Details

sample55.0ms

Algorithm

intervals

Results

23.0ms	53×	body	1280	valid
11.0ms	38×	body	640	valid
9.0ms	144×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid

simplify21.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize11.0ms

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)))
17.4b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite35.0ms

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:

10.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
11.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
11.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series185.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
84.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify63.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (54.0ms)

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

prune244.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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

rewrite26.0ms

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:

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)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (sin x) (sin (* 0.5 x)))
81.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
43.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify77.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (65.0ms)

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

prune360.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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:

7.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
5.0ms	(/ (sin x) (sin (* 0.5 x)))
9.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series195.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
48.0ms	(/ (sin x) (sin (* 0.5 x)))
85.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	433	924
1	2247	743
2	5001	724

prune284.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (sin x) 3.0)
0.3b	(/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0))
0.4b	(* (/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0)) (sin (* 0.5 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

5.0ms	(* (sin x) 3.0)
7.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0))
10.0ms	(* (/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0)) (sin (* 0.5 x)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (sin x) 3.0)
65.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0))
85.0ms	(* (/ (* 8.0 (sin (* x 0.5))) (* (sin x) 3.0)) (sin (* 0.5 x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	382	750
1	2106	563
2	5003	543

prune192.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes35.0ms

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	15	9
1	17	9
2	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

719.0ms	1506×	body	1280	valid
401.0ms	1281×	body	640	valid
266.0ms	4277×	body	80	valid
127.0ms	617×	body	320	valid
49.0ms	319×	body	160	valid