Details

Time bar (total: 14.2s)

sample52.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
6.0ms256×pre80true

simplify44.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite935.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
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 add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
185.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
375.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
242.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
128.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
264.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify80.0ms

Counts
212 → 212

prune866.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite947.0ms

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-exp-log add-cbrt-cube
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 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
326.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
335.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
77.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
190.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series936.0ms

Counts
4 → 12
Calls
4 calls:
333.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
367.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
98.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
138.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify90.0ms

Counts
264 → 264

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
72×add-sqr-sqrt
57×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×add-exp-log add-cbrt-cube
8×sqrt-div
7×associate-/l* distribute-lft-out--
6×pow1
5×flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num div-inv
1×sqrt-undiv flip3-- prod-exp flip-- cbrt-unprod
Counts
4 → 141
Calls
4 calls:
165.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
78.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
11.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
102.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
69.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
78.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify67.0ms

Counts
153 → 153

prune838.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.7b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
35.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite822.0ms

Algorithm
rewrite-expression-head
Rules
427×*-un-lft-identity
351×times-frac
168×add-sqr-sqrt add-cube-cbrt
148×distribute-lft-out
105×sqrt-prod
51×associate-/r*
17×associate-/r/
15×add-exp-log add-cbrt-cube associate-/l*
14×sqrt-div
11×flip3-+ flip-+
9×div-inv
6×cbrt-undiv div-exp associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 330
Calls
4 calls:
38.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
112.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
445.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
206.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.2s

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
235.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
650.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
158.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify148.0ms

Counts
342 → 342

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.5b

regimes185.0ms

Accuracy

47.7% (8.5b remaining)

Error of 10.6b against oracle of 2.0b and baseline of 18.3b

bsearch66.0ms

Steps
ItersRangePoint
6
3.311520226141117e+143
1.9535048208484335e+144
1.3055472335622916e+144

simplify56.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
795.0ms8000×body80valid
639.0ms8000×pre80true