Details

sample202.0ms

Algorithm

intervals

Results

88.0ms	91×	body	1280	valid
18.0ms	60×	body	640	valid
7.0ms	31×	body	320	valid
4.0ms	65×	body	80	valid
1.0ms	9×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

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

prune98.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize33.0ms

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))

rewrite33.0ms

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×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

8.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
10.0ms	(cos (+ a b))

series294.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* r (sin b))
206.0ms	(/ (* r (sin b)) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify2.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	5051
3	2951
2	667
1	216
0	98

prune481.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

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))))

rewrite78.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

14.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
10.0ms	(* (sin a) (sin b))
45.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (sin b))
66.0ms	(* (sin a) (sin b))
335.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4983
2	1193
1	386
0	153

prune768.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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))

rewrite96.0ms

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×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `cos-mult` `log1p-expm1-u` `associate-/l/`
3×	`associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
23.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
24.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
18.0ms	(* (sin a) (sin b))

series744.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
176.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
381.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
66.0ms	(* (sin a) (sin b))

simplify2.2s

Counts

157 → 157

Iterations

Iter	Nodes
done	5001
2	2013
1	659
0	251

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
33×	`add-cube-cbrt`
30×	`times-frac`
21×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
7×	`fma-neg`
6×	`pow1` `div-inv` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

16.0ms	(* (cos a) (cos b))
44.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
28.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
11.0ms	(/ (* (cos a) (cos b)) (sin b))

series595.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos a) (cos b))
126.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
299.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
110.0ms	(/ (* (cos a) (cos b)) (sin b))

simplify1.5s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	1277
1	471
0	212

prune958.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes338.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.3s	2868×	body	1280	valid
1.3s	1875×	body	640	valid
420.0ms	2150×	body	80	valid
317.0ms	768×	body	320	valid
81.0ms	339×	body	160	valid