Details

sample253.0ms

Algorithm

intervals

Results

123.0ms	105×	body	1280	valid
33.0ms	59×	body	640	valid
9.0ms	24×	body	320	valid
7.0ms	60×	body	80	valid
2.0ms	8×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite32.0ms

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

series187.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* r (sin b))
118.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify1.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	2023
3	2023
2	671
1	212
0	95

prune313.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

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))))

rewrite90.0ms

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)))
11.0ms	(* r (sin b))
30.0ms	(* (sin a) (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(* r (sin b))
64.0ms	(* (sin a) (sin b))
318.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.3s

Counts

92 → 92

Iterations

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

prune807.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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))

rewrite185.0ms

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:

29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series746.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
369.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
171.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
76.0ms	(* (sin a) (sin b))

simplify1.4s

Counts

116 → 116

Iterations

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

prune737.0ms

Pruning

11 alts after pruning (11 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)))
0.1b	(* (sin b) r)
0.2b	(* (sin a) (sin b))
0.3b	(/ (* (sin b) r) (- (* (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×	`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:

23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* (sin b) r)
11.0ms	(* (sin a) (sin b))
29.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin b) r)
58.0ms	(* (sin a) (sin b))
341.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	2008
3	2008
2	1199
1	367
0	144

prune601.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes289.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.2s	2947×	body	1280	valid
1.7s	1870×	body	640	valid
1.0s	742×	body	320	valid
496.0ms	2117×	body	80	valid
124.0ms	325×	body	160	valid