Details

sample290.0ms

Algorithm

intervals

Results

104.0ms	100×	body	1280	valid
34.0ms	54×	body	640	valid
13.0ms	28×	body	320	valid
9.0ms	67×	body	80	valid
2.0ms	7×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite48.0ms

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:

14.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(cos (+ a b))

series242.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* r (sin b))
134.0ms	(/ (* r (sin b)) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5070
3	2428
2	611
1	223
0	101

prune404.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

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

rewrite139.0ms

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:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
29.0ms	(* (sin a) (sin b))
55.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms	(* r (sin b))
55.0ms	(* (sin a) (sin b))
318.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1177
1	391
0	157

prune624.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

14.0ms	(* r (sin b))
44.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
134.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* r (sin b))
156.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
69.0ms	(* (sin a) (sin b))
338.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify2.7s

Counts

138 → 138

Iterations

Iter	Nodes
done	5000
3	4659
2	1522
1	509
0	195

prune943.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

17.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
86.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
23.0ms	(* (sin b) (sin a))
53.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
330.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
72.0ms	(* (sin b) (sin a))
153.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify2.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1547
1	472
0	190

prune919.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes305.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
2	20
1	18
0	12

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2928×	body	1280	valid
1.5s	1854×	body	640	valid
361.0ms	2083×	body	80	valid
356.0ms	787×	body	320	valid
88.0ms	352×	body	160	valid