Details

Time bar (total: 2.2m)

sample101.0ms

Algorithm
intervals
Results
26.0ms205×body80valid
18.0ms8×body320valid
16.0ms21×body1280valid
11.0ms256×pre80true
9.0ms18×body640valid
1.0ms4×body160valid

simplify103.0ms

Calls
1 calls:
Slowest
103.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize39.0ms

Local error

Found 3 expressions with local error:

21.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
17×add-cbrt-cube add-exp-log
12×associate-/r/
10×flip3-+ flip-+ associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp
6×associate-/r* div-inv
4×frac-times
3×pow1 flip3-- insert-posit16 flip-- add-log-exp
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative
Calls
3 calls:
Slowest
103.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
33.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
21.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series476.0ms

Calls
3 calls:
Slowest
226.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
178.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
72.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify20.4s

Calls
107 calls:
Slowest
728.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
725.0ms
(/ (sqrt (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
604.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
586.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
567.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize30.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.5b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
94×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
51×associate-*r*
20×add-cbrt-cube add-exp-log associate-/r/
18×associate-/l*
13×flip3-+ flip-+
10×div-inv
7×cbrt-undiv div-exp
6×pow1 associate-/r*
4×insert-posit16 add-log-exp
3×div-sub associate-*l* prod-exp cbrt-unprod associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative flip3-- pow-prod-down associate-*r/ *-commutative flip--
Calls
4 calls:
Slowest
53.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
37.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
26.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series509.0ms

Calls
4 calls:
Slowest
195.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
151.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
114.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
49.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify37.6s

Calls
224 calls:
Slowest
1.0s
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
969.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
746.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
706.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
696.0ms
(sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.9b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.9b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
1.5b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
51×associate-*r*
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
9×flip3-+ flip-+
8×associate-/r/
6×pow1
4×insert-posit16 div-inv add-log-exp
3×cbrt-undiv +-commutative div-exp associate-*l* prod-exp cbrt-unprod
2×frac-times associate-*l/
1×pow-prod-down associate-*r/ *-commutative
Calls
4 calls:
Slowest
37.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
32.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
31.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
29.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series677.0ms

Calls
4 calls:
Slowest
183.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
175.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
169.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
150.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify17.5s

Calls
79 calls:
Slowest
1.1s
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
1.0s
(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
661.0ms
(sqrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
655.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
620.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize50.0ms

Local error

Found 4 expressions with local error:

2.8b
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
2.4b
(- (* 1.0 1.0) (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
1.5b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
1.5b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×associate-*r*
82×*-un-lft-identity
80×add-sqr-sqrt add-cube-cbrt
22×add-cbrt-cube add-exp-log
16×associate-/r/
13×flip3-+ flip-+
8×pow1 div-inv add-log-exp
6×cbrt-undiv div-exp associate-*l* prod-exp cbrt-unprod
4×frac-times associate-*l/ insert-posit16
2×pow-prod-down associate-*r/ *-commutative
1×+-commutative sum-log sub-neg flip3-- distribute-rgt-out-- diff-log sum-cubes flip-- distribute-lft-out
Calls
4 calls:
Slowest
61.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
54.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
12.0ms
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
5.0ms
(- (* 1.0 1.0) (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))

series7.4s

Calls
4 calls:
Slowest
6.7s
(+ (pow (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 3) (pow 1.0 3))
296.0ms
(- (* 1.0 1.0) (* (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
221.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
175.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify34.3s

Calls
152 calls:
Slowest
987.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
976.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
634.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
633.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
633.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

regimes369.0ms

Accuracy

2.9% (6.0b remaining)

Error of 12.1b against oracle of 6.1b and baseline of 12.2b

bsearch193.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s6375×body80valid
404.0ms8000×pre80true
402.0ms495×body1280valid
351.0ms598×body640valid
138.0ms354×body320valid
47.0ms178×body160valid