Details

Time bar (total: 32.4s)

sample32.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
4.0ms256×pre80true

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01435
13335
211135
355035
4408735
done500035

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
182.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
722.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
787.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
500.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
198.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
270.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
129.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.4s

Counts
477 → 477
Iterations

Useful iterations: done (2.3s)

IterNodesCost
060325954
1144325182
2475424241
done500123501

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
954×times-frac
828×*-un-lft-identity
383×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
33×flip3-+ flip-+
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 524
Calls
4 calls:
54.0ms
(+ (+ alpha beta) (* beta alpha))
486.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
654.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
420.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (+ alpha beta) (* beta alpha))
184.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
187.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
111.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.6s

Counts
536 → 536
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
060827532
1148226661
2499125612
done500125612

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
0.1b
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
1777×times-frac
1545×*-un-lft-identity
761×add-sqr-sqrt
747×sqrt-prod
678×add-cube-cbrt
497×distribute-lft-out
321×associate-*r*
104×associate-/r/
71×associate-/l*
63×associate-*l*
54×flip3-+ flip-+
52×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
11×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 888
Calls
4 calls:
1.6s
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
493.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
465.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
492.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
251.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
200.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
99.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
476.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.8s

Counts
900 → 900
Iterations

Useful iterations: done (1.7s)

IterNodesCost
091152975
1182250323
done500147683

prune3.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0)))
1.8b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
54×times-frac
33×add-sqr-sqrt
31×add-cube-cbrt
22×associate-/l*
20×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
14×associate-/r/
13×distribute-lft-out
9×add-log-exp
8×frac-times
7×cbrt-undiv div-exp
6×pow1
5×associate-*r*
4×associate-*r/ associate-*l/ associate-/r* div-inv
3×associate-*l* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 142
Calls
4 calls:
33.0ms
(+ (+ alpha beta) (* beta alpha))
119.0ms
(* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0)))
589.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0))))
538.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (+ alpha beta) (* beta alpha))
31.0ms
(* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0)))
228.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (* 2.0 1.0) (+ alpha beta)) (+ beta (+ alpha 3.0))))
115.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.5s

Counts
154 → 154
Iterations

Useful iterations: 2 (909.0ms)

IterNodesCost
02694605
18194536
240704078
done50014078

prune646.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes90.0ms

Accuracy

59.1% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.8b

bsearch111.0ms

Steps
ItersRangePoint
8
1.7519304510016456e+160
7.027642810475786e+162
6.375269332570683e+160

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03058
14458
done4458

end0.0ms

sample1.3s

Algorithm
intervals
Results
885.0ms8000×body80valid
217.0ms8000×pre80true