Details

Time bar (total: 56.6s)

sample80.0ms

Algorithm
intervals
Results
17.0ms20×body1280valid
16.0ms204×body80valid
9.0ms24×body640valid
7.0ms256×pre80true
1.0ms4×body320valid
1.0ms4×body160valid

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
done5003
42146
3448
297
131
015

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize43.0ms

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))
1.2b
(+ (/ (/ (* (+ 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)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-cbrt-cube add-exp-log
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv associate-/r* div-exp div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*l* associate-*l/ associate-*r/ insert-posit16
3×prod-exp cbrt-unprod
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in
1×+-commutative sum-log pow-prod-down *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 148
Calls
4 calls:
62.0ms
(* (+ alpha beta) (- beta alpha))
390.0ms
(/ (/ (* (+ 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)
70.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series1.6s

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (+ alpha beta) (- beta alpha))
636.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
703.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
193.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify5.5s

Counts
160 → 160
Iterations
IterNodes
done5005
23638
1785
0267

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
0.1b
(/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))
3.3b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
4.1b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
319×times-frac
290×*-un-lft-identity
215×add-sqr-sqrt
140×add-cube-cbrt
84×associate-*r*
42×distribute-lft-out
33×distribute-lft-out-- difference-of-squares
31×associate-/l*
20×add-cbrt-cube add-exp-log associate-/r/
13×flip3-+ flip-+
10×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l* insert-posit16
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 → 297
Calls
4 calls:
197.0ms
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
308.0ms
(/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))
460.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
130.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
411.0ms
(/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))
545.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
397.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

simplify7.2s

Counts
309 → 309
Iterations
IterNodes
done5010
24240
11128
0388

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))))
1.3b
(* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha))))
4.1b
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha)))) 1.0)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
56×add-sqr-sqrt
50×times-frac add-exp-log
41×associate-*r*
33×add-cube-cbrt
32×add-cbrt-cube
22×prod-exp
12×div-exp cbrt-unprod distribute-lft-out
11×frac-times pow1 associate-*l/
10×flip3-+ flip-+
9×distribute-lft-out-- difference-of-squares
7×cbrt-undiv
6×associate-/r/ add-log-exp
5×associate-*l* associate-/l*
4×associate-/r* pow-prod-down associate-*r/ insert-posit16
3×rec-exp 1-exp div-inv
2×*-commutative unswap-sqr associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-- div-sub un-div-inv flip--
Counts
4 → 167
Calls
4 calls:
242.0ms
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
426.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))))
535.0ms
(* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha))))
437.0ms
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha)))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))
174.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))))
570.0ms
(* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha))))
360.0ms
(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha))))) (/ 1 (+ (* 2.0 i) (+ beta alpha)))) 1.0)

simplify6.4s

Counts
179 → 179
Iterations
IterNodes
done5000
23462
1892
0283

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

localize180.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
4.1b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
4.1b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
4.1b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
141×times-frac
118×*-un-lft-identity
95×add-sqr-sqrt
84×associate-*r*
62×add-cube-cbrt
16×distribute-lft-out
13×add-cbrt-cube add-exp-log
12×distribute-lft-out-- difference-of-squares
10×add-log-exp
9×flip3-+ flip-+
8×associate-/r/
6×pow1
4×associate-*l* insert-posit16 div-inv
3×cbrt-undiv +-commutative sum-log div-exp prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/
1×pow-prod-down associate-*r/ *-commutative
Counts
4 → 148
Calls
4 calls:
548.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
146.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
133.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
200.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
605.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha))))
480.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
491.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)
437.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ 2.0 (+ (* 2.0 i) (+ beta alpha)))) (+ (* 2.0 i) (+ beta alpha)))) 1.0)

simplify6.1s

Counts
160 → 160
Iterations
IterNodes
done5001
23320
1851
0272

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

regimes1.1s

Accuracy

13.9% (5.5b remaining)

Error of 11.2b against oracle of 5.6b and baseline of 12.1b

bsearch394.0ms

Steps
ItersRangePoint
8
1.0894395962051653e+190
2.8929330243571157e+194
1.3719954394698665e+190
8
5.094536971308387e+146
4.38061499353291e+149
2.7096468634095695e+149
8
1.8394685690263203e+130
9.906063471096378e+134
2.0420602585183155e+134

simplify62.0ms

Iterations
IterNodes
done70
170
052

end0.0ms

sample2.5s

Algorithm
intervals
Results
995.0ms6395×body80valid
373.0ms8000×pre80true
273.0ms547×body1280valid
230.0ms527×body640valid
130.0ms353×body320valid
30.0ms178×body160valid