Details

sample63.0ms

Algorithm

intervals

Results

22.0ms	45×	body	1280	valid
17.0ms	43×	body	640	valid
10.0ms	148×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	5×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 17.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
17.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

Calls

3 calls:

11.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
87.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify68.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	412	862
1	2127	656
2	5001	637

prune271.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	79	15	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	15	95

Merged error: 0.1b

Counts

95 → 15

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 116

Calls

3 calls:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
5.0ms	(/ (sin x) (sin (* 0.5 x)))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify83.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	550	1204
1	2727	1016
2	5001	992

prune352.0ms

Filtered

125 candidates to 96 candidates (76.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	12	2	14
Picked	1	0	1
Done	0	0	0
Total	131	9	140

Merged error: 0b

Counts

140 → 9

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
0.2b	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
0.2b	(/ (sin x) (sin (* 0.5 x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
20×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative`

Counts

3 → 91

Calls

3 calls:

9.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
10.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
5.0ms	(/ (sin x) (sin (* 0.5 x)))

series190.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
83.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
47.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	433	924
1	2228	739
2	5002	723

prune259.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	100	9	109

Merged error: 0b

Counts

109 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
0.4b	(pow (/ (sin x) (sin (* x 0.5))) 3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `times-frac`
50×	`add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-l`
7×	`pow1`
6×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-r` `associate-/r` `associate-/l`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `rem-cbrt-cube`

Counts

4 → 155

Calls

4 calls:

5.0ms	(/ (sin x) (sin (* x 0.5)))
6.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
6.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)

series230.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (sin x) (sin (* x 0.5)))
43.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
91.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)

simplify86.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	541	1314
1	2355	1210
2	5002	1199

prune345.0ms

Filtered

167 candidates to 100 candidates (59.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	167	9	176

Merged error: 0b

Counts

176 → 9

regimes42.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

761.0ms	1548×	body	1280	valid
391.0ms	1270×	body	640	valid
320.0ms	4258×	body	80	valid
131.0ms	611×	body	320	valid
54.0ms	313×	body	160	valid

Details

sample63.0ms

simplify28.0ms

prune3.0ms

localize12.0ms

rewrite33.0ms

series188.0ms

simplify68.0ms

prune271.0ms

localize15.0ms

rewrite28.0ms

series173.0ms

simplify83.0ms

prune352.0ms

localize15.0ms

rewrite27.0ms

series190.0ms

simplify75.0ms

prune259.0ms

localize15.0ms

rewrite30.0ms

series230.0ms

simplify86.0ms

prune345.0ms

regimes42.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

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