Details

sample63.0ms

Algorithm

intervals

Results

30.0ms	60×	body	1280	valid
10.0ms	33×	body	640	valid
8.0ms	136×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify26.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

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)))
12.0b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite56.0ms

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:

21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
21.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series201.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
90.0ms	(/ (* (* (/ 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 (59.0ms)

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

prune279.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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

rewrite35.0ms

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:

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

series190.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
53.0ms	(/ (sin x) (sin (* 0.5 x)))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify81.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (68.0ms)

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

prune403.0ms

Filtered

125 candidates to 95 candidates (76.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
0.1b	(* (/ (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	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
10.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))
71.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
46.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	433	924
1	2228	739
2	5001	723

prune313.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0)
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
0.4b	(pow (/ (sin x) (sin (* 0.5 x))) 3)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
70×	`cbrt-prod`
65×	`times-frac`
59×	`add-cube-cbrt` `*-un-lft-identity`
41×	`unpow-prod-down` `cube-prod`
35×	`associate-l`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-r` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 180

Calls

4 calls:

30.0ms	(* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
6.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
6.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

series264.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3)) 3.0)
47.0ms	(/ (sin x) (sin (* 0.5 x)))
53.0ms	(cbrt (pow (/ (sin x) (sin (* 0.5 x))) 3))
94.0ms	(pow (/ (sin x) (sin (* 0.5 x))) 3)

simplify86.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	468	1572
1	2163	1464
2	5001	1451

prune525.0ms

Filtered

192 candidates to 112 candidates (58.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	11
1	20	11
2	20	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

763.0ms	1512×	body	1280	valid
392.0ms	1218×	body	640	valid
270.0ms	4302×	body	80	valid
139.0ms	629×	body	320	valid
49.0ms	339×	body	160	valid