Details

Time bar (total: 4.3m)

sample69.0ms

Algorithm
intervals
Results
40.0ms256×body80valid
12.0ms256×pre80true

simplify528.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
528.0ms
(/ (/ (* (* 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: 52.2b

localize51.0ms

Local error

Found 4 expressions with local error:

45.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
38.2b
(/ (/ (* (* 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)))

rewrite655.0ms

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
286.0ms
(/ (/ (* (* 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))
138.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
130.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
95.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* 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))
247.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
152.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
100.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify1.1m

Counts
239 → 216
Calls
239 calls:
Slowest
1.7s
(* (* (* (* 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)))))
1.1s
(/ (/ (* (* 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))))) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))
884.0ms
(/ (/ (* (* 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))))
764.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))) (sqrt (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.8b

localize85.0ms

Local error

Found 4 expressions with local error:

35.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite664.0ms

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
305.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
152.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
134.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
419.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
318.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
152.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
114.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2m

Counts
358 → 268
Calls
358 calls:
Slowest
1.2s
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
917.0ms
(/ (* (* (/ (* 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))))
848.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
698.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
666.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.8b

localize50.0ms

Local error

Found 4 expressions with local error:

35.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
21×times-frac
18×sqrt-prod
11×add-cbrt-cube add-exp-log
9×associate-/r*
6×pow1 flip3-+ sqrt-div flip-+
4×associate-/r/ insert-posit16 associate-/l* add-log-exp associate-/l/
3×cbrt-undiv div-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/ div-inv
1×prod-exp cbrt-unprod
Counts
4 → 102
Calls
4 calls:
Slowest
82.0ms
(/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
62.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
6.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
6.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series948.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
604.0ms
(/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))
157.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
98.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
89.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify12.7s

Counts
93 → 114
Calls
93 calls:
Slowest
873.0ms
(/ (* (* (* i i) i) (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
779.0ms
(/ (* (* (* i (+ (+ alpha beta) i)) (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
350.0ms
(* i (- (* (+ alpha beta) (+ alpha beta)) (* i i)))
331.0ms
(/ (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))) (* (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))))
325.0ms
(sqrt (- (* beta alpha) (* i (+ (+ alpha beta) i))))

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 35.8b

localize68.0ms

Local error

Found 4 expressions with local error:

35.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
0.2b
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
336×times-frac
325×*-un-lft-identity
218×add-sqr-sqrt
154×add-cube-cbrt
79×distribute-lft-out
44×associate-/l*
32×associate-/r/ difference-of-squares
18×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
8×cbrt-undiv div-exp
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- flip--
Counts
4 → 328
Calls
4 calls:
Slowest
242.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
234.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
157.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
93.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
370.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
138.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
90.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

simplify1.4m

Counts
488 → 340
Calls
488 calls:
Slowest
991.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
773.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (- (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
708.0ms
(/ (/ (cbrt (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
690.0ms
(/ (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
663.0ms
(/ (/ (sqrt (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

prune5.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.9b

regimes315.0ms

Accuracy

46.9% (8.4b remaining)

Error of 10.4b against oracle of 1.9b and baseline of 17.8b

bsearch122.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.9s8000×body80valid
340.0ms8000×pre80true