Details

sample383.0ms

Algorithm

intervals

Results

197.0ms	108×	body	1280	valid
53.0ms	56×	body	640	valid
14.0ms	25×	body	320	valid
10.0ms	57×	body	80	valid
4.0ms	10×	body	160	valid

simplify139.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize66.0ms

Local error

Found 3 expressions with local error:

1.9b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin 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:

Slowest

26.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))
15.0ms	(* r (sin b))

series310.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

185.0ms	(/ (* r (sin b)) (cos (+ a b)))
80.0ms	(* r (sin b))
45.0ms	(cos (+ a b))

simplify980.0ms

Counts: 65 → 65

prune837.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:

Slowest

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
8.0ms	(* r (sin b))

series619.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
126.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
74.0ms	(* (sin a) (sin b))
63.0ms	(* r (sin b))

simplify2.0s

Counts: 102 → 102

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite249.0ms

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:

Slowest

140.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
45.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(* (sin a) (sin b))

series707.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

337.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
176.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
66.0ms	(* (sin a) (sin b))

simplify2.0s

Counts: 126 → 126

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

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:

Slowest

55.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
35.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
22.0ms	(* (sin b) (sin a))
20.0ms	(* (sin b) r)

series601.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

363.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
132.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
65.0ms	(* (sin b) (sin a))
41.0ms	(* (sin b) r)

simplify2.4s

Counts: 102 → 102

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes324.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.8s	2993×	body	1280	valid
2.4s	1807×	body	640	valid
417.0ms	746×	body	320	valid
389.0ms	2118×	body	80	valid
143.0ms	337×	body	160	valid