Details

Time bar (total: 19.3s)

sample290.0ms

Algorithm
intervals
Results
104.0ms60×body640valid
90.0ms94×body1280valid
11.0ms30×body320valid
10.0ms65×body80valid
2.0ms7×body160valid

simplify80.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize65.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (sin b) (cos (+ a b)))
0.2b
(* r (/ (sin b) (cos (+ a b))))
3.9b
(cos (+ a b))

rewrite166.0ms

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:
25.0ms
(/ (sin b) (cos (+ a b)))
84.0ms
(* r (/ (sin b) (cos (+ a b))))
29.0ms
(cos (+ a b))

series274.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (sin b) (cos (+ a b)))
194.0ms
(* r (/ (sin b) (cos (+ a b))))
32.0ms
(cos (+ a b))

simplify2.1s

Counts
76 → 76

prune294.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite207.0ms

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:
25.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms
(* (sin a) (sin b))
125.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series719.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
174.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
63.0ms
(* (sin a) (sin b))
360.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify923.0ms

Counts
112 → 112

prune510.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

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×cos-mult sin-mult
4×associate-/r/
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 → 77
Calls
4 calls:
19.0ms
(* (cos a) (cos b))
18.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
25.0ms
(* (sin a) (sin b))
44.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (cos a) (cos b))
126.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
65.0ms
(* (sin a) (sin b))
359.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify857.0ms

Counts
89 → 89

prune402.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* r (/ (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
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
0.3b
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
89×pow1
42×add-exp-log add-cbrt-cube
38×pow-prod-down
37×associate-*r*
24×cos-mult sin-mult
23×prod-exp cbrt-unprod
20×associate-*r/
19×add-sqr-sqrt
16×associate-/r/
14×add-cube-cbrt *-un-lft-identity
13×frac-times times-frac associate-*l/
9×frac-sub
8×pow-sqr pow-prod-up
6×associate-*l*
5×sub-div
4×pow-plus *-commutative add-log-exp
3×difference-of-squares
2×cbrt-undiv pow2 flip3-+ swap-sqr div-exp frac-add flip-+ unswap-sqr
1×distribute-rgt-in flip3-- distribute-lft-in flip-- div-inv
Counts
4 → 154
Calls
4 calls:
592.0ms
(* (* r (/ (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))))
498.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
65.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
63.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

series1.2s

Counts
4 → 12
Calls
4 calls:
659.0ms
(* (* r (/ (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))))
406.0ms
(* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))))
80.0ms
(* (* (sin a) (sin b)) (* (sin a) (sin b)))
71.0ms
(* (* (cos a) (cos b)) (* (cos a) (cos b)))

simplify652.0ms

Counts
166 → 166

prune649.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes257.0ms

Accuracy

28.9% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.2s

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.8s2916×body1280valid
1.3s1826×body640valid
386.0ms2134×body80valid
328.0ms784×body320valid
112.0ms341×body160valid