Details

sample141.0ms

Algorithm

intervals

Results

76.0ms	60×	body	2560	valid
41.0ms	102×	body	1280	valid
10.0ms	49×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	11×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.0b	(- 1.0 (cos x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify78.0ms

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373
done	5001	373

prune161.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.3b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

49.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
28.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify61.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	434	688
1	1925	638
2	5001	618
done	5001	618

prune287.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos x) 1.0)
0.5b	(+ (cos x) 1.0)
0.7b	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
26×	`sqrt-prod`
19×	`pow1`
16×	`difference-of-squares`
12×	`add-cube-cbrt` `unpow-prod-down` `sqrt-div` `cube-prod`
11×	`swap-sqr`
10×	`add-log-exp`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `sqr-pow`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-up` `distribute-lft-out--`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `associate-r/` `associate-l/` `sum-log`
1×	`difference-cubes` `pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

6.0ms	(+ (cos x) 1.0)
6.0ms	(+ (cos x) 1.0)
43.0ms	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series86.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (cos x) 1.0)
11.0ms	(+ (cos x) 1.0)
11.0ms	(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
54.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify44.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	320	807
1	1181	749
2	5001	735
done	5001	735

prune381.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
0.6b	(log (exp (+ (cos x) 1.0)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-pow` `add-cbrt-cube` `distribute-lft-out--`
4×	`log-prod` `exp-prod`
3×	`pow-unpow`
2×	`distribute-lft-out`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `unpow3` `rem-log-exp` `exp-sum` `pow-exp` `sum-log` `flip--` `flip-+` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

6.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
17.0ms	(log (exp (+ (cos x) 1.0)))
23.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series103.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cos x) 3)
11.0ms	(+ (cos x) 1.0)
11.0ms	(log (exp (+ (cos x) 1.0)))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify41.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	306	525
1	1147	494
2	5001	474
done	5001	474

prune245.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

regimes170.0ms

Accuracy

98.2% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.1b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	40
1	46	40
done	46	40

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	1566×	body	2560	valid
1.4s	2786×	body	1280	valid
435.0ms	1962×	body	640	valid
132.0ms	911×	body	320	valid
51.0ms	435×	body	160	valid
20.0ms	337×	body	80	valid
10.0ms	3×	body	5120	valid