Details

sample241.0ms

Algorithm

intervals

Results

115.0ms	91×	body	1280	valid
29.0ms	60×	body	640	valid
11.0ms	31×	body	320	valid
9.0ms	65×	body	80	valid
2.0ms	9×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite563.0ms

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:

502.0ms	(* r (sin b))
19.0ms	(/ (* r (sin b)) (cos (+ a b)))
39.0ms	(cos (+ a b))

series240.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
169.0ms	(/ (* r (sin b)) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
2	870
1	211
0	92

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (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:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
13.0ms	(* (sin a) (sin b))
40.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* r (sin b))
87.0ms	(* (sin a) (sin b))
387.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1577
1	365
0	141

prune731.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (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))

rewrite159.0ms

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:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
107.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

series792.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
403.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
167.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))

simplify1.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	1878
1	441
0	171

prune831.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (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))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `frac-2neg` `flip3--` `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:

27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
26.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
24.0ms	(* (sin a) (sin b))

series651.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
173.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
313.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
52.0ms	(* (sin a) (sin b))

simplify1.8s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2969
1	639
0	240

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes400.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.0s	2868×	body	1280	valid
1.2s	1875×	body	640	valid
703.0ms	2150×	body	80	valid
285.0ms	768×	body	320	valid
79.0ms	339×	body	160	valid