Details

sample413.0ms

Algorithm

intervals

Results

168.0ms	68×	body	640	valid
92.0ms	88×	body	1280	valid
42.0ms	6×	body	160	valid
11.0ms	26×	body	320	valid
8.0ms	68×	body	80	valid

simplify69.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.6b	(cos (+ a b))

rewrite88.0ms

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*` `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 → 47

Calls

3 calls:

17.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
21.0ms	(cos (+ a b))

series414.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* r (sin b))
309.0ms	(/ (* r (sin b)) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify1.4s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
2	870
1	211
0	92

prune398.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

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))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

15.0ms	(* r (sin b))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(* (sin a) (sin b))

series550.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* r (sin b))
98.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
316.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
83.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1579
1	365
0	141

prune694.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

series728.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
359.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
187.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
57.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1878
1	441
0	171

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
0.2b	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `add-log-exp` `associate-/l/`
3×	`sin-mult`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

50.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
40.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
19.0ms	(* (sin a) (sin b))
37.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series806.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
191.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
55.0ms	(* (sin a) (sin b))
178.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify1.1s

Counts

212 → 212

Iterations

Iter	Nodes
done	5000
1	821
0	292

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes537.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.9s	2888×	body	1280	valid
1.4s	1804×	body	640	valid
408.0ms	2179×	body	80	valid
331.0ms	782×	body	320	valid
79.0ms	347×	body	160	valid