Details

sample319.0ms

Algorithm

intervals

Results

156.0ms	95×	body	1280	valid
38.0ms	48×	body	640	valid
14.0ms	68×	body	80	valid
13.0ms	27×	body	320	valid
7.0ms	18×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

10.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
34.0ms	(cos (+ a b))

series230.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* r (sin b))
141.0ms	(/ (* r (sin b)) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify931.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
2	870
1	214
0	95

prune299.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (cos a) (cos b))
8.0ms	(* r (sin b))
33.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))

series517.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos a) (cos b))
67.0ms	(* r (sin b))
313.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1742
1	395
0	162

prune686.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 109

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
99.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
22.0ms	(* (sin a) (sin b))
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cos a) (cos b))
349.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
67.0ms	(* (sin a) (sin b))
178.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2043
1	470
0	192

prune775.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* (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)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp` `associate-/l/`
3×	`cos-mult` `sin-mult`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `associate-/r/` `frac-sub` `flip--` `sub-div`

Counts

4 → 144

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
11.0ms	(* (sin a) (sin b))
31.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
11.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos a) (cos b))
67.0ms	(* (sin a) (sin b))
161.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
348.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify1.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	3033
1	649
0	257

prune950.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes279.0ms

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	16
1	16
0	13

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.3s	2918×	body	1280	valid
1.8s	1912×	body	640	valid
841.0ms	705×	body	320	valid
351.0ms	2095×	body	80	valid
212.0ms	370×	body	160	valid