Details

Time bar (total: 2.5m)

sample66.0ms

Algorithm
intervals
Results
24.0ms208×body80valid
9.0ms256×pre80true
8.0ms17×body640valid
7.0ms14×body1280valid
4.0ms11×body320valid
1.0ms6×body160valid

simplify124.0ms

Calls
1 calls:
Slowest
124.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize25.0ms

Local error

Found 3 expressions with local error:

19.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite155.0ms

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
79.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
56.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
17.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series472.0ms

Calls
3 calls:
Slowest
212.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
184.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
76.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify20.6s

Calls
107 calls:
Slowest
672.0ms
(/ (* (* (/ (* (+ 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)))
656.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
600.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
599.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
573.0ms
(/ (* (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize30.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.2b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite163.0ms

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
55.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
50.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
39.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
12.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series499.0ms

Calls
4 calls:
Slowest
182.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
145.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
128.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
44.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify37.0s

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))))
867.0ms
(/ (/ (* (* (- 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)))
700.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
647.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
636.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize8.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.2b
(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
3.2b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.2b
(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
51×associate-*r*
45×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×add-exp-log
13×add-cbrt-cube
9×flip3-+ flip-+
8×pow1 associate-/r/
6×log-prod
4×log-div exp-prod insert-posit16 div-inv add-log-exp
3×cbrt-undiv div-exp associate-*l* exp-sum prod-exp cbrt-unprod
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative rem-log-exp pow-prod-down associate-*r/ *-commutative rem-exp-log
Calls
4 calls:
Slowest
31.0ms
(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
26.0ms
(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
26.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
15.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series791.0ms

Calls
4 calls:
Slowest
257.0ms
(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
208.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
170.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
156.0ms
(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))

simplify19.7s

Calls
95 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))))
682.0ms
(cbrt (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
671.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
636.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
634.0ms
(/ (/ (sqrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

5.8b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.2b
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
345×times-frac
190×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
120×sqrt-prod
96×associate-*r*
34×associate-/r/
32×add-cbrt-cube add-exp-log
30×associate-*l* div-inv
19×associate-/l*
18×flip3-+ flip-+
13×cbrt-undiv div-exp
12×associate-/r*
8×sqrt-div
6×pow1 prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
2×clear-num frac-2neg div-sub associate-/l/
1×frac-times +-commutative pow-prod-down associate-*l/ associate-*r/ *-commutative
Calls
4 calls:
Slowest
68.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
46.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
38.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
19.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series668.0ms

Calls
4 calls:
Slowest
225.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
198.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
159.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
86.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify56.5s

Calls
424 calls:
Slowest
852.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (pow (+ (+ alpha beta) (* 2 i)) 3) (pow 2.0 3))))
673.0ms
(* (/ (* (* (/ (+ alpha beta) 1) (/ (+ alpha beta) 1)) (/ (+ alpha beta) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
635.0ms
(* (* (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
625.0ms
(* (/ (* (* (/ (+ alpha beta) 1) (/ (+ alpha beta) 1)) (/ (+ alpha beta) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (* (* (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
524.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

prune5.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

regimes338.0ms

Accuracy

15.4% (5.1b remaining)

Error of 11.1b against oracle of 6.0b and baseline of 12.0b

bsearch104.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.1s6402×body80valid
425.0ms591×body640valid
413.0ms470×body1280valid
396.0ms8000×pre80true
145.0ms349×body320valid
52.0ms188×body160valid