Details

sample329.0ms

Algorithm

intervals

Results

134.0ms	93×	body	1280	valid
51.0ms	61×	body	640	valid
12.0ms	26×	body	320	valid
11.0ms	68×	body	80	valid
3.0ms	8×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	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

localize64.0ms

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))

rewrite61.0ms

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:

15.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(cos (+ a b))

series248.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* r (sin b))
159.0ms	(/ (* r (sin b)) (cos (+ a b)))
41.0ms	(cos (+ a b))

simplify628.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2189
2	582
1	212
0	101

prune329.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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))))

rewrite106.0ms

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:

26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
20.0ms	(* (sin a) (sin b))
50.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms	(* r (sin b))
48.0ms	(* (sin a) (sin b))
285.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	4407
2	1152
1	382
0	157

prune671.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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))

rewrite105.0ms

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:

36.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
28.0ms	(* (sin a) (sin b))
11.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
26.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series649.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
56.0ms	(* (sin a) (sin b))
323.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
161.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify2.7s

Counts

161 → 161

Iterations

Iter	Nodes
3	6427
2	1819
1	647
0	255

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize61.0ms

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

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

527×	`times-frac`
248×	`add-sqr-sqrt`
246×	`*-un-lft-identity` `add-cube-cbrt`
61×	`associate-/r/`
35×	`div-inv`
34×	`add-exp-log`
31×	`sin-mult`
30×	`cos-mult`
23×	`associate-/l*`
22×	`add-cbrt-cube`
19×	`associate-/r*` `div-exp`
15×	`flip3--` `frac-sub` `flip--` `sub-div`
10×	`cbrt-undiv`
7×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow` `unswap-sqr` `associate-/l/`

Counts

4 → 368

Calls

4 calls:

11.0ms	(/ 1 (sin b))
23.0ms	(* (sin a) (sin b))
43.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
90.0ms	(/ (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (sin b)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (sin b))
57.0ms	(* (sin a) (sin b))
267.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
347.0ms	(/ (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (sin b)))

simplify26.6s

Counts

380 → 380

Iterations

Iter	Nodes
2	4431
1	1846
0	609

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes232.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	16
1	16
0	14

end0.0ms

sample6.9s

Algorithm

intervals

Results

4.1s	2814×	body	1280	valid
1.6s	1909×	body	640	valid
414.0ms	790×	body	320	valid
340.0ms	2107×	body	80	valid
137.0ms	383×	body	160	valid