Details

sample106.0ms

Algorithm

intervals

Results

48.0ms	92×	body	1280	valid
19.0ms	58×	body	640	valid
18.0ms	24×	body	320	valid
5.0ms	72×	body	80	valid
2.0ms	11×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite51.0ms

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:

24.0ms	(* r (sin b))
13.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series180.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
112.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify29.0ms

Counts: 56 → 56

prune145.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
10.0ms	(* r (sin b))
13.0ms	(* (sin a) (sin b))
34.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos a) (cos b))
45.0ms	(* r (sin b))
49.0ms	(* (sin a) (sin b))
249.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify43.0ms

Counts: 93 → 93

prune308.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

11.0ms	(* (cos a) (cos b))
13.0ms	(* (sin a) (sin b))
38.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
55.0ms	(* (sin a) (sin b))
129.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
262.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify68.0ms

Counts: 152 → 152

prune556.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* r (sin b)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

9.0ms	(* r (sin b))
34.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
15.0ms	(* (sin a) (sin b))
96.0ms	(* (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* r (sin b)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (sin b))
114.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
49.0ms	(* (sin a) (sin b))
300.0ms	(* (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* r (sin b)))

simplify55.0ms

Counts: 125 → 125

prune344.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.4s	2948×	body	1280	valid
779.0ms	1861×	body	640	valid
271.0ms	2078×	body	80	valid
239.0ms	754×	body	320	valid
59.0ms	362×	body	160	valid