Details

sample527.0ms

Algorithm

intervals

Results

289.0ms	108×	body	1280	valid
84.0ms	56×	body	640	valid
21.0ms	25×	body	320	valid
15.0ms	57×	body	80	valid
5.0ms	10×	body	160	valid

simplify63.0ms

Counts: 1 → 1

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize26.0ms

Local error

Found 3 expressions with local error:

1.9b	(cos (+ a b))
0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

Slowest

35.0ms	(* r (/ (sin b) (cos (+ a b))))
35.0ms	(/ (sin b) (cos (+ a b)))
9.0ms	(cos (+ a b))

series449.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

174.0ms	(cos (+ a b))
149.0ms	(* r (/ (sin b) (cos (+ a b))))
126.0ms	(/ (sin b) (cos (+ a b)))

simplify747.0ms

Counts: 79 → 79

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

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)))

rewrite227.0ms

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

140.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))

series747.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

373.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
160.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
129.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
85.0ms	(* (sin a) (sin b))

simplify1.7s

Counts: 116 → 116

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

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))

rewrite191.0ms

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×	`cos-mult` `insert-posit16` `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 → 118

Calls

4 calls:

Slowest

89.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
61.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
15.0ms	(* r (sin b))

series585.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

302.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
139.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))
70.0ms	(* r (sin b))

simplify2.3s

Counts: 130 → 130

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize161.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.3b	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

160×	`pow1`
68×	`pow-prod-down`
52×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
16×	`pow-sqr` `pow-prod-up`
8×	`pow-plus` `cos-mult` `sin-mult`
4×	`pow2` `add-sqr-sqrt` `frac-times` `-un-lft-identity` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `-commutative` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

Slowest

77.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
58.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
56.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
42.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

78.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
72.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
67.0ms	(* (* (sin b) (sin a)) (* (sin b) (sin a)))
63.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify2.1s

Counts: 164 → 164

prune3.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes432.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.8s	2993×	body	1280	valid
1.7s	1807×	body	640	valid
425.0ms	746×	body	320	valid
372.0ms	2118×	body	80	valid
124.0ms	337×	body	160	valid