Details

sample335.0ms

Algorithm

intervals

Results

172.0ms	97×	body	1280	valid
54.0ms	65×	body	640	valid
12.0ms	63×	body	80	valid
10.0ms	20×	body	320	valid
4.0ms	11×	body	160	valid

simplify75.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize25.0ms

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))

rewrite46.0ms

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

19.0ms	(/ (* r (sin b)) (cos (+ a b)))
17.0ms	(cos (+ a b))
8.0ms	(* r (sin b))

series233.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

158.0ms	(/ (* r (sin b)) (cos (+ a b)))
51.0ms	(* r (sin b))
24.0ms	(cos (+ a b))

simplify877.0ms

Counts: 59 → 59

prune756.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

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)))

rewrite97.0ms

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

48.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
30.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
7.0ms	(* r (sin b))

series605.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

319.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
148.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms	(* (sin a) (sin b))
67.0ms	(* r (sin b))

simplify1.9s

Counts: 92 → 92

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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)))

rewrite167.0ms

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

94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

620.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
386.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
103.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))

simplify1.6s

Counts: 116 → 116

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* (sin b) r)

rewrite82.0ms

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

27.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
21.0ms	(* (sin a) (sin b))
8.0ms	(* (sin b) r)

series610.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

397.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* (sin a) (sin b))
43.0ms	(* (sin b) r)

simplify2.1s

Counts: 92 → 92

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes304.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.9s

Algorithm

intervals

Results

4.7s	2941×	body	1280	valid
1.8s	1889×	body	640	valid
575.0ms	770×	body	320	valid
366.0ms	2072×	body	80	valid
171.0ms	328×	body	160	valid