Details

sample90.0ms

Algorithm

intervals

Results

30.0ms	141×	body	80	valid
29.0ms	46×	body	1280	valid
11.0ms	28×	body	640	valid
7.0ms	25×	body	320	valid
3.0ms	16×	body	160	valid

simplify391.0ms

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

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite213.0ms

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:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
31.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
88.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series251.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
67.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
104.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.6s

Counts

94 → 94

Iterations

Useful iterations: 2 (307.0ms)

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

prune327.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 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)))

rewrite157.0ms

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:

73.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
24.0ms	(/ (sin x) (sin (* 0.5 x)))
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
74.0ms	(/ (sin x) (sin (* 0.5 x)))
72.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.6s

Counts

125 → 125

Iterations

Useful iterations: 2 (472.0ms)

Iter	Nodes	Cost
0	222	2116
1	527	1956
2	1843	1662
done	5000	1662

prune556.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
0.1b	(/ (sin (* 0.5 x)) 3.0)
0.1b	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

32.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
14.0ms	(/ (sin (* 0.5 x)) 3.0)
23.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
26.0ms	(/ (sin x) (sin (* 0.5 x)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
37.0ms	(/ (sin (* 0.5 x)) 3.0)
127.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
82.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify1.5s

Counts

157 → 157

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	2482
1	563	2375
2	1915	1986
done	5000	1984

prune597.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
0.7b	(cbrt (sin (* 0.5 x)))
0.7b	(cbrt (sin (* 0.5 x)))
0.7b	(cbrt (sin (* 0.5 x)))

rewrite60.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

39.0ms	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
9.0ms	(cbrt (sin (* 0.5 x)))
3.0ms	(cbrt (sin (* 0.5 x)))
5.0ms	(cbrt (sin (* 0.5 x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (cbrt (sin (* 0.5 x))) (cbrt (sin (* 0.5 x))))
259.0ms	(cbrt (sin (* 0.5 x)))
279.0ms	(cbrt (sin (* 0.5 x)))
252.0ms	(cbrt (sin (* 0.5 x)))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	93	1226
1	206	1128
2	594	934
3	2221	857
done	5001	830

prune353.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	13	16
done	13	16

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.8s	1546×	body	1280	valid
1.0s	1256×	body	640	valid
781.0ms	4253×	body	80	valid
293.0ms	634×	body	320	valid
97.0ms	311×	body	160	valid