Details

Time bar (total: 18.5s)

sample235.0ms

Algorithm
intervals
Results
72.0ms50×body640valid
54.0ms89×body1280valid
14.0ms34×body320valid
6.0ms73×body80valid
2.0ms10×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
089
1129
2169
3209
4219
done219

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
2.8b
(cos (+ a b))

rewrite112.0ms

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:
60.0ms
(* r (/ (sin b) (cos (+ a b))))
20.0ms
(/ (sin b) (cos (+ a b)))
25.0ms
(cos (+ a b))

series272.0ms

Counts
3 → 9
Calls
3 calls:
165.0ms
(* r (/ (sin b) (cos (+ a b))))
59.0ms
(/ (sin b) (cos (+ a b)))
47.0ms
(cos (+ a b))

simplify809.0ms

Counts
76 → 76
Iterations

Useful iterations: done (805.0ms)

IterNodesCost
0116909
1272887
21040801
done5000791

prune309.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

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 b) (sin a)))
31.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
120.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
20.0ms
(* (sin b) (sin a))

series718.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
160.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
350.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
62.0ms
(* (sin b) (sin a))

simplify1.6s

Counts
112 → 112
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01752072
14382028
219641842
done50031753

prune673.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite338.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
141×add-sqr-sqrt
134×add-cube-cbrt *-un-lft-identity
126×distribute-lft-neg-in distribute-rgt-neg-in
111×associate-*r*
42×neg-mul-1
13×add-exp-log add-cbrt-cube
10×associate-/r* associate-/l*
8×pow1 associate-/r/ distribute-neg-frac
7×sin-mult
6×associate-*l* cos-mult add-log-exp
3×flip3-- prod-exp frac-sub flip-- cbrt-unprod sub-div unswap-sqr
2×cbrt-undiv distribute-frac-neg div-exp pow-prod-down *-commutative div-inv
1×neg-sub0 sub-neg frac-2neg diff-log div-sub associate-*r/ clear-num distribute-rgt-neg-out
Counts
4 → 299
Calls
4 calls:
37.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
78.0ms
(/ (- (sin b)) (- (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
184.0ms
(* r (/ (- (sin b)) (- (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
13.0ms
(* (sin b) (sin a))

series694.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (* (cos a) (cos b)) (* (sin b) (sin a)))
197.0ms
(/ (- (sin b)) (- (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
337.0ms
(* r (/ (- (sin b)) (- (- (* (cos a) (cos b)) (* (sin b) (sin a))))))
58.0ms
(* (sin b) (sin a))

simplify2.6s

Counts
311 → 311
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
04087274
111007048
249716816
done50016816

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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:
17.0ms
(* r (sin b))
41.0ms
(- (* (sin a) (sin b)) (* (cos b) (cos a)))
33.0ms
(/ (* r (sin b)) (- (* (sin a) (sin b)) (* (cos b) (cos a))))
18.0ms
(* (sin a) (sin b))

series656.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* r (sin b))
132.0ms
(- (* (sin a) (sin b)) (* (cos b) (cos a)))
407.0ms
(/ (* r (sin b)) (- (* (sin a) (sin b)) (* (cos b) (cos a))))
75.0ms
(* (sin a) (sin b))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01421257
13711225
216001085
done50011045

prune445.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes230.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01317
11817
22417
done2417

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.9s2913×body1280valid
1.2s1797×body640valid
649.0ms2129×body80valid
431.0ms788×body320valid
90.0ms374×body160valid