Details

sample338.0ms

Algorithm

intervals

Results

158.0ms	108×	body	1280	valid
42.0ms	56×	body	640	valid
12.0ms	25×	body	320	valid
9.0ms	57×	body	80	valid
4.0ms	10×	body	160	valid

simplify52.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize64.0ms

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))

rewrite97.0ms

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

54.0ms	(* r (sin b))
22.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(cos (+ a b))

series511.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

366.0ms	(/ (* r (sin b)) (cos (+ a b)))
75.0ms	(cos (+ a b))
70.0ms	(* r (sin b))

simplify830.0ms

Counts: 59 → 59

prune873.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

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

rewrite98.0ms

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

41.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
10.0ms	(* r (sin b))

series662.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

361.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
160.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
70.0ms	(* r (sin b))

simplify2.0s

Counts: 92 → 92

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

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)))

rewrite210.0ms

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

128.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series747.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

365.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
172.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
125.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
84.0ms	(* (sin a) (sin b))

simplify1.6s

Counts: 116 → 116

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos a) (cos b)) (sin b))
0.2b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
0.0b	(* (cos a) (cos b))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `associate-/r/` `cos-mult` `cbrt-unprod` `div-inv` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 96

Calls

4 calls:

Slowest

36.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
28.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
21.0ms	(/ (* (cos a) (cos b)) (sin b))
19.0ms	(* (cos a) (cos b))

series599.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

295.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
129.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
99.0ms	(/ (* (cos a) (cos b)) (sin b))
75.0ms	(* (cos a) (cos b))

simplify1.6s

Counts: 108 → 108

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes436.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.9s	2993×	body	1280	valid
1.7s	1807×	body	640	valid
419.0ms	746×	body	320	valid
414.0ms	2118×	body	80	valid
130.0ms	337×	body	160	valid