Details

sample272.0ms

Algorithm

intervals

Results

123.0ms	93×	body	1280	valid
28.0ms	57×	body	640	valid
10.0ms	22×	body	320	valid
8.0ms	70×	body	80	valid
4.0ms	14×	body	160	valid

simplify96.0ms

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: 14.8b

localize51.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.4b	(cos (+ a b))

rewrite56.0ms

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:

17.0ms	(* r (sin b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(cos (+ a b))

series462.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* r (sin b))
317.0ms	(/ (* r (sin b)) (cos (+ a b)))
72.0ms	(cos (+ a b))

simplify4.6s

Counts

59 → 59

Iterations

Iter	Nodes
done	5015
3	2732
2	632
1	214
0	95

prune866.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

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))))

rewrite134.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* r (sin b))
30.0ms	(* (sin a) (sin b))
54.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series996.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* r (sin b))
113.0ms	(* (sin a) (sin b))
609.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1148
1	369
0	145

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite269.0ms

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:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
149.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(* (sin a) (sin b))
44.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series1.2s

Counts

4 → 12

Calls

4 calls:

184.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
621.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
77.0ms	(* (sin a) (sin b))
312.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
2	1465
1	443
0	175

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
23.5b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite637.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
14×	`cbrt-div`
11×	`frac-times` `associate-*l/`
10×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`associate-/r/`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `pow-plus` `div-exp` `*-commutative`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

28.0ms	(* (sin a) (sin b))
244.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
75.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
272.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series965.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (sin a) (sin b))
589.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
150.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
110.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify4.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1744
1	518
0	202

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes1.0s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.8s	2902×	body	1280	valid
1.6s	1902×	body	640	valid
302.0ms	2112×	body	80	valid
226.0ms	724×	body	320	valid
79.0ms	361×	body	160	valid