Details

sample144.0ms

Algorithm

intervals

Results

44.0ms	45×	body	1280	valid
26.0ms	39×	body	640	valid
24.0ms	16×	body	160	valid
17.0ms	129×	body	80	valid
13.0ms	27×	body	320	valid

simplify373.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize38.0ms

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)))
13.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
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×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 85

Calls

3 calls:

73.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
67.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series289.0ms

Counts

3 → 9

Calls

3 calls:

104.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
138.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2504
1	424
0	169

prune598.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

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-r`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l`
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:

25.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
19.0ms	(/ (sin (* x 0.5)) (sin x))
40.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
66.0ms	(/ (sin (* x 0.5)) (sin x))
120.0ms	(* (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3384
1	499
0	181

prune736.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 8.0 (sin (* x 0.5))) 3.0)
0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
36×	`add-sqr-sqrt`
27×	`times-frac`
23×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-cbrt-cube`
13×	`associate-r` `prod-exp`
12×	`div-exp`
11×	`associate-l`
9×	`unpow-prod-down`
6×	`associate-/r*` `pow-exp` `unswap-sqr`
4×	`pow1` `cbrt-undiv` `div-inv` `associate-/l*`
3×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 106

Calls

3 calls:

27.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
19.0ms	(/ (sin (* x 0.5)) (sin x))
54.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

series287.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
87.0ms	(/ (sin (* x 0.5)) (sin x))
137.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

simplify1.5s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2828
1	507
0	201

prune666.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.2b	(expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))
0.2b	(log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0))))
0.2b	(* (pow (log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))) 1) (/ (sin (* x 0.5)) (sin x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

10.0ms	(/ (sin (* x 0.5)) (sin x))
0.0ms	(expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))
0.0ms	(log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0))))
25.0ms	(* (pow (log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))) 1) (/ (sin (* x 0.5)) (sin x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sin (* x 0.5)) (sin x))
129.0ms	(expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))
277.0ms	(log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0))))
600.0ms	(* (pow (log1p (expm1 (/ (sin (* x 0.5)) (/ 3.0 8.0)))) 1) (/ (sin (* x 0.5)) (sin x)))

simplify1.4s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	2111
1	396
0	175

prune741.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	1517×	body	1280	valid
881.0ms	1213×	body	640	valid
599.0ms	4311×	body	80	valid
353.0ms	633×	body	320	valid
145.0ms	326×	body	160	valid