Details

Time bar (total: 11.2s)

sample32.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.8b
(/ (/ (* (* 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))
46.7b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite541.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
68.0ms
(* i (+ (+ alpha beta) i))
100.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
226.0ms
(/ (/ (* (* 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))
136.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
23.0ms
(* i (+ (+ alpha beta) i))
106.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
826.0ms
(/ (/ (* (* 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))
186.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify69.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012085419
150014944

prune587.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.7b

localize22.0ms

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)))
35.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite660.0ms

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:
194.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
262.0ms
(/ (/ (+ (* 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)))
128.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series802.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
340.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify75.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010985877
150015622

prune835.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
35.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite765.0ms

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×add-exp-log add-cbrt-cube
23×associate-/l*
21×associate-/r*
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 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
262.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
296.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
64.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
131.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series783.0ms

Counts
4 → 12
Calls
4 calls:
344.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
218.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify70.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010935896
150025635

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (+ (+ alpha beta) (* 2.0 i)))
14.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
22.5b
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
35.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite532.0ms

Algorithm
rewrite-expression-head
Rules
291×times-frac
239×add-sqr-sqrt
188×*-un-lft-identity
138×add-cube-cbrt
103×sqrt-prod
50×difference-of-squares
33×associate-/r*
25×distribute-lft-out--
19×associate-/r/
18×sqrt-div
16×add-exp-log add-cbrt-cube
12×flip3-+ flip-+
10×div-inv associate-/l*
6×cbrt-undiv div-exp associate-/l/
5×pow1
4×add-log-exp
3×frac-2neg clear-num
2×associate-*r/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 div-sub prod-exp flip-- cbrt-unprod
Counts
4 → 275
Calls
4 calls:
28.0ms
(sqrt (+ (+ alpha beta) (* 2.0 i)))
128.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
293.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series1.3s

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (+ (+ alpha beta) (* 2.0 i)))
363.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i))))
735.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify81.0ms

Algorithm
egg-herbie
Counts
287 → 287
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014317308
150017024

prune918.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 35.7b

regimes288.0ms

Accuracy

36.1% (2.4b remaining)

Error of 36.2b against oracle of 33.8b and baseline of 37.5b

bsearch56.0ms

Steps
ItersRangePoint
9
1.6148053271615414e+215
8.79518010075976e+220
2.5654069168267007e+215

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample682.0ms

Algorithm
intervals
Results
319.0ms8000×body80valid
114.0ms8000×pre80true