Details

Time bar (total: 19.0s)

sample46.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
6.0ms256×pre80true

simplify578.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01435
13335
211135
355735
done500135

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize16.0ms

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))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

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:
187.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
464.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
689.0ms
(/ (/ (/ (+ (+ (+ 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))
481.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
196.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
219.0ms
(/ (/ (/ (+ (+ (+ 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))
90.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify885.0ms

Counts
477 → 477
Iterations

Useful iterations: done (854.0ms)

IterNodesCost
060325954
1160825182
done500024265

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize21.0ms

Local error

Found 3 expressions with local error:

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)))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
954×times-frac
827×*-un-lft-identity
382×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
32×flip3-+ flip-+
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 511
Calls
3 calls:
464.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
663.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
407.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series463.0ms

Counts
3 → 9
Calls
3 calls:
193.0ms
(/ (/ (+ (+ (+ 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)))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify832.0ms

Counts
520 → 520
Iterations

Useful iterations: done (778.0ms)

IterNodesCost
058427351
1157126487
done500125464

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
624×times-frac
522×sqrt-prod
425×*-un-lft-identity
325×add-sqr-sqrt
323×add-cube-cbrt
55×associate-/l*
51×distribute-lft-out
24×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×sqrt-undiv associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 464
Calls
4 calls:
395.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
256.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
156.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
189.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series571.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
165.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
85.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify582.0ms

Counts
476 → 476
Iterations

Useful iterations: done (552.0ms)

IterNodesCost
045523023
1113520455
done500119556

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.6b

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ alpha (+ beta (* 2.0 1.0))))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite526.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×cbrt-div
12×cbrt-prod
10×flip3-+ flip-+
9×add-exp-log add-sqr-sqrt add-cube-cbrt
8×associate-/l/
7×add-cbrt-cube
5×distribute-lft-out
4×pow1 frac-times times-frac associate-/r* add-log-exp
3×pow1/3
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
292.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ alpha (+ beta (* 2.0 1.0))))
75.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
76.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
79.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series631.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ alpha (+ beta (* 2.0 1.0))))
95.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
128.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
91.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01732506
14842399
221382167
done50002142

prune601.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.6b

regimes110.0ms

Accuracy

54.3% (1.2b remaining)

Error of 2.4b against oracle of 1.1b and baseline of 3.8b

bsearch33.0ms

Steps
ItersRangePoint
4
5.64112133829597e+173
1.045369472320571e+174
6.632569412339182e+173

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02036
12836
done2836

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8000×body80valid
247.0ms8000×pre80true