Details

sample654.0ms

Algorithm

intervals

Results

233.0ms	93×	body	1280	valid
137.0ms	61×	body	640	valid
20.0ms	26×	body	320	valid
19.0ms	68×	body	80	valid
4.0ms	8×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize57.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite43.0ms

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:

8.0ms	(* r (sin b))
14.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series238.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* r (sin b))
155.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify992.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	2023
3	2023
2	671
1	212
0	95

prune586.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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))))

rewrite89.0ms

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` `insert-posit16`
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 → 80

Calls

4 calls:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(* r (sin b))
53.0ms	(* (sin a) (sin b))
304.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2164
3	2164
2	1237
1	365
0	145

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `div-inv` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

15.0ms	(* r (sin b))
63.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms	(* (sin a) (sin b))
65.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* r (sin b))
156.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
76.0ms	(* (sin a) (sin b))
377.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	2046
3	2046
2	1521
1	509
0	187

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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`
4×	`insert-posit16`
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 → 104

Calls

4 calls:

26.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
91.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
21.0ms	(* (sin b) (sin a))
30.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
364.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
67.0ms	(* (sin b) (sin a))
143.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2008
3	2008
2	1501
1	441
0	178

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes201.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.0s	2814×	body	1280	valid
1.9s	1909×	body	640	valid
470.0ms	2107×	body	80	valid
470.0ms	790×	body	320	valid
177.0ms	383×	body	160	valid