Details

sample79.0ms

Algorithm

intervals

Results

38.0ms	88×	body	1280	valid
19.0ms	64×	body	640	valid
5.0ms	70×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5
done	20	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.5b	(cos (+ a b))

rewrite40.0ms

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:

9.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series164.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
101.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify32.0ms

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256
done	5001	256

prune136.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite69.0ms

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:

9.0ms	(* r (sin b))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
28.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* (sin a) (sin b))
223.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663
done	5001	663

prune285.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
12.0ms	(* (sin a) (sin b))

series491.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
233.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
50.0ms	(* (sin a) (sin b))

simplify69.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	570	2147
1	2453	2011
2	5001	1990
done	5001	1990

prune515.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(/ (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))
14.0ms	(/ r (/ (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b)))
12.0ms	(* (sin a) (sin b))

series490.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
126.0ms	(/ (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))
235.0ms	(/ r (/ (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b)))
46.0ms	(* (sin a) (sin b))

simplify65.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	520	1470
1	2143	1289
2	5001	1283
done	5001	1283

prune330.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes174.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	21	11
2	21	11
done	21	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2976×	body	1280	valid
427.0ms	1808×	body	640	valid
129.0ms	767×	body	320	valid
117.0ms	2095×	body	80	valid
42.0ms	356×	body	160	valid