Details

analyze780.0ms (13.6%)

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 17 to 15 computations (11.8% saved)

sample64.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	66×	body	1024	valid
14.0ms	140×	body	128	valid
8.0ms	30×	body	512	valid
4.0ms	20×	body	256	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	50	22
1	50	22

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.1b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
0.3b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
14.9b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
10×	`add-sqr-sqrt_binary64_16127` `pow1_binary64_16166`
8×	`*-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140`
7×	`cbrt-unprod_binary64_16138` `prod-exp_binary64_16154`
6×	`associate-l_binary64_16046`
4×	`pow-prod-down_binary64_16176` `associate-r_binary64_16045`
3×	`div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `add-log-exp_binary64_16144` `times-frac_binary64_16111` `associate-/r*_binary64_16049`
2×	`*-commutative_binary64_16036`
1×	`div-inv_binary64_16102` `unswap-sqr_binary64_16073` `frac-2neg_binary64_16116` `associate-/l*_binary64_16050` `clear-num_binary64_16104`

Counts

3 → 59

Calls

3 calls:

8.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
4.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series103.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
28.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
16.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4934	1066
1	4934	1066

prune98.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	12	69

Error

0.1b

Counts

69 → 12

Compiler

Compiled 1364 to 1044 computations (23.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
14×	`add-sqr-sqrt_binary64_16127`
10×	`-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140` `associate-r*_binary64_16045`
7×	`pow1_binary64_16166`
6×	`cbrt-unprod_binary64_16138` `times-frac_binary64_16111` `prod-exp_binary64_16154` `associate-l_binary64_16046`
4×	`div-exp_binary64_16156` `cbrt-undiv_binary64_16139`
3×	`add-log-exp_binary64_16144` `associate-/r*_binary64_16049`
2×	`div-inv_binary64_16102` `unswap-sqr_binary64_16073` `pow-prod-down_binary64_16176` `*-commutative_binary64_16036`
1×	`associate-r/_binary64_16047` `frac-2neg_binary64_16116` `associate-/l_binary64_16050` `clear-num_binary64_16104`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
5.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

series117.0ms (2%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
40.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
16.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4958	1245
1	4958	1245

prune103.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Error

0.0b

Counts

87 → 14

Compiler

Compiled 1628 to 1229 computations (24.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))
0.3b	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
0.3b	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
20×	`add-sqr-sqrt_binary64_16127`
19×	`associate-r_binary64_16045`
14×	`*-un-lft-identity_binary64_16105` `cbrt-unprod_binary64_16138` `add-cube-cbrt_binary64_16140` `prod-exp_binary64_16154`
13×	`pow1_binary64_16166`
7×	`sqrt-prod_binary64_16121` `associate-l_binary64_16046`
6×	`div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `times-frac_binary64_16111`
5×	`pow-prod-down_binary64_16176`
4×	`add-log-exp_binary64_16144`
3×	`unswap-sqr_binary64_16073` `-commutative_binary64_16036` `associate-/r_binary64_16049`
2×	`div-inv_binary64_16102`
1×	`associate-r/_binary64_16047` `frac-2neg_binary64_16116` `associate-/l_binary64_16050` `clear-num_binary64_16104`

Counts

4 → 95

Calls

4 calls:

12.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
9.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
8.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

series238.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
75.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
38.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
24.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4911	1758
1	4911	1758

prune141.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	6	7	13
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Error

0.0b

Counts

121 → 11

Compiler

Compiled 2313 to 1800 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x))))
0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
0.4b	(/.f64 8/3 (sin.f64 x))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_16127`
20×	`*-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140`
19×	`add-exp-log_binary64_16143` `times-frac_binary64_16111` `add-cbrt-cube_binary64_16141`
14×	`associate-r_binary64_16045`
10×	`pow1_binary64_16166`
7×	`cbrt-unprod_binary64_16138` `prod-exp_binary64_16154`
6×	`associate-l_binary64_16046`
4×	`pow-prod-down_binary64_16176`
3×	`associate-r/_binary64_16047` `div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `add-log-exp_binary64_16144` `associate-/r_binary64_16049` `associate-/l*_binary64_16050`
2×	`div-inv_binary64_16102` `unswap-sqr_binary64_16073` `*-commutative_binary64_16036`
1×	`frac-2neg_binary64_16116` `clear-num_binary64_16104`

Counts

3 → 80

Calls

3 calls:

9.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x))))
8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
3.0ms	(/.f64 8/3 (sin.f64 x))

series148.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x))))
48.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 8/3 (sin.f64 x)))
21.0ms	(/.f64 8/3 (sin.f64 x))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5192	1405

prune95.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	89	11	100

Error

0.0b

Counts

100 → 11

Compiler

Compiled 1651 to 1191 computations (27.9% saved)

regimes212.0ms (3.7%)

Accuracy

Total 0.4b remaining (98.4%)

Threshold costs 0.4b (98.4%)

Compiler

Compiled 2104 to 1806 computations (14.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample3.0s (53%)

Algorithm

1×

intervals

Results

857.0ms	2027×	body	1024	valid
460.0ms	4506×	body	128	valid
267.0ms	948×	body	512	valid
105.0ms	517×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 1086 to 934 computations (14% saved)

Details

analyze780.0ms (13.6%)

sample64.0ms (1.1%)

simplify98.0ms (1.7%)

prune8.0ms (0.1%)

localize9.0ms (0.2%)

rewrite24.0ms (0.4%)

series103.0ms (1.8%)

simplify90.0ms (1.6%)

prune98.0ms (1.7%)

localize11.0ms (0.2%)

rewrite23.0ms (0.4%)

series117.0ms (2%)

simplify75.0ms (1.3%)

prune103.0ms (1.8%)

localize11.0ms (0.2%)

rewrite44.0ms (0.8%)

series238.0ms (4.1%)

simplify92.0ms (1.6%)

prune141.0ms (2.5%)

localize8.0ms (0.1%)

rewrite26.0ms (0.5%)

series148.0ms (2.6%)

simplify75.0ms (1.3%)

prune95.0ms (1.7%)

regimes212.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (53%)

Profiling