Details

sample760.0ms

Algorithm

intervals

Results

183.0ms	105×	body	1280	valid
54.0ms	59×	body	640	valid
15.0ms	24×	body	320	valid
12.0ms	60×	body	80	valid
3.0ms	8×	body	160	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize46.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

13.0ms	(* r (/ (sin b) (cos (+ a b))))
9.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series203.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(* r (/ (sin b) (cos (+ a b))))
47.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify992.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2008
3	2008
2	844
1	271
0	120

prune318.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
103.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
50.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))

series640.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
319.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
3	2016
2	1478
1	439
0	175

prune827.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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

rewrite86.0ms

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:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(* r (sin b))
15.0ms	(* (sin a) (sin b))
34.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms	(* r (sin b))
61.0ms	(* (sin a) (sin b))
311.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2164
3	2164
2	1237
1	365
0	145

prune589.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
0.3b	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
26.1b	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

rewrite452.0ms

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-*r/`
10×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`associate-/r/`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-*l/` `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` `cube-unmult` `swap-sqr` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

11.0ms	(* (sin b) (sin a))
201.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
64.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
174.0ms	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin b) (sin a))
296.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))))
76.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
68.0ms	(cbrt (* (* (sin b) (sin a)) (* (* (sin b) (sin a)) (* (sin b) (sin a)))))

simplify1.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	2001
3	2001
2	1776
1	528
0	207

prune621.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.2s	2947×	body	1280	valid
1.8s	1870×	body	640	valid
748.0ms	2117×	body	80	valid
466.0ms	742×	body	320	valid
153.0ms	325×	body	160	valid