Details

sample280.0ms

Algorithm

intervals

Results

134.0ms	104×	body	1280	valid
27.0ms	50×	body	640	valid
11.0ms	29×	body	320	valid
7.0ms	62×	body	80	valid
3.0ms	11×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.6b	(cos (+ a b))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

39.0ms	(* r (/ (sin b) (cos (+ a b))))
21.0ms	(/ (sin b) (cos (+ a b)))
16.0ms	(cos (+ a b))

series280.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(* r (/ (sin b) (cos (+ a b))))
76.0ms	(/ (sin b) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify74.0ms

Counts: 76 → 76

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite246.0ms

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:

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
127.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(* (sin a) (sin b))
46.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series801.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
332.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
81.0ms	(* (sin a) (sin b))
227.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify171.0ms

Counts: 112 → 112

prune627.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `pow-flip` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

70.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
23.0ms	(* (sin a) (sin b))
24.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
61.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series946.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
87.0ms	(* (sin a) (sin b))
251.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
167.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify95.0ms

Counts: 212 → 212

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-l`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/` `clear-num`

Counts

4 → 100

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
111.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))
13.0ms	(* (sin a) (sin b))

series806.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
253.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
351.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))
69.0ms	(* (sin a) (sin b))

simplify58.0ms

Counts: 112 → 112

prune446.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

19% (0.3b remaining)

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

bsearch0.0ms

simplify82.0ms

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	2904×	body	1280	valid
1.0s	1843×	body	640	valid
288.0ms	2146×	body	80	valid
280.0ms	770×	body	320	valid
71.0ms	339×	body	160	valid