Details

sample971.0ms

Algorithm

intervals

Results

193.0ms	94×	body	1280	valid
47.0ms	62×	body	640	valid
40.0ms	68×	body	80	valid
11.0ms	21×	body	320	valid
9.0ms	11×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

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

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize81.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ b a)))
2.2b	(cos (+ b a))

rewrite126.0ms

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:

18.0ms	(* r (sin b))
30.0ms	(/ (* r (sin b)) (cos (+ b a)))
53.0ms	(cos (+ b a))

series219.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* r (sin b))
130.0ms	(/ (* r (sin b)) (cos (+ b a)))
43.0ms	(cos (+ b a))

simplify1.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
2	944
1	210
0	93

prune454.0ms

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

rewrite74.0ms

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:

7.0ms	(* r (sin b))
13.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
17.0ms	(* (sin b) (sin a))
35.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* r (sin b))
91.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
85.0ms	(* (sin b) (sin a))
337.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin b) (sin a))))

simplify736.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1800
1	374
0	146

prune699.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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:

25.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
87.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
11.0ms	(* (sin b) (sin a))

series695.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
180.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
331.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
73.0ms	(* (sin b) (sin a))

simplify1.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1969
1	443
0	176

prune905.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
32.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r)
9.0ms	(* (sin b) (sin a))
14.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r))

series808.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
227.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r)
65.0ms	(* (sin b) (sin a))
384.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r))

simplify1.4s

Counts

147 → 147

Iterations

Iter	Nodes
done	5001
2	3608
1	660
0	250

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes358.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	2960×	body	1280	valid
1.5s	1897×	body	640	valid
726.0ms	2060×	body	80	valid
283.0ms	707×	body	320	valid
191.0ms	376×	body	160	valid