Details

Time bar (total: 7.3m)

sample75.0ms

Algorithm
intervals
Results
42.0ms256×body80valid
15.0ms256×pre80true

simplify495.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
494.0ms
(/ (/ (* (* 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))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize43.0ms

Local error

Found 4 expressions with local error:

47.8b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
35.8b
(/ (/ (* (* 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
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite688.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down insert-posit16 add-log-exp
3×swap-sqr
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 204
Calls
4 calls:
Slowest
273.0ms
(/ (/ (* (* 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))
161.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
160.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
87.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (/ (* (* 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))
314.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
140.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
76.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify1.1m

Counts
239 → 216
Calls
239 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)))))
936.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3))))
913.0ms
(/ (/ (* (* 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))))
784.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 32.6b

localize80.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite750.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- flip--
Counts
4 → 256
Calls
4 calls:
Slowest
317.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
177.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
166.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
85.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
448.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
315.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
161.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
126.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
358 → 268
Calls
358 calls:
Slowest
987.0ms
(/ (* (* (/ (* 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))))
865.0ms
(/ (* (* (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
810.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
792.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
785.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.6b

localize66.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.0b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite742.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×difference-of-squares
31×associate-/r/
25×associate-/r* add-cbrt-cube add-exp-log
19×associate-/l*
17×flip3-+ flip-+
16×sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
7×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×prod-exp associate-*r/ cbrt-unprod
1×flip3-- div-sub flip--
Counts
4 → 257
Calls
4 calls:
Slowest
289.0ms
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
243.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
125.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
413.0ms
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
347.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
176.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
124.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
358 → 269
Calls
358 calls:
Slowest
880.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
871.0ms
(/ (* (* (/ (* 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))))
736.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
707.0ms
(/ 1 (/ (* (cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))))
682.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

prune4.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.1b

localize53.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
0.5b
(/ i (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
0.3b
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

rewrite678.0ms

Algorithm
rewrite-expression-head
Rules
1020×times-frac
869×*-un-lft-identity
473×add-sqr-sqrt
409×add-cube-cbrt
240×distribute-lft-out
110×associate-/r*
56×associate-/r/
32×difference-of-squares
31×div-inv
27×flip3-+ flip-+
22×add-cbrt-cube add-exp-log
17×associate-/l*
16×sqrt-prod distribute-lft-out--
11×cbrt-undiv div-exp
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- div-sub flip--
Counts
4 → 579
Calls
4 calls:
Slowest
252.0ms
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
199.0ms
(/ i (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
107.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
99.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
418.0ms
(/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))
376.0ms
(/ i (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
175.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
100.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

simplify3.2m

Counts
921 → 591
Calls
921 calls:
Slowest
811.0ms
(/ (* (* i i) i) (/ (* (* (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (* (* (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))))
726.0ms
(/ i (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2 i))))))
618.0ms
(/ (cbrt i) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ 1 (+ (+ alpha beta) (* 2 i)))))
599.0ms
(/ (sqrt i) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ 1 (+ (+ alpha beta) (* 2 i)))))
594.0ms
(/ (sqrt i) (/ (cbrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (cbrt (+ (+ alpha beta) (* 2 i))))))

prune9.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

regimes288.0ms

Accuracy

44.8% (9.7b remaining)

Error of 10.7b against oracle of 1.0b and baseline of 18.6b

bsearch86.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
2.0s8000×body80valid
451.0ms8000×pre80true