Details

Time bar (total: 1.4m)

sample97.0ms

Algorithm
intervals
Results
39.0ms199×body80valid
11.0ms17×body1280valid
11.0ms20×body640valid
10.0ms256×pre80true
5.0ms15×body320valid
1.0ms5×body160valid

simplify131.0ms

Calls
1 calls:
Slowest
131.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize53.0ms

Local error

Found 4 expressions with local error:

20.8b
(/ (* (+ 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))
0.0b
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

rewrite825.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
15×add-log-exp
14×associate-/r/
12×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* sum-log div-exp div-inv
4×frac-times pow1 insert-posit16
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Calls
4 calls:
Slowest
465.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
171.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
112.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
74.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series842.0ms

Calls
4 calls:
Slowest
403.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
295.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
112.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
31.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify26.1s

Calls
136 calls:
Slowest
691.0ms
(/ (* (* (/ (* (+ 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)))
679.0ms
(- (- (+ (log (+ alpha beta)) (log (- beta alpha))) (log (+ (+ alpha beta) (* 2 i)))) (log (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
671.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
658.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
635.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.0b
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite678.0ms

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-cbrt-cube add-exp-log
8×flip3-+ flip-+
7×associate-/r* distribute-lft-out-- difference-of-squares associate-/l/
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod insert-posit16 distribute-lft-out
3×div-inv
2×clear-num frac-2neg associate-*r/ unswap-sqr
1×+-commutative sum-log flip3-- div-sub pow-prod-down *-commutative flip--
Calls
4 calls:
Slowest
417.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
139.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
82.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
37.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series817.0ms

Calls
4 calls:
Slowest
346.0ms
(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
259.0ms
(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
120.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
91.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify13.8s

Calls
122 calls:
Slowest
1.0s
(/ (* (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
828.0ms
(* (+ (* beta beta) (- (* alpha alpha) (* beta alpha))) (+ (+ alpha beta) (* 2 i)))
678.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
642.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
610.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize67.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (* 1.0 1.0) (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
1.4b
(+ (pow (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.1b
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

rewrite943.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
46×add-sqr-sqrt
42×associate-*r*
32×times-frac
24×add-cube-cbrt
14×add-cbrt-cube add-exp-log
8×pow1 associate-*l* add-log-exp
7×flip3-+ flip-+ distribute-lft-out
6×distribute-lft-out-- difference-of-squares
4×frac-times unpow-prod-down cube-prod associate-*l/ prod-exp associate-/r/ cbrt-unprod insert-posit16 unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*r/ *-commutative div-inv
1×+-commutative sum-log sub-neg flip3-- distribute-rgt-out-- diff-log sum-cubes flip--
Calls
4 calls:
Slowest
746.0ms
(+ (pow (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
94.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
92.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
7.0ms
(- (* 1.0 1.0) (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))

series7.8s

Calls
4 calls:
Slowest
7.2s
(+ (pow (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 3) (pow 1.0 3))
430.0ms
(- (* 1.0 1.0) (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0))
121.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
117.0ms
(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

simplify13.5s

Calls
104 calls:
Slowest
666.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
625.0ms
(* (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))))
589.0ms
(/ (exp (* 1.0 1.0)) (exp (* (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)))
528.0ms
(- (+ (* 0.25 (pow beta 2)) 1.0) (* 0.25 (pow alpha 2)))
464.0ms
(* (+ (* beta beta) (- (* alpha alpha) (* beta alpha))) (+ (+ alpha beta) (* 2 i)))

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize83.0ms

Local error

Found 4 expressions with local error:

10.6b
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.6b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.6b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.6b
(cbrt (+ (+ alpha beta) (* 2 i)))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×pow1/3
1×+-commutative sum-log
Calls
4 calls:
Slowest
292.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
20.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
13.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))

series1.1s

Calls
4 calls:
Slowest
450.0ms
(+ (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
221.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
212.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
202.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))

simplify3.9s

Calls
28 calls:
Slowest
474.0ms
(* (exp (* (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
359.0ms
(- (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))) (* 4.0 (/ 1 (pow alpha 2))))
318.0ms
(- (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))) (* 4.0 (/ 1 (pow alpha 2))))
272.0ms
(cbrt (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
250.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

regimes473.0ms

Accuracy

11.2% (6.0b remaining)

Error of 11.9b against oracle of 5.9b and baseline of 12.7b

bsearch582.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s6339×body80valid
887.0ms8000×pre80true
454.0ms540×body1280valid
364.0ms576×body640valid
201.0ms359×body320valid
49.0ms186×body160valid