Details

sample375.0ms

Algorithm

intervals

Results

110.0ms	90×	body	1280	valid
96.0ms	68×	body	640	valid
18.0ms	60×	body	80	valid
13.0ms	24×	body	320	valid
6.0ms	14×	body	160	valid

simplify65.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize18.0ms

Local error

Found 3 expressions with local error:

2.7b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite58.0ms

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

20.0ms	(cos (+ a b))
19.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(* r (sin b))

series186.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

106.0ms	(/ (* r (sin b)) (cos (+ a b)))
42.0ms	(* r (sin b))
37.0ms	(cos (+ a b))

simplify775.0ms

Counts: 59 → 59

prune676.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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)))

rewrite81.0ms

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

28.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
20.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))

series535.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

309.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
70.0ms	(* (sin a) (sin b))
46.0ms	(* r (sin b))

simplify1.7s

Counts: 92 → 92

prune1.2s

Pruning

10 alts after pruning (10 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)))

rewrite185.0ms

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

96.0ms	(* 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)))
11.0ms	(* (sin a) (sin b))

series693.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

368.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
129.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
112.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))

simplify2.2s

Counts: 116 → 116

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

27.1b	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
0.2b	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
40×	`sin-mult`
25×	`add-sqr-sqrt`
23×	`add-cbrt-cube` `associate-r` `add-exp-log`
21×	`cbrt-div`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`pow-prod-down` `associate-/r/`
16×	`frac-times` `associate-*l/`
14×	`cos-mult` `frac-sub`
11×	`associate-*r/`
10×	`prod-exp` `cbrt-unprod`
4×	`associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`cbrt-undiv` `pow-plus` `flip3--` `div-exp` `*-commutative` `div-inv` `flip--` `unswap-sqr`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube`

Counts

4 → 135

Calls

4 calls:

Slowest

633.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
155.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
149.0ms	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))
61.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

265.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a)))))))
170.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))))
85.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
85.0ms	(cbrt (* (* (* (sin b) (sin a)) (* (sin b) (sin a))) (* (sin b) (sin a))))

simplify1.1s

Counts: 147 → 147

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes312.0ms

Accuracy

0% (0.3b remaining)

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

bsearch7.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	2903×	body	1280	valid
1.8s	1956×	body	640	valid
912.0ms	756×	body	320	valid
364.0ms	2016×	body	80	valid
137.0ms	370×	body	160	valid