Details

Time bar (total: 16.5s)

sample66.0ms

Algorithm
intervals
Results
31.0ms248×body80valid
4.0msbody1280valid
1.0msbody640valid
0.0msbody320valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
01519
12919
26819
318917
436717
549717
666117
7169317
done500117

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* 2.0 r1) r2) (cos (- a1 a2)))
2.9b
(cos (- a1 a2))
4.2b
(- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2))))
31.0b
(sqrt (- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2)))))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
13×add-cbrt-cube add-exp-log
add-log-exp
add-sqr-sqrt
*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
cos-diff
associate-*r* sqrt-prod
distribute-rgt-in cos-sum sub-neg distribute-lft-in flip3-- sqrt-div diff-log flip-- associate--r+
rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-*l* associate--l+ *-commutative
Counts
4 → 64
Calls
4 calls:
115.0ms
(* (* (* 2.0 r1) r2) (cos (- a1 a2)))
20.0ms
(cos (- a1 a2))
114.0ms
(- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2))))
106.0ms
(sqrt (- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2)))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (* (* 2.0 r1) r2) (cos (- a1 a2)))
33.0ms
(cos (- a1 a2))
124.0ms
(- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2))))
273.0ms
(sqrt (- (+ (* r1 r1) (* r2 r2)) (* (* (* 2.0 r1) r2) (cos (- a1 a2)))))

simplify2.3s

Counts
76 → 76
Iterations

Useful iterations: 2 (479.0ms)

IterNodesCost
01391457
13641359
221291233
done50011233

prune502.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.2b

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2))))
1.0b
(+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1)))))
6.9b
(* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))
31.0b
(sqrt (- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
25×add-cbrt-cube add-exp-log
15×pow-prod-down prod-exp cbrt-unprod
11×add-log-exp
add-sqr-sqrt
*-un-lft-identity associate-*r/ add-cube-cbrt sin-mult
associate-+r+ sqrt-div frac-sub
sub-neg flip3-+ sqrt-prod flip-+
distribute-rgt-in sum-log distribute-lft-in flip3-- diff-log flip--
+-commutative rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* associate--l+ *-commutative
Counts
4 → 77
Calls
4 calls:
131.0ms
(- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2))))
21.0ms
(+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1)))))
145.0ms
(* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))
122.0ms
(sqrt (- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
259.0ms
(- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2))))
144.0ms
(+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1)))))
162.0ms
(* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))
857.0ms
(sqrt (- (+ (* r1 r1) (* r2 (- r2 (* (* (cos a1) (cos a2)) (* 2.0 r1))))) (* (* (* 2.0 r1) r2) (* (sin a1) (sin a2)))))

simplify3.5s

Counts
89 → 89
Iterations

Useful iterations: 2 (811.0ms)

IterNodesCost
01902878
15632636
232782379
done50012379

prune707.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.9b

regimes1.2s

Accuracy

49.8% (13.1b remaining)

Error of 18.3b against oracle of 5.1b and baseline of 31.3b

bsearch703.0ms

Steps
ItersRangePoint
7
8.118882087641906e-06
0.000689657585566607
0.0005806824695993502
8
1.738453008839565e-132
9.766628192739036e-129
5.115803934409726e-132
7
2.7255026950609655e-201
7.53026429731197e-200
3.1147245199177167e-200
3
1.4909991364309658e-229
1.894721282206072e-229
1.578758057424873e-229
9
-3.1647617934541664e-127
-7.748756135046356e-136
-2.4400815278368915e-135
8
-0.045201555905920524
-7.250512869097592e-05
-0.0192950764772948

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
047139
158139
done58139

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.5s7691×body80valid
184.0ms155×body1280valid
64.0ms109×body640valid
12.0ms27×body320valid
5.0ms18×body160valid