Details

sample488.0ms

Algorithm

intervals

Results

269.0ms	97×	body	1280	valid
71.0ms	65×	body	640	valid
16.0ms	63×	body	80	valid
15.0ms	20×	body	320	valid
5.0ms	11×	body	160	valid

simplify107.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize35.0ms

Local error

Found 3 expressions with local error:

4.2b	(cos (+ a b))
0.3b	(/ (* 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×	`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

22.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))
15.0ms	(* r (sin b))

series276.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

160.0ms	(/ (* r (sin b)) (cos (+ a b)))
61.0ms	(cos (+ a b))
55.0ms	(* r (sin b))

simplify905.0ms

Counts: 65 → 65

prune799.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 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)))

rewrite99.0ms

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

49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(* (sin a) (sin b))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))

series604.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

334.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
67.0ms	(* r (sin b))

simplify2.4s

Counts: 102 → 102

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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

rewrite230.0ms

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

122.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
51.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
30.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(* (sin a) (sin b))

series766.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

346.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
213.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
123.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))

simplify1.9s

Counts: 126 → 126

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize61.0ms

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))

rewrite197.0ms

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×	`expm1-log1p-u` `cos-mult` `insert-posit16` `log1p-expm1-u` `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 → 126

Calls

4 calls:

Slowest

115.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
39.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))
17.0ms	(* r (sin b))

series683.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

342.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
179.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms	(* (sin a) (sin b))
74.0ms	(* r (sin b))

simplify2.4s

Counts: 138 → 138

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes289.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.5s	2941×	body	1280	valid
1.5s	1889×	body	640	valid
578.0ms	770×	body	320	valid
440.0ms	2072×	body	80	valid
113.0ms	328×	body	160	valid