Details

sample124.0ms

Algorithm

intervals

Results

48.0ms	44×	body	640	valid
35.0ms	46×	body	1280	valid
13.0ms	132×	body	80	valid
7.0ms	20×	body	320	valid
4.0ms	14×	body	160	valid

simplify441.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize26.0ms

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)))
15.1b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite219.0ms

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:

72.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
108.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series289.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
75.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
116.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.7s

Counts

94 → 94

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	169	1554
1	405	1349
2	1480	1080
done	5000	1080

prune442.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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)))

rewrite104.0ms

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:

13.0ms	(/ (sin x) (sin (* 0.5 x)))
43.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series247.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(/ (sin x) (sin (* 0.5 x)))
113.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
51.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.5s

Counts

125 → 125

Iterations

Useful iterations: 2 (386.0ms)

Iter	Nodes	Cost
0	222	2116
1	527	1956
2	1845	1662
done	5001	1662

prune526.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize18.0ms

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))))

rewrite86.0ms

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` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

28.0ms	(/ (sin (* 0.5 x)) 3.0)
20.0ms	(/ (sin x) (sin (* 0.5 x)))
31.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

series248.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (sin (* 0.5 x)) 3.0)
77.0ms	(/ (sin x) (sin (* 0.5 x)))
125.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	210	2055
1	492	1969
2	1740	1625
done	5000	1623

prune476.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(expm1 (/ (sin x) (sin (* 0.5 x))))
0.2b	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
0.2b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
6×	`associate-/r*`
5×	`cbrt-undiv` `div-exp` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `associate-*r/` `associate-/l/` `expm1-udef`

Counts

4 → 77

Calls

4 calls:

19.0ms	(/ (sin x) (sin (* 0.5 x)))
1.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
0.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
18.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (sin x) (sin (* 0.5 x)))
177.0ms	(expm1 (/ (sin x) (sin (* 0.5 x))))
327.0ms	(log1p (expm1 (/ (sin x) (sin (* 0.5 x)))))
423.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (log1p (expm1 (/ (sin x) (sin (* 0.5 x))))))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	167	1426
1	362	1290
2	1121	1052
done	5001	1047

prune396.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	15	18
done	15	18

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	1266×	body	640	valid
1.2s	1496×	body	1280	valid
897.0ms	4284×	body	80	valid
377.0ms	623×	body	320	valid
73.0ms	331×	body	160	valid