Details

Time bar (total: 22.2s)

sample57.0ms

Algorithm
intervals
Results
17.0ms213×body80valid
6.0ms256×pre80true
5.0ms16×body640valid
5.0ms12×body1280valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify807.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

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:
268.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
822.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
89.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series930.0ms

Counts
3 → 9
Calls
3 calls:
364.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
428.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
138.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.4s

Counts
120 → 120

prune441.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite980.0ms

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-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
235.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
533.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
110.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series979.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
195.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
291.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
407.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify711.0ms

Counts
307 → 307

prune821.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.2b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite988.0ms

Algorithm
rewrite-expression-head
Rules
306×times-frac
275×*-un-lft-identity
196×add-sqr-sqrt
133×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
27×distribute-lft-out-- difference-of-squares
22×associate-/r/
21×associate-/l*
18×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×cbrt-prod
11×div-inv
6×pow1 cbrt-undiv div-exp add-log-exp
4×associate-*l* associate-/r*
3×unpow-prod-down cube-prod prod-exp cbrt-unprod unswap-sqr
2×cube-div frac-times cbrt-div div-sub associate-*l/
1×+-commutative cube-mult frac-2neg pow1/3 unpow3 associate-*r/ pow-prod-down clear-num sum-log *-commutative rem-cbrt-cube associate-/l/ sqr-pow
Counts
4 → 278
Calls
4 calls:
197.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
218.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
447.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
104.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
329.0ms
(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
349.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
352.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify628.0ms

Counts
290 → 290

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.2b
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
4.6b
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
39×add-cbrt-cube
28×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
13×*-un-lft-identity
9×pow1 frac-times
8×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt flip3-+ flip-+
6×associate-*r/ add-log-exp
5×associate-*l/
4×cbrt-div associate-*l*
3×pow-prod-down distribute-lft-out
2×pow1/3
1×+-commutative associate-*r* sum-log *-commutative
Counts
4 → 91
Calls
4 calls:
61.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
85.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.2s
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
1.1s
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
280.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
272.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
334.0ms
(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
461.0ms
(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify1.5s

Counts
103 → 103

prune565.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

regimes273.0ms

Accuracy

15.8% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.2b

bsearch176.0ms

Steps
ItersRangePoint
8
5.14843531564086e+216
1.7312343178982873e+219
3.7228928237747555e+218

simplify942.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
689.0ms8000×pre80true
564.0ms6381×body80valid
284.0ms486×body1280valid
268.0ms574×body640valid
75.0ms324×body320valid
35.0ms235×body160valid