Details

Time bar (total: 4.7m)

sample91.0ms

Algorithm
intervals
Results
52.0ms256×body80valid
14.0ms256×pre80true

simplify411.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
411.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize55.0ms

Local error

Found 4 expressions with local error:

45.8b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
39.8b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(+ (* beta alpha) (* i (+ (+ alpha beta) i)))

rewrite584.0ms

Algorithm
rewrite-expression-head
Rules
59×add-cbrt-cube add-exp-log
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
38×add-sqr-sqrt
32×frac-times
28×associate-*r/
24×*-un-lft-identity add-cube-cbrt
21×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
9×pow1 associate-/l/
7×div-inv
6×add-log-exp
5×associate-/r*
4×insert-posit16
3×associate-*r* pow-prod-down
2×distribute-rgt-in associate-+r+ clear-num frac-2neg distribute-lft-in
1×+-commutative sum-log flip3-- associate-*l* *-commutative flip--
Counts
4 → 182
Calls
4 calls:
Slowest
285.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
175.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
103.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
15.0ms
(+ (* beta alpha) (* i (+ (+ alpha beta) i)))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
276.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
156.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
49.0ms
(+ (* beta alpha) (* i (+ (+ alpha beta) i)))

simplify1.3m

Counts
255 → 194
Calls
255 calls:
Slowest
1.2s
(* (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
1.2s
(* (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
1.0s
(* (* (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))) (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))))
991.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
955.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))) (* (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)) (cbrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))))

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize76.0ms

Local error

Found 4 expressions with local error:

38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-cbrt-cube add-exp-log
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 308
Calls
4 calls:
Slowest
727.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
254.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
147.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
64.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series3.7s

Counts
4 → 12
Calls
4 calls:
Slowest
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
329.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
149.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
94.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.5m

Counts
377 → 320
Calls
377 calls:
Slowest
1.3s
(* (* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))) (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
1.3s
(* (* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (* (* (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
1.2s
(* (* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (/ (* (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (* (* (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))))
995.0ms
(/ (* (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
961.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune4.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.6b

localize107.0ms

Local error

Found 4 expressions with local error:

37.9b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.9b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.4b
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
221×times-frac
201×*-un-lft-identity
111×add-sqr-sqrt
109×add-cube-cbrt
106×sqrt-prod
46×distribute-lft-out
23×associate-/l*
16×add-exp-log
14×add-cbrt-cube
8×associate-/r* div-inv
7×div-exp
6×pow1
5×cbrt-undiv flip3-+ flip-+
4×sqrt-div associate-/r/ insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/
1×1-exp prod-exp cbrt-unprod
Counts
4 → 214
Calls
4 calls:
Slowest
158.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
116.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
72.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
60.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify59.0s

Counts
347 → 226
Calls
347 calls:
Slowest
903.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
814.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
536.0ms
(/ (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))) (/ (sqrt (cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) 1))
514.0ms
(/ (* i (+ (+ alpha beta) i)) 1)
348.0ms
(sqrt (- (* beta alpha) (* i (+ (+ alpha beta) i))))

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 36.6b

localize90.0ms

Local error

Found 4 expressions with local error:

38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
15×add-cbrt-cube add-exp-log
12×associate-/r*
10×associate-/l*
8×flip3-+ associate-/r/ flip-+ associate-/l/
5×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 div-inv add-log-exp
2×associate-*r/
1×prod-exp cbrt-unprod
Counts
4 → 122
Calls
4 calls:
Slowest
163.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
139.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
154.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
145.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
121.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify30.6s

Counts
168 → 134
Calls
168 calls:
Slowest
909.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
891.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
669.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
655.0ms
(* (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
624.0ms
(* (* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 36.6b

regimes235.0ms

Accuracy

43.6% (1.6b remaining)

Error of 35.4b against oracle of 33.8b and baseline of 36.7b

bsearch108.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.0s8000×body80valid
437.0ms8000×pre80true