Details

Time bar (total: 1.1m)

sample73.0ms

Algorithm
intervals
Results
22.0ms222×body80valid
8.0ms256×pre80true
5.0ms13×body640valid
3.0ms11×body320valid
3.0ms6×body1280valid
1.0ms4×body160valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5001
42483
3453
2102
131
015

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize46.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite993.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
213.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
723.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
52.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series946.0ms

Counts
3 → 9
Calls
3 calls:
344.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
479.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
123.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.9s

Counts
120 → 120
Iterations
IterNodes
done5001
24479
1697
0225

prune921.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.4b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite905.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 295
Calls
4 calls:
48.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
260.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
116.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
457.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
258.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
471.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
354.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify1.7s

Counts
307 → 307
Iterations
IterNodes
done5000
11139
0385

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
2.4b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite695.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 295
Calls
4 calls:
38.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
197.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
6.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
434.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
259.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
496.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
376.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify1.5s

Counts
307 → 307
Iterations
IterNodes
done5000
11139
0385

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize90.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- beta alpha))
0.6b
(cbrt (- beta alpha))
2.1b
(+ 1.0 (* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))))
2.4b
(* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))))))

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
8434×times-frac
4486×*-un-lft-identity
3130×add-sqr-sqrt
2878×associate-*r*
2826×cbrt-prod
2760×cbrt-div
2452×add-cube-cbrt
1886×associate-/r/
1381×flip3-+ flip-+
886×frac-times
703×distribute-lft-out
444×associate-*l/
443×associate-*r/
314×distribute-lft-out-- difference-of-squares
287×div-inv
90×add-exp-log
56×add-cbrt-cube
42×cbrt-undiv div-exp
28×prod-exp cbrt-unprod
13×unswap-sqr
6×pow1 add-log-exp
4×associate-*l*
2×flip3-- pow1/3 flip--
1×+-commutative sum-log pow-prod-down *-commutative
Counts
4 → 2982
Calls
4 calls:
7.0ms
(cbrt (- beta alpha))
7.0ms
(cbrt (- beta alpha))
12.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))))
1.8s
(* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt (- beta alpha))
222.0ms
(cbrt (- beta alpha))
508.0ms
(+ 1.0 (* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))))
402.0ms
(* (+ alpha beta) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i)))))))

simplify13.5s

Counts
2994 → 2994
Iterations
IterNodes
done5000
04375

prune29.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

regimes495.0ms

Accuracy

0% (6.1b remaining)

Error of 12.1b against oracle of 6.0b and baseline of 12.1b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done27
127
021

end0.0ms

sample2.0s

Algorithm
intervals
Results
721.0ms6394×body80valid
274.0ms493×body1280valid
267.0ms563×body640valid
258.0ms8000×pre80true
88.0ms366×body320valid
30.0ms184×body160valid