Details

sample80.0ms

Algorithm

intervals

Results

44.0ms	99×	body	1280	valid
16.0ms	64×	body	640	valid
4.0ms	24×	body	320	valid
3.0ms	59×	body	80	valid
1.0ms	10×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.3b	(cos (+ a b))

rewrite16.0ms

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:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series161.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
99.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify961.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (254.0ms)

Iter	Nodes	Cost
0	90	535
1	199	525
2	556	447
3	2202	443
done	5001	443

prune145.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

3.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
218.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

88 → 88

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	140	1256
1	343	1224
2	1092	1170
3	4074	1011
done	5001	1010

prune273.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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

rewrite45.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
212.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	170	2072
1	404	2024
2	1174	1834
3	3750	1715
done	5000	1714

prune388.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.3b	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
82×	`pow1`
65×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
35×	`add-exp-log` `add-cbrt-cube`
34×	`pow-prod-down`
27×	`cos-mult` `sin-mult`
22×	`associate-/r*`
16×	`prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `difference-of-squares`
12×	`associate-r/` `associate-l/`
10×	`frac-times`
9×	`frac-sub`
8×	`pow-sqr` `pow-prod-up`
7×	`associate-/l*`
6×	`div-inv`
5×	`flip3-+` `frac-add` `flip-+` `sub-div`
4×	`cbrt-undiv` `pow-plus` `div-exp` `add-log-exp`
2×	`pow2` `frac-2neg` `swap-sqr` `associate-r` `associate-l` `clear-num` `*-commutative`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 219

Calls

4 calls:

26.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
16.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
45.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(/ (sin b) (/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))))
52.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
206.0ms	(/ (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))))
57.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify1.4s

Counts

231 → 231

Iterations

Useful iterations: 2 (593.0ms)

Iter	Nodes	Cost
0	349	9250
1	896	7876
2	4052	7374
done	5001	7374

prune904.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	21	42
done	21	42

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2963×	body	1280	valid
491.0ms	1882×	body	640	valid
136.0ms	733×	body	320	valid
121.0ms	2086×	body	80	valid
44.0ms	339×	body	160	valid