Details

sample511.0ms

Algorithm

intervals

Results

197.0ms	90×	body	1280	valid
60.0ms	28×	body	320	valid
57.0ms	56×	body	640	valid
49.0ms	72×	body	80	valid
5.0ms	10×	body	160	valid

simplify69.0ms

Counts: 1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize39.0ms

Local error

Found 3 expressions with local error:

3.4b	(cos (+ a b))
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))

rewrite85.0ms

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:

Slowest

34.0ms	(cos (+ a b))
25.0ms	(* r (/ (sin b) (cos (+ a b))))
19.0ms	(/ (sin b) (cos (+ a b)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

157.0ms	(* r (/ (sin b) (cos (+ a b))))
74.0ms	(/ (sin b) (cos (+ a b)))
39.0ms	(cos (+ a b))

simplify793.0ms

Counts: 79 → 79

prune874.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

Slowest

110.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
53.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(* (cos a) (cos b))
11.0ms	(* (sin a) (sin b))

series611.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
181.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
72.0ms	(* (cos a) (cos b))
58.0ms	(* (sin a) (sin b))

simplify1.7s

Counts: 121 → 121

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin b))
0.6b	(cbrt (sin b))
0.6b	(cbrt (sin b))
0.5b	(* (cbrt (sin b)) (cbrt (sin b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

Slowest

24.0ms	(* (cbrt (sin b)) (cbrt (sin b)))
3.0ms	(cbrt (sin b))
3.0ms	(cbrt (sin b))
3.0ms	(cbrt (sin b))

series565.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(* (cbrt (sin b)) (cbrt (sin b)))
143.0ms	(cbrt (sin b))
134.0ms	(cbrt (sin b))
120.0ms	(cbrt (sin b))

simplify2.7s

Counts: 89 → 89

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

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×	`cos-mult` `insert-posit16` `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 → 118

Calls

4 calls:

Slowest

75.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
67.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))
17.0ms	(* r (sin b))

series612.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

324.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
65.0ms	(* r (sin b))
63.0ms	(* (sin a) (sin b))

simplify2.4s

Counts: 130 → 130

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes287.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.7s	2953×	body	1280	valid
2.4s	1793×	body	640	valid
481.0ms	801×	body	320	valid
389.0ms	2106×	body	80	valid
152.0ms	349×	body	160	valid