Details

sample362.0ms

Algorithm

intervals

Results

210.0ms	53×	body	640	valid
68.0ms	100×	body	1280	valid
7.0ms	27×	body	320	valid
6.0ms	62×	body	80	valid
3.0ms	14×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

10.0ms	(* r (sin b))
15.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series184.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
114.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify626.0ms

Counts

56 → 56

Iterations

Useful iterations: done (624.0ms)

Iter	Nodes	Cost
0	90	535
1	206	525
2	855	455
done	5000	443

prune257.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

12.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
62.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))

series648.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* r (sin b))
133.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
357.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
86.0ms	(* (sin a) (sin b))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	140	1256
1	361	1224
2	1706	1084
done	5000	1028

prune572.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
0.2b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))
0.2b	(/ (* (cos a) (cos b)) (sin b))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`times-frac`
20×	`add-cube-cbrt`
15×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/r/`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `cos-mult` `frac-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
41.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
64.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))
14.0ms	(/ (* (cos a) (cos b)) (sin b))

series592.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos a) (cos b))
141.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1))
269.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (/ (sin a) 1)))
122.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.6s

Counts

116 → 116

Iterations

Useful iterations: 2 (360.0ms)

Iter	Nodes	Cost
0	202	2120
1	440	1866
2	2259	1738
done	5000	1738

prune587.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
0.2b	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
0.2b	(* (sin b) (sin a))
0.2b	(* (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (* (sin b) 1))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-l` `add-cbrt-cube`
18×	`times-frac`
11×	`pow1` `prod-exp`
8×	`associate-/r/`
7×	`cbrt-unprod` `sin-mult`
6×	`cos-mult` `add-log-exp`
4×	`div-exp` `associate-r` `pow-prod-down`
3×	`cbrt-undiv` `flip3--` `associate-/r` `frac-sub` `flip--` `associate-/l` `sub-div`
2×	`1-exp` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*l/` `clear-num` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

32.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
24.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
16.0ms	(* (sin b) (sin a))
124.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (* (sin b) 1))

series788.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
277.0ms	(/ r (- (* (cos a) (cos b)) (* (sin b) (sin a))))
53.0ms	(* (sin b) (sin a))
314.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin b) (sin a)))) (* (sin b) 1))

simplify1.4s

Counts

115 → 115

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	187	2163
1	503	2021
2	2058	1775
done	5001	1760

prune548.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	2983×	body	1280	valid
2.1s	1826×	body	640	valid
360.0ms	2093×	body	80	valid
277.0ms	738×	body	320	valid
124.0ms	360×	body	160	valid