Details

Time bar (total: 33.0s)

sample50.0ms

Algorithm
intervals
Results
12.0ms187×body80valid
6.0ms20×body1280valid
5.0ms256×pre80true
5.0ms23×body640valid
4.0ms18×body320valid
1.0ms8×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
13129
210229
345429
4246229
done500029

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r* div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*r/ associate-*l* associate-*l/
3×prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 144
Calls
4 calls:
46.0ms
(* (+ alpha beta) (- beta alpha))
254.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
850.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
68.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series949.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (+ alpha beta) (- beta alpha))
360.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
427.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
100.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify617.0ms

Counts
156 → 156
Iterations

Useful iterations: done (607.0ms)

IterNodesCost
02634471
17904238
done50013984

prune681.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
2.5b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
96×associate-/l*
79×distribute-lft-out-- difference-of-squares
60×associate-/r/
33×div-inv
30×associate-/r*
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 645
Calls
4 calls:
321.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
87.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
101.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
1.1s
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
329.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
118.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
198.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
422.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify1.5s

Counts
657 → 657
Iterations

Useful iterations: done (1.4s)

IterNodesCost
070527143
1197026090
done500025700

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.8b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.8b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
2.5b
(+ (* (/ 1 (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite814.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3
1×+-commutative sum-log
Counts
4 → 50
Calls
4 calls:
16.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
17.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
763.0ms
(+ (* (/ 1 (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
207.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
250.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
219.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
482.0ms
(+ (* (/ 1 (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify755.0ms

Counts
62 → 62
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
01141904
13111880
211801668
done50011596

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.8b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
2.5b
(+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))))
2.9b
(log (+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))))

rewrite11.7s

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1 add-exp-log
4×cbrt-div log-prod flip3-+ add-cbrt-cube flip-+
2×log-div pow1/3 distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
4 → 53
Calls
4 calls:
18.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
30.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
5.8s
(+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))))
5.9s
(log (+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
229.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
229.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
501.0ms
(+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))))
509.0ms
(log (+ 1.0 (/ (/ (/ (+ alpha beta) (/ (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))))))

simplify994.0ms

Counts
65 → 65
Iterations

Useful iterations: done (990.0ms)

IterNodesCost
01483204
13793071
214792726
done50012690

prune491.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.6b

regimes447.0ms

Accuracy

11.3% (7.1b remaining)

Error of 11.2b against oracle of 4.1b and baseline of 12.1b

bsearch63.0ms

Steps
ItersRangePoint
5
2.2692661968115645e+132
4.9715408910126116e+132
4.511384635113818e+132

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042202
150202
done50202

end0.0ms

sample2.4s

Algorithm
intervals
Results
685.0ms6398×body80valid
659.0ms504×body1280valid
320.0ms8000×pre80true
177.0ms556×body640valid
85.0ms354×body320valid
29.0ms188×body160valid