Details

sample55.0ms

Algorithm

intervals

Results

17.0ms	39×	body	1280	valid
12.0ms	43×	body	640	valid
9.0ms	146×	body	80	valid
7.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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: 15.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.5b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite27.0ms

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×	`associate-/r*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 79

Calls

3 calls:

8.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series170.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
78.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune209.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 0.1b

Counts

89 → 9

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite25.0ms

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×	`associate-r` `add-log-exp`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin x) (sin (* 0.5 x)))
80.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify64.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5002	956

prune281.0ms

Filtered

119 candidates to 90 candidates (75.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Merged error: 0b

Counts

128 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 105

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
13.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

series155.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin (* 0.5 x)) 3.0)
38.0ms	(/ (sin x) (sin (* 0.5 x)))
77.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

simplify63.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	504	1132
1	2553	976
2	5002	950

prune443.0ms

Filtered

114 candidates to 85 candidates (74.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Merged error: 0b

Counts

122 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
96×	`cbrt-prod`
79×	`add-sqr-sqrt`
74×	`add-cube-cbrt` `*-un-lft-identity`
52×	`unpow-prod-down` `cube-prod`
35×	`associate-/r*`
21×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-l`
10×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
4×	`cube-mult` `unpow3` `prod-exp` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cube-div` `pow-unpow` `associate-r`
2×	`cbrt-div` `associate-*l/` `pow-exp` `rem-cube-cbrt` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `clear-num` `associate-/r/` `-commutative` `rem-cbrt-cube` `associate-/l/` `associate-/l`

Counts

4 → 209

Calls

4 calls:

25.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (cbrt (pow (/ (sin x) (sin (* x 0.5))) 3)))
13.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
9.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (cbrt (pow (/ (sin x) (sin (* x 0.5))) 3)))
43.0ms	(cbrt (pow (/ (sin x) (sin (* x 0.5))) 3))
81.0ms	(pow (/ (sin x) (sin (* x 0.5))) 3)
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify100.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	733	2304
1	3652	2063
2	5001	2035

prune417.0ms

Filtered

221 candidates to 115 candidates (52.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	221	8	229

Merged error: 0b

Counts

229 → 8

regimes61.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

725.0ms	1521×	body	1280	valid
389.0ms	1307×	body	640	valid
270.0ms	4277×	body	80	valid
124.0ms	598×	body	320	valid
42.0ms	297×	body	160	valid

Details

sample55.0ms

simplify16.0ms

prune2.0ms

localize10.0ms

rewrite27.0ms

series170.0ms

simplify54.0ms

prune209.0ms

localize13.0ms

rewrite25.0ms

series163.0ms

simplify64.0ms

prune281.0ms

localize10.0ms

rewrite24.0ms

series155.0ms

simplify63.0ms

prune443.0ms

localize15.0ms

rewrite76.0ms

series252.0ms

simplify100.0ms

prune417.0ms

regimes61.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

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