Details

sample488.0ms

Algorithm

intervals

Results

127.0ms	102×	body	1280	valid
86.0ms	62×	body	640	valid
21.0ms	35×	body	320	valid
12.0ms	51×	body	80	valid
2.0ms	6×	body	160	valid

simplify79.0ms

Counts: 1 → 1

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize86.0ms

Local error

Found 3 expressions with local error:

5.7b	(cos (+ a b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite88.0ms

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

42.0ms	(cos (+ a b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(* r (sin b))

series397.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

288.0ms	(/ (* r (sin b)) (cos (+ a b)))
77.0ms	(* r (sin b))
31.0ms	(cos (+ a b))

simplify706.0ms

Counts: 59 → 59

prune967.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

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

rewrite86.0ms

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

38.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* (sin a) (sin b))
15.0ms	(* r (sin b))

series573.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

340.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
105.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
87.0ms	(* (sin a) (sin b))
41.0ms	(* r (sin b))

simplify1.6s

Counts: 92 → 92

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

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

104.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
181.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
92.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
81.0ms	(* (sin a) (sin b))

simplify2.0s

Counts: 116 → 116

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (exp (* (sin a) (sin b))))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.2b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

Slowest

44.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
17.0ms	(* (sin a) (sin b))
13.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
8.0ms	(log (exp (* (sin a) (sin b))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

272.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
111.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
60.0ms	(* (sin a) (sin b))
54.0ms	(log (exp (* (sin a) (sin b))))

simplify1.5s

Counts: 87 → 87

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes283.0ms

Accuracy

0% (0.4b remaining)

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

bsearch6.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.0s	2921×	body	1280	valid
2.1s	1789×	body	640	valid
573.0ms	759×	body	320	valid
350.0ms	2168×	body	80	valid
205.0ms	367×	body	160	valid