Details

sample102.0ms

Algorithm

intervals

Results

32.0ms	37×	body	1280	valid
20.0ms	34×	body	640	valid
17.0ms	149×	body	80	valid
9.0ms	25×	body	320	valid
3.0ms	11×	body	160	valid

simplify334.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	313
6	313
5	275
4	171
3	90
2	43
1	20
0	11

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) 3.0)
0.2b	(* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0))
15.1b	(/ (* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0)) (/ (sin x) 8.0))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 116

Calls

3 calls:

10.0ms	(/ (sin (* x 0.5)) 3.0)
29.0ms	(* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0))
47.0ms	(/ (* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0)) (/ (sin x) 8.0))

series286.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (sin (* x 0.5)) 3.0)
89.0ms	(* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0))
125.0ms	(/ (* (sin (* x 0.5)) (/ (sin (* x 0.5)) 3.0)) (/ (sin x) 8.0))

simplify2.7s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	4759
1	614
0	230

prune783.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-l`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`associate-/r*`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 100

Calls

3 calls:

14.0ms	(/ (* (sin (* x 0.5)) 8.0) 3.0)
50.0ms	(* (/ (sin (* x 0.5)) (sin x)) (/ (* (sin (* x 0.5)) 8.0) 3.0))
20.0ms	(/ (sin (* x 0.5)) (sin x))

series253.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (* (sin (* x 0.5)) 8.0) 3.0)
135.0ms	(* (/ (sin (* x 0.5)) (sin x)) (/ (* (sin (* x 0.5)) 8.0) 3.0))
66.0ms	(/ (sin (* x 0.5)) (sin x))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
2	2767
1	488
0	179

prune682.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin (* x 0.5)) (sin x)) (log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))))
0.1b	(log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0)))
0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-/r` `associate-r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `log1p-expm1` `-commutative` `expm1-udef`

Counts

4 → 85

Calls

4 calls:

26.0ms	(* (/ (sin (* x 0.5)) (sin x)) (log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))))
0.0ms	(log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0)))
19.0ms	(/ (sin (* x 0.5)) (sin x))
1.0ms	(expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

941.0ms	(* (/ (sin (* x 0.5)) (sin x)) (log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))))
251.0ms	(log1p (expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0)))
57.0ms	(/ (sin (* x 0.5)) (sin x))
94.0ms	(expm1 (* (/ (sin (* 0.5 x)) 3.0) 8.0))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1553
1	335
0	154

prune605.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize21.0ms

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

12.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
9.0ms	(/ (sin (* 0.5 x)) 3.0)
13.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (sin x))
37.0ms	(* (sin (* x 0.5)) (/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (sin x)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
39.0ms	(/ (sin (* 0.5 x)) 3.0)
76.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (sin x))
122.0ms	(* (sin (* x 0.5)) (/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (sin x)))

simplify1.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	2884
1	515
0	208

prune640.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes164.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	15

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.1s	1523×	body	1280	valid
1.5s	1269×	body	640	valid
724.0ms	4242×	body	80	valid
253.0ms	633×	body	320	valid
87.0ms	333×	body	160	valid