Details

sample360.0ms

Algorithm

intervals

Results

117.0ms	92×	body	1280	valid
78.0ms	53×	body	640	valid
16.0ms	26×	body	320	valid
14.0ms	74×	body	80	valid
5.0ms	11×	body	160	valid

simplify46.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize39.0ms

Local error

Found 3 expressions with local error:

3.5b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite73.0ms

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×	`associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `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 → 50

Calls

3 calls:

Slowest

30.0ms	(cos (+ a b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(* r (sin b))

series239.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

131.0ms	(/ (* r (sin b)) (cos (+ a b)))
65.0ms	(* r (sin b))
43.0ms	(cos (+ a b))

simplify858.0ms

Counts: 59 → 59

prune769.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

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)))

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×	`associate-/r/` `cos-mult` `insert-posit16`
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` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

Slowest

62.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))
16.0ms	(* r (sin b))

series554.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

284.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
147.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
64.0ms	(* (sin a) (sin b))
58.0ms	(* r (sin b))

simplify1.8s

Counts: 92 → 92

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

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×	`insert-posit16`
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` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

Slowest

102.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
16.0ms	(* (sin a) (sin b))

series682.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

328.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
155.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms	(* (sin a) (sin b))

simplify1.6s

Counts: 116 → 116

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

23.8b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.2b	(* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

198×	`pow1`
86×	`pow-prod-down`
62×	`add-cbrt-cube` `add-exp-log`
40×	`prod-exp` `cbrt-unprod` `sin-mult`
38×	`pow-prod-up`
19×	`pow-plus`
16×	`frac-times` `associate-*l/` `pow-sqr`
14×	`cbrt-div`
10×	`associate-*r/`
9×	`associate-/r/`
7×	`cos-mult` `frac-sub`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow2` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `pow3` `*-commutative`
1×	`cbrt-prod` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*`

Counts

4 → 169

Calls

4 calls:

Slowest

181.0ms	(* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))
122.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))
119.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
42.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

348.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
92.0ms	(* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b)))
69.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
58.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify1.6s

Counts: 181 → 181

prune2.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes265.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.4s	2981×	body	1280	valid
1.7s	1785×	body	640	valid
721.0ms	2101×	body	80	valid
533.0ms	779×	body	320	valid
128.0ms	357×	body	160	valid