Details

Time bar (total: 27.6s)

sample255.0ms

Algorithm
intervals
Results
70.0ms90×body1280valid
57.0ms66×body80valid
32.0ms63×body640valid
10.0ms27×body320valid
3.0ms10×body160valid

simplify36.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
089
1129
2169
3209
4219
done219

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.2b
(* r (/ (sin b) (cos (+ a b))))
0.2b
(/ (sin b) (cos (+ a b)))
5.5b
(cos (+ a b))

rewrite84.0ms

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×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u 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 → 73
Calls
3 calls:
36.0ms
(* r (/ (sin b) (cos (+ a b))))
16.0ms
(/ (sin b) (cos (+ a b)))
25.0ms
(cos (+ a b))

series276.0ms

Counts
3 → 9
Calls
3 calls:
160.0ms
(* r (/ (sin b) (cos (+ a b))))
72.0ms
(/ (sin b) (cos (+ a b)))
44.0ms
(cos (+ a b))

simplify3.6s

Counts
82 → 82
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0122955
1260924
2659834
31814830
done5001824

prune377.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite271.0ms

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
4×expm1-log1p-u log1p-expm1-u
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 fma-neg diff-log associate-*r/ prod-diff clear-num
Counts
4 → 110
Calls
4 calls:
21.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
158.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
67.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(* (sin a) (sin b))

series685.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
331.0ms
(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
144.0ms
(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
78.0ms
(* (sin a) (sin b))

simplify3.6s

Counts
122 → 122
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01812200
14302141
212431949
337311826
done50001821

prune626.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* r (sin b))
0.2b
(- (* (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))

rewrite95.0ms

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×expm1-log1p-u associate-/r/ cos-mult log1p-expm1-u
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 fma-neg diff-log prod-diff clear-num div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
16.0ms
(* r (sin b))
23.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
31.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
20.0ms
(* (sin a) (sin b))

series593.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* r (sin b))
131.0ms
(- (* (cos a) (cos b)) (* (sin a) (sin b)))
338.0ms
(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
62.0ms
(* (sin a) (sin b))

simplify3.7s

Counts
98 → 98
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01521364
13701324
211581196
341681081
done50001078

prune504.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b
(* (sin a) (sin b))
0.3b
(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.4b
(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-exp-log add-cbrt-cube
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r* associate-*l* associate-/r* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv sin-mult expm1-udef unswap-sqr
Counts
4 → 72
Calls
4 calls:
18.0ms
(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
26.0ms
(* (sin a) (sin b))
1.0ms
(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
1.0ms
(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ (sin b) (log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
79.0ms
(* (sin a) (sin b))
222.0ms
(log1p (expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
187.0ms
(expm1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify5.2s

Counts
84 → 84
Iterations

Useful iterations: 4 (3.2s)

IterNodesCost
01291396
12531263
26111145
314721136
447691109
done50001109

prune516.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
11516
done1516

end0.0ms

sample6.0s

Algorithm
intervals
Results
3.6s2814×body1280valid
1.3s1927×body640valid
334.0ms769×body320valid
286.0ms2165×body80valid
129.0ms327×body160valid