Details

Time bar (total: 43.2s)

sample111.0ms

Algorithm
intervals
Results
44.0ms207×body80valid
9.0ms256×pre80true
8.0ms15×body1280valid
7.0ms17×body640valid
3.0ms10×body320valid
1.0ms7×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210229
345429
4246229
done500029

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.8s

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:
69.0ms
(* (+ alpha beta) (- beta alpha))
374.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.2s
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
117.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series1.3s

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (+ alpha beta) (- beta alpha))
472.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
567.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
158.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify765.0ms

Counts
156 → 156
Iterations

Useful iterations: done (754.0ms)

IterNodesCost
02634471
17904238
done50013984

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.9b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* associate-/l/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod distribute-lft-out
3×div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 129
Calls
4 calls:
86.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
296.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
204.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
930.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
505.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
153.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
523.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify3.9s

Counts
141 → 141
Iterations

Useful iterations: done (3.9s)

IterNodesCost
02273335
16853162
246292878
done50022868

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.9b
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
75×times-frac
61×*-un-lft-identity
52×add-exp-log
49×add-sqr-sqrt
38×add-cube-cbrt
32×add-cbrt-cube
28×associate-/r/
25×div-exp
21×associate-*r*
15×flip3-+ flip-+
14×associate-/r*
13×cbrt-undiv
12×frac-times associate-*l/
10×prod-exp
9×distribute-lft-out
8×div-inv
7×pow1 associate-/l*
6×associate-*r/ cbrt-unprod add-log-exp
4×rec-exp 1-exp associate-*l*
3×distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num associate-/l/ unswap-sqr
1×+-commutative pow-flip pow-prod-down sum-log *-commutative inv-pow
Counts
4 → 174
Calls
4 calls:
533.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
180.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
331.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.4s
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
292.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
152.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
419.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
498.0ms
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify816.0ms

Counts
186 → 186
Iterations

Useful iterations: done (804.0ms)

IterNodesCost
03085820
18955484
done50004940

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize98.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
0.4b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.9b
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))
2.0b
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
112×times-frac
82×*-un-lft-identity
72×add-exp-log
55×add-sqr-sqrt
48×add-cube-cbrt
42×associate-/r/
40×div-exp
32×add-cbrt-cube
26×associate-/r*
17×flip3-+ flip-+ distribute-lft-out
16×cbrt-undiv frac-times associate-*l/
15×div-inv
12×prod-exp
8×unpow-prod-down rec-exp 1-exp cube-prod associate-*r/ add-log-exp
6×pow1 associate-/l*
4×cbrt-unprod
3×difference-of-squares
2×pow-flip frac-2neg clear-num distribute-lft-out-- inv-pow
1×+-commutative sub-neg flip3-- diff-log sum-log sum-cubes flip--
Counts
4 → 206
Calls
4 calls:
337.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
334.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
1.7s
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))
359.0ms
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))

series9.8s

Counts
4 → 12
Calls
4 calls:
413.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
422.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
8.7s
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))
329.0ms
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))

simplify3.3s

Counts
218 → 218
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02738255
17797615
241237081
done50007065

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

regimes1.1s

Accuracy

75.4% (1.6b remaining)

Error of 7.7b against oracle of 6.1b and baseline of 12.6b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03476
14276
done4276

end0.0ms

sample3.2s

Algorithm
intervals
Results
842.0ms505×body1280valid
831.0ms6328×body80valid
442.0ms8000×pre80true
373.0ms597×body640valid
122.0ms366×body320valid
42.0ms204×body160valid