Details

Time bar (total: 5.0s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify75.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.1b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-/l/
12×associate-/r/
10×flip3-+ flip-+
9×associate-/l*
6×associate-+l+ frac-2neg clear-num div-inv
3×+-commutative
Counts
4 → 46
Calls
4 calls:
6.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
13.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
17.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0333571
11470564
25002564

prune154.0ms

Filtered
58 candidates to 47 candidates (81.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New50858
Fresh000
Picked101
Done000
Total51859

Merged error: 1.6b

Counts
59 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
43×associate-/l/
30×frac-times
25×clear-num
23×frac-2neg
16×flip3-+ flip-+
14×associate-/r/
10×associate-*l/
8×associate-/l*
7×div-inv
6×associate-*r/ associate-*r* associate-*l*
4×un-div-inv
2×*-commutative
1×inv-pow
Counts
4 → 83
Calls
4 calls:
4.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
19.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
9.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
137.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
147.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify68.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04701083
125401054
250031054

prune227.0ms

Filtered
95 candidates to 68 candidates (71.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89695
Fresh527
Picked011
Done000
Total949103

Merged error: 1.6b

Counts
103 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b
(* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))
0.4b
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))))
3.9b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
138×frac-times
107×flip3-+ flip-+
84×distribute-neg-frac
67×associate-/r/
48×associate-*r/
45×associate-*r*
44×associate-/l/
39×associate-*l/
24×distribute-neg-in times-frac
23×frac-2neg clear-num
20×distribute-rgt-in distribute-lft-in *-commutative
18×associate-*l*
15×neg-mul-1
12×+-commutative associate-+l+
8×associate-/r* div-inv
4×distribute-rgt-neg-out
3×associate-/l*
1×distribute-frac-neg
Counts
4 → 207
Calls
4 calls:
34.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))))
24.0ms
(* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))
42.0ms
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))))
15.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series644.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0)))))
160.0ms
(* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))
158.0ms
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (* (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (- (+ (+ alpha beta) (* 2.0 1.0))))))
88.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014114910
150014839

prune777.0ms

Filtered
219 candidates to 177 candidates (80.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2145219
Fresh527
Picked101
Done011
Total2208228

Merged error: 0.2b

Counts
228 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.4b
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
79×associate-/r/
57×associate-*r*
48×times-frac
45×flip3-+ flip-+
36×frac-times
33×neg-mul-1
29×associate-/r*
24×associate-/l/
18×associate-*r/ div-inv
17×*-commutative
15×clear-num
13×frac-2neg
12×distribute-neg-frac
9×associate-/l*
6×associate-+l+
4×associate-*l/
3×+-commutative
2×distribute-frac-neg un-div-inv distribute-rgt-neg-out
Counts
4 → 136
Calls
4 calls:
6.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
21.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
24.0ms
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
246.0ms
(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
159.0ms
(/ (* 1 (- 1)) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09212667
150012561

prune471.0ms

Filtered
148 candidates to 123 candidates (83.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1471148
Fresh156
Picked011
Done011
Total1488156

Merged error: 0.2b

Counts
156 → 8

regimes82.0ms

Accuracy

72.1% (0.9b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.5b

bsearch41.0ms

Steps
ItersRangePoint
5
6.909088993170465e+162
2.3763768138887338e+163
7.0064345418082844e+162

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05031
16931
27831
38231
48931
58931

end0.0ms

sample675.0ms

Algorithm
intervals
Results
440.0ms8000×body80valid
95.0ms8000×pre80true