Details

Time bar (total: 18.1s)

sample32.0ms

Algorithm
intervals
Results
7.0ms197×body80valid
4.0ms256×pre80true
3.0ms24×body640valid
2.0ms19×body320valid
2.0ms10×body1280valid
0.0ms6×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
13129
210229
345229
4209029
done500129

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize13.0ms

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))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite770.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
175.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
540.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
50.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series605.0ms

Counts
3 → 9
Calls
3 calls:
238.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
285.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
82.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.0s

Counts
120 → 120
Iterations

Useful iterations: 2 (370.0ms)

IterNodesCost
02254035
16753821
229493577
done50003577

prune340.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.6b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
674.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
180.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
133.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
166.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series915.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
235.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
139.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
294.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify753.0ms

Counts
497 → 497
Iterations

Useful iterations: done (726.0ms)

IterNodesCost
056820612
1167519182
done500118531

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.6b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
670.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
182.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
132.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
165.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series924.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
227.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
146.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
300.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify973.0ms

Counts
497 → 497
Iterations

Useful iterations: done (950.0ms)

IterNodesCost
056820612
1167519182
done500118531

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.6b
(+ (* (/ 1 1) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
672.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
181.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
132.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
484.0ms
(+ (* (/ 1 1) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series910.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
232.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
137.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
298.0ms
(+ (* (/ 1 1) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify760.0ms

Counts
497 → 497
Iterations

Useful iterations: done (737.0ms)

IterNodesCost
057120684
1168919182
done500118531

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

regimes211.0ms

Accuracy

13.1% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 12.7b

bsearch51.0ms

Steps
ItersRangePoint
7
1.2814798534538045e+116
1.7935190318167123e+118
7.366216039173236e+116

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03578
14278
done4278

end0.0ms

sample835.0ms

Algorithm
intervals
Results
230.0ms6310×body80valid
122.0ms8000×pre80true
88.0ms490×body1280valid
87.0ms591×body640valid
50.0ms414×body320valid
14.0ms195×body160valid