Details

Time bar (total: 24.4s)

sample61.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
4.0ms256×pre80true

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize19.0ms

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))))
35.6b
(/ (/ (* (* 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))
46.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite606.0ms

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:
136.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
99.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
225.0ms
(/ (/ (* (* 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))
134.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.0s

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
100.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
704.0ms
(/ (/ (* (* 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))
158.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify73.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune3.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
259.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
756.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
64.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.6s

Counts
4 → 12
Calls
4 calls:
302.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.1s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
108.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify121.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0168310749
150019903

prune5.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.8b

localize21.0ms

Local error

Found 4 expressions with local error:

31.0b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
34.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite511.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
14×*-un-lft-identity
12×add-sqr-sqrt
10×add-cube-cbrt
8×cbrt-undiv sqrt-div div-exp
7×flip3-+ times-frac associate-/r* flip-+ associate-/l/
6×pow1 sqrt-prod
5×prod-exp cbrt-unprod
4×associate-*r/ associate-/r/ add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num div-inv distribute-lft-out associate-/l*
1×associate-*l/
Counts
4 → 89
Calls
4 calls:
426.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
63.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
11.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series850.0ms

Counts
4 → 12
Calls
4 calls:
666.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
50.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
53.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify89.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06381492
135541275
250031273

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 33.8b

localize23.0ms

Local error

Found 4 expressions with local error:

21.5b
(/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
31.0b
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
118×times-frac
66×sqrt-prod
59×*-un-lft-identity
57×add-sqr-sqrt
55×add-cube-cbrt
33×add-exp-log add-cbrt-cube
24×sqrt-div
18×associate-/r/
15×cbrt-undiv div-exp
13×flip3-+ flip-+ associate-/l*
10×associate-/r*
9×div-inv
6×pow1 prod-exp cbrt-unprod associate-/l/
4×add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num distribute-lft-out
1×associate-*l/
Counts
4 → 175
Calls
4 calls:
114.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
249.0ms
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series898.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
682.0ms
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
49.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
53.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify127.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09783939
149033301
250013301

prune3.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 33.8b

regimes496.0ms

Accuracy

36.1% (2.4b remaining)

Error of 36.3b against oracle of 33.9b and baseline of 37.7b

bsearch246.0ms

Steps
ItersRangePoint
9
4.776176866724937e+190
3.3153925665153056e+196
4.843824484430097e+190

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03637
13637

end0.0ms

sample1.2s

Algorithm
intervals
Results
872.0ms8000×body80valid
130.0ms8000×pre80true