))
	29.6b	(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))))
	2.1b	(.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 x))) 5) (cbrt.f64 (cbrt.f64 (sin.f64 x))))) (/.f64 (.f64 8/3 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (sin.f64 x))))
	14.1b	(/.f64 (log1p.f64 (expm1.f64 (.f64 8/3 (pow.f64 (sin.f64 (.f64 x 1/2)) 2)))) (sin.f64 x))
	39.1b	(.f64 (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 2) (sin.f64 x)))) (sqrt.f64 (.f64 8/3 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 2) (sin.f64 x)))))
	0.5b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (.f64 8/3 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x))) 3)))
	1.4b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (/.f64 (.f64 8/3 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (sin.f64 x)))))
	0.7b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2)))) (.f64 (/.f64 8/3 (sin.f64 x)) (sin.f64 (.f64 x 1/2))))))

Compiler

Compiled 4058 to 2970 computations (26.8% saved)

regimes1.0s (12.4%)

Accuracy

Total 0.5b remaining (89.8%)

Threshold costs 0.5b (89.8%)

Counts

329 → 1

Compiler

Compiled 14136 to 11070 computations (21.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	12	22
2	12	22

end258.0ms (3.2%)

Compiler: Compiled 367 to 286 computations (22.1% saved)

Details

analyze1.2s (14.4%)

sample3.5s (43.2%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series27.0ms (0.3%)

rewrite19.0ms (0.2%)

simplify87.0ms (1.1%)

prune171.0ms (2.1%)

localize13.0ms (0.2%)

series647.0ms (7.9%)

rewrite33.0ms (0.4%)

simplify160.0ms (2%)

prune221.0ms (2.7%)

localize8.0ms (0.1%)

series29.0ms (0.4%)

rewrite28.0ms (0.3%)

simplify115.0ms (1.4%)

prune235.0ms (2.9%)

localize11.0ms (0.1%)

series38.0ms (0.5%)

rewrite20.0ms (0.2%)

simplify127.0ms (1.6%)

prune180.0ms (2.2%)

regimes1.0s (12.4%)

simplify2.0ms (0%)

end258.0ms (3.2%)

Profiling