Details

Time bar (total: 3.9s)

sample25.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
4.0ms256×pre80true

simplify85.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.1b

Counts
2 → 2

localize12.0ms

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)))

rewrite51.0ms

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)
14.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
19.0ms
(/ (/ (/ (+ (+ (+ 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)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
141.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (/ (/ (+ (+ (+ 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))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify45.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0346554
11545502
25001490

prune179.0ms

Filtered
58 candidates to 47 candidates (81.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New50858
Fresh101
Picked101
Done000
Total52860

Merged error: 1.7b

Counts
60 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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 3.0)))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-/l/
12×associate-/r/
10×flip3-+ flip-+
9×associate-/l*
6×frac-2neg clear-num div-inv
2×+-commutative associate-+l+
Counts
4 → 44
Calls
4 calls:
5.0ms
(+ (+ alpha beta) (* beta alpha))
17.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
146.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
158.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0365514
11720459
25003452

prune177.0ms

Filtered
56 candidates to 44 candidates (78.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New52456
Fresh437
Picked101
Done000
Total57764

Merged error: 1.7b

Counts
64 → 7

localize19.0ms

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 3.0)))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite52.0ms

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)))
15.0ms
(* (/ (+ (+ (+ 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 3.0)))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
156.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ beta 3.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify73.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0498996
12644838
25001831

prune282.0ms

Filtered
95 candidates to 72 candidates (75.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New93295
Fresh246
Picked011
Done000
Total957102

Merged error: 1.7b

Counts
102 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
0.4b
(/ 1 (* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))))
3.9b
(/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l/
13×associate-/r/
10×associate-*r/ associate-*r*
9×associate-*l*
8×flip3-+ flip-+ associate-/l/
7×associate-/r*
6×fma-udef
5×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative div-inv
1×inv-pow
Counts
4 → 49
Calls
4 calls:
8.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
7.0ms
(* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
13.0ms
(/ 1 (* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))))
7.0ms
(/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0))

series611.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
125.0ms
(* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
159.0ms
(/ 1 (* (fma 1.0 2.0 (+ alpha beta)) (* (/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0)) (fma 1.0 2.0 (+ alpha beta)))))
93.0ms
(/ (+ alpha (+ beta 3.0)) (+ (+ (fma alpha beta beta) alpha) 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0361503
11421500
25003497

prune181.0ms

Filtered
61 candidates to 49 candidates (80.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New59261
Fresh235
Picked011
Done011
Total61768

Merged error: 0.1b

Counts
68 → 7

regimes78.0ms

Accuracy

70% (1.1b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.6b

bsearch75.0ms

Steps
ItersRangePoint
9
1.2638933579139666e+159
6.311864492386349e+166
2.925890748252608e+159

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
14324

end0.0ms

sample545.0ms

Algorithm
intervals
Results
305.0ms8000×body80valid
94.0ms8000×pre80true