Details

sample205.0ms

Algorithm

intervals

Results

54.0ms	93×	body	1280	valid
23.0ms	65×	body	640	valid
8.0ms	20×	body	320	valid
6.0ms	69×	body	80	valid
2.0ms	10×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune68.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.5b	(cos (+ a b))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

18.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series294.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* r (sin b))
175.0ms	(/ (* r (sin b)) (cos (+ a b)))
57.0ms	(cos (+ a b))

simplify62.0ms

Counts: 56 → 56

prune233.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

18.0ms	(* r (sin b))
37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* r (sin b))
147.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms	(* (sin a) (sin b))
331.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Counts: 88 → 88

prune482.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

155.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
38.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
22.0ms	(* (sin a) (sin b))
38.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series779.0ms

Counts

4 → 12

Calls

4 calls:

388.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
142.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
66.0ms	(* (sin a) (sin b))
183.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify148.0ms

Counts: 112 → 112

prune684.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
25.8b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

13.0ms	(* (sin a) (sin b))
44.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
16.0ms	(pow (* (sin a) (sin b)) 3)
5.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series451.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin a) (sin b))
188.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
98.0ms	(pow (* (sin a) (sin b)) 3)
102.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify49.0ms

Counts: 102 → 102

prune598.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes351.0ms

Accuracy

13.2% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify198.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.0s	2952×	body	1280	valid
1.2s	1821×	body	640	valid
810.0ms	2097×	body	80	valid
308.0ms	773×	body	320	valid
133.0ms	362×	body	160	valid