Details

sample103.0ms

Algorithm

intervals

Results

53.0ms	53×	body	1280	valid
17.0ms	36×	body	640	valid
13.0ms	143×	body	80	valid
5.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize13.0ms

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)))
13.7b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite534.0ms

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:

86.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
38.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
405.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series209.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
94.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify56.0ms

Counts: 88 → 88

prune313.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
0.2b	(/ (sin x) (sin (* (/ 1.0 2.0) x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite129.0ms

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:

54.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
23.0ms	(/ (sin x) (sin (* (/ 1.0 2.0) x)))
44.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
50.0ms	(/ (sin x) (sin (* (/ 1.0 2.0) x)))
50.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify67.0ms

Counts: 119 → 119

prune421.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* (/ 1.0 2.0) x)) 3.0)
0.1b	(/ (* 8.0 (/ (sin (* (/ 1.0 2.0) x)) 3.0)) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
0.2b	(/ (sin x) (sin (* (/ 1.0 2.0) x)))

rewrite90.0ms

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:

19.0ms	(/ (sin (* (/ 1.0 2.0) x)) 3.0)
44.0ms	(/ (* 8.0 (/ (sin (* (/ 1.0 2.0) x)) 3.0)) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
20.0ms	(/ (sin x) (sin (* (/ 1.0 2.0) x)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (sin (* (/ 1.0 2.0) x)) 3.0)
106.0ms	(/ (* 8.0 (/ (sin (* (/ 1.0 2.0) x)) 3.0)) (/ (sin x) (sin (* (/ 1.0 2.0) x))))
60.0ms	(/ (sin x) (sin (* (/ 1.0 2.0) x)))

simplify68.0ms

Counts: 114 → 114

prune325.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin x)) (cbrt (sin x)))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))
0.6b	(cbrt (sin x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

22.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))
2.0ms	(cbrt (sin x))

series604.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (cbrt (sin x)) (cbrt (sin x)))
112.0ms	(cbrt (sin x))
151.0ms	(cbrt (sin x))
170.0ms	(cbrt (sin x))

simplify62.0ms

Counts: 85 → 85

prune371.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify10.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.3s	1254×	body	640	valid
1.3s	1466×	body	1280	valid
411.0ms	4344×	body	80	valid
245.0ms	617×	body	320	valid
70.0ms	319×	body	160	valid