Details

sample400.0ms

Algorithm

intervals

Results

183.0ms	87×	body	1280	valid
67.0ms	72×	body	640	valid
15.0ms	71×	body	80	valid
10.0ms	15×	body	320	valid
5.0ms	11×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	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: 16.2b

localize65.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite35.0ms

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:

8.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series183.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
114.0ms	(/ (* r (sin b)) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify736.0ms

Counts

59 → 59

Iterations

Iter	Nodes
3	2151
2	565
1	203
0	95

prune599.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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

rewrite69.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
15.0ms	(* (sin a) (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
41.0ms	(* r (sin b))
49.0ms	(* (sin a) (sin b))
273.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.2s

Counts

92 → 92

Iterations

Iter	Nodes
3	4272
2	1111
1	358
0	145

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

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` `insert-posit16` `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 → 139

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
15.0ms	(* (sin a) (sin b))
39.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series711.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
340.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
62.0ms	(* (sin a) (sin b))
201.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify2.7s

Counts

151 → 151

Iterations

Iter	Nodes
3	6920
2	1887
1	627
0	244

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-l`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/`

Counts

4 → 104

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
111.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series768.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
267.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
67.0ms	(* (sin a) (sin b))
315.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify4.4s

Counts

116 → 116

Iterations

Iter	Nodes
3	3952
2	1327
1	425
0	175

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes317.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	11
0	11

end0.0ms

sample7.3s

Algorithm

intervals

Results

4.1s	2929×	body	1280	valid
2.0s	1864×	body	640	valid
431.0ms	737×	body	320	valid
403.0ms	2146×	body	80	valid
149.0ms	325×	body	160	valid