Details

sample747.0ms

Algorithm

intervals

Results

264.0ms	56×	body	640	valid
234.0ms	90×	body	1280	valid
52.0ms	28×	body	320	valid
48.0ms	72×	body	80	valid
6.0ms	10×	body	160	valid

simplify144.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize27.0ms

Local error

Found 3 expressions with local error:

3.4b	(cos (+ a b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite53.0ms

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

24.0ms	(cos (+ a b))
16.0ms	(/ (* r (sin b)) (cos (+ a b)))
9.0ms	(* r (sin b))

series188.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

112.0ms	(/ (* r (sin b)) (cos (+ a b)))
48.0ms	(* r (sin b))
27.0ms	(cos (+ a b))

simplify941.0ms

Counts: 59 → 59

prune612.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

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))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 85

Calls

4 calls:

Slowest

53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
26.0ms	(* (sin a) (sin b))
9.0ms	(* (cos a) (cos b))
9.0ms	(* r (sin b))

series472.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))
56.0ms	(* (cos a) (cos b))
54.0ms	(* r (sin b))

simplify1.9s

Counts: 97 → 97

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 109

Calls

4 calls:

Slowest

83.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms	(* (cos a) (cos b))
11.0ms	(* (sin a) (sin b))

series614.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

340.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
154.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
68.0ms	(* (sin a) (sin b))
52.0ms	(* (cos a) (cos b))

simplify2.2s

Counts: 121 → 121

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
0.3b	(/ (* (cos a) (cos b)) (sin b))
0.1b	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
0.1b	(* (cos a) (cos b))

rewrite84.0ms

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

28.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
23.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
19.0ms	(* (cos a) (cos b))
13.0ms	(/ (* (cos a) (cos b)) (sin b))

series534.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

266.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))
131.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
79.0ms	(/ (* (cos a) (cos b)) (sin b))
58.0ms	(* (cos a) (cos b))

simplify1.7s

Counts: 108 → 108

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.2s	2953×	body	1280	valid
1.5s	1793×	body	640	valid
425.0ms	801×	body	320	valid
385.0ms	2106×	body	80	valid
117.0ms	349×	body	160	valid