Details

sample434.0ms

Algorithm

intervals

Results

164.0ms	61×	body	640	valid
151.0ms	93×	body	1280	valid
18.0ms	26×	body	320	valid
14.0ms	68×	body	80	valid
4.0ms	8×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize44.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite57.0ms

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*` `insert-posit16` `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 → 56

Calls

3 calls:

16.0ms	(* r (sin b))
22.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(cos (+ a b))

series259.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* r (sin b))
145.0ms	(/ (* r (sin b)) (cos (+ a b)))
37.0ms	(cos (+ a b))

simplify1.1s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
3	2000
2	611
1	223
0	101

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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

rewrite112.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
11.0ms	(* r (sin b))
15.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* r (sin b))
74.0ms	(* (sin a) (sin b))
326.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	2126
3	2126
2	1177
1	391
0	157

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

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` `insert-posit16` `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 → 149

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* (sin a) (sin b))
25.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
40.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series708.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms	(* (sin a) (sin b))
315.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
179.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify1.0s

Counts

161 → 161

Iterations

Iter	Nodes
done	2001
2	2001
1	657
0	255

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ r (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b))))
0.3b	(* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`times-frac`
22×	`add-cbrt-cube`
16×	`associate-r`
11×	`div-exp`
10×	`associate-/r/`
9×	`pow1` `prod-exp` `sin-mult`
8×	`frac-times` `associate-*l/` `cos-mult`
6×	`cbrt-undiv` `associate-l` `associate-/l*`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `flip3--` `frac-sub` `insert-posit16` `log1p-expm1-u` `flip--` `sub-div` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `1-exp` `div-inv`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 141

Calls

4 calls:

6.0ms	(/ 1 (sin b))
18.0ms	(* (sin a) (sin b))
62.0ms	(/ r (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b))))
74.0ms	(* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (sin b))
64.0ms	(* (sin a) (sin b))
373.0ms	(/ r (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b))))
143.0ms	(* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (/ 1 (sin b)))

simplify1.6s

Counts

153 → 153

Iterations

Iter	Nodes
done	2003
3	2003
2	1952
1	575
0	232

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes303.0ms

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	15
1	15
0	12

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.0s	2814×	body	1280	valid
2.1s	1909×	body	640	valid
472.0ms	790×	body	320	valid
380.0ms	2107×	body	80	valid
197.0ms	383×	body	160	valid