Details

sample216.0ms

Algorithm

intervals

Results

70.0ms	100×	body	1280	valid
21.0ms	51×	body	640	valid
10.0ms	28×	body	320	valid
7.0ms	68×	body	80	valid
4.0ms	9×	body	160	valid

simplify96.0ms

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: 13.4b

localize28.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite71.0ms

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:

19.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

series255.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* r (sin b))
160.0ms	(/ (* r (sin b)) (cos (+ a b)))
46.0ms	(cos (+ a b))

simplify3.5s

Counts

56 → 56

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	90	535
1	198	525
2	550	447
3	2112	443
done	5001	439

prune202.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

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:

38.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
20.0ms	(* r (sin b))
34.0ms	(* (sin a) (sin b))
61.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (sin b))
63.0ms	(* (sin a) (sin b))
408.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	140	1256
1	345	1224
2	1091	1076
3	3873	989
done	5000	989

prune464.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
38.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
100.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
17.0ms	(* (sin a) (sin b))

series731.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
189.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
348.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
68.0ms	(* (sin a) (sin b))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	170	2072
1	403	2024
2	1167	1834
3	3373	1715
done	5000	1715

prune639.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

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` `add-log-exp`
6×	`associate-r` `associate-l`
3×	`times-frac` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod` `sin-mult`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `frac-add` `sum-log` `cos-mult` `*-commutative` `flip-+` `distribute-neg-frac` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+r-` `frac-2neg` `unsub-neg` `neg-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

29.0ms	(+ (* (cos a) (cos b)) (- (* (sin a) (sin b))))
19.0ms	(* r (sin b))
25.0ms	(* (sin a) (sin b))
63.0ms	(/ (* r (sin b)) (+ (* (cos a) (cos b)) (- (* (sin a) (sin b)))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (* (cos a) (cos b)) (- (* (sin a) (sin b))))
62.0ms	(* r (sin b))
72.0ms	(* (sin a) (sin b))
395.0ms	(/ (* r (sin b)) (+ (* (cos a) (cos b)) (- (* (sin a) (sin b)))))

simplify3.8s

Counts

89 → 89

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	145	1277
1	362	1203
2	1222	1042
3	4614	1033
done	5002	1033

prune399.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes296.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.2s	2954×	body	1280	valid
1.4s	1762×	body	640	valid
337.0ms	843×	body	320	valid
276.0ms	2134×	body	80	valid
73.0ms	308×	body	160	valid