Details

sample382.0ms

Algorithm

intervals

Results

124.0ms	88×	body	1280	valid
43.0ms	26×	body	320	valid
42.0ms	68×	body	640	valid
10.0ms	68×	body	80	valid
2.0ms	6×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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:

8.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ b a)))
15.0ms	(cos (+ b a))

series511.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(* r (sin b))
272.0ms	(/ (* r (sin b)) (cos (+ b a)))
49.0ms	(cos (+ b a))

simplify1.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
2	944
1	210
0	93

prune398.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

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

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`
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))
14.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
19.0ms	(* (sin b) (sin a))

series613.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* r (sin b))
125.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
367.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
59.0ms	(* (sin b) (sin a))

simplify1.7s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1828
1	374
0	146

prune682.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
55.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin b) (sin a))))
19.0ms	(* (sin b) (sin a))
99.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
132.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin b) (sin a))))
86.0ms	(* (sin b) (sin a))
387.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin b) (sin a)))))

simplify2.4s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	3159
1	525
0	186

prune881.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

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 b) (cos a)) (* (sin a) (sin b)))
47.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) r)
18.0ms	(* (sin a) (sin b))
18.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) r))

series863.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
222.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) r)
88.0ms	(* (sin a) (sin b))
423.0ms	(/ (sin b) (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) r))

simplify1.4s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
2	3475
1	663
0	251

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes446.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.9s	2888×	body	1280	valid
1.1s	1804×	body	640	valid
774.0ms	2179×	body	80	valid
363.0ms	782×	body	320	valid
94.0ms	347×	body	160	valid