Details

sample105.0ms

Algorithm

intervals

Results

60.0ms	92×	body	1280	valid
16.0ms	53×	body	640	valid
6.0ms	72×	body	80	valid
5.0ms	25×	body	320	valid
4.0ms	15×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite48.0ms

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:

9.0ms	(* r (sin b))
13.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series176.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
108.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify30.0ms

Counts: 56 → 56

prune141.0ms

Pruning

6 alts after pruning (6 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	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite72.0ms

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:

11.0ms	(* (cos a) (cos b))
10.0ms	(* r (sin b))
36.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series394.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos a) (cos b))
43.0ms	(* r (sin b))
245.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
57.0ms	(* (sin a) (sin b))

simplify43.0ms

Counts: 93 → 93

prune319.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

11.0ms	(* (cos b) (cos a))
77.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))
32.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos b) (cos a))
246.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
56.0ms	(* (sin a) (sin b))
127.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify50.0ms

Counts: 117 → 117

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
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` `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-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

9.0ms	(* r (sin b))
36.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
75.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* r (sin b))
109.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
53.0ms	(* (sin a) (sin b))
243.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify60.0ms

Counts: 126 → 126

prune330.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes156.0ms

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

sample4.0s

Algorithm

intervals

Results

2.2s	2929×	body	1280	valid
1.0s	1872×	body	640	valid
225.0ms	2086×	body	80	valid
222.0ms	788×	body	320	valid
55.0ms	328×	body	160	valid