Details

Time bar (total: 4.9s)

sample28.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
4.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

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)
15.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
18.0ms
(/ (/ (/ (+ (+ (+ 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)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ 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)))
150.0ms
(/ (/ (/ (+ (+ (+ 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))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (39.0ms)

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: 1.6b

Counts
60 → 8

localize17.0ms

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)))

rewrite53.0ms

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))))
21.0ms
(/ (* (/ (+ (+ (+ 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))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 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))))
153.0ms
(/ (* (/ (+ (+ (+ 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))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify74.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
04821074
12618892
25001873

prune276.0ms

Filtered
95 candidates to 72 candidates (75.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New90595
Fresh527
Picked011
Done000
Total958103

Merged error: 1.6b

Counts
103 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
73×associate-/r/
36×frac-times associate-/r*
32×clear-num
30×frac-2neg
24×associate-*l*
20×div-inv
18×times-frac
16×flip3-+ flip-+
14×*-commutative
12×associate-*l/ associate-/l/
6×associate-*r/
4×associate-*r*
2×un-div-inv associate-/l*
Counts
4 → 114
Calls
4 calls:
8.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) 1))
9.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
13.0ms
(/ (* 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
6.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))

series628.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) 1))
134.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
168.0ms
(/ (* 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))) (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
87.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06071358
126591336
250011334

prune361.0ms

Filtered
126 candidates to 93 candidates (73.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1233126
Fresh426
Picked011
Done011
Total1277134

Merged error: 0.2b

Counts
134 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0))))
0.5b
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta)))))
7.4b
(* (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta))))) (* (- (fma 1.0 2.0 (+ alpha beta)) 1.0) (- 1)))
17.8b
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
85×associate-/r*
65×associate-/r/
62×associate-*l/
47×associate-*l*
32×frac-times
30×*-commutative
24×difference-of-squares
21×flip3-- flip--
13×frac-2neg clear-num
12×associate-/l/
11×div-inv
8×associate-*r*
6×flip3-+ flip-+
5×neg-mul-1
2×associate-*r/ distribute-rgt-neg-out
1×inv-pow
Counts
4 → 111
Calls
4 calls:
8.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0))))
12.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta)))))
19.0ms
(* (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta))))) (* (- (fma 1.0 2.0 (+ alpha beta)) 1.0) (- 1)))
8.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))

series806.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0))))
214.0ms
(/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta)))))
217.0ms
(* (/ 1 (* (/ (fma 1.0 2.0 (+ alpha beta)) (/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))) (- (fma 1.0 2.0 (+ alpha beta))))) (* (- (fma 1.0 2.0 (+ alpha beta)) 1.0) (- 1)))
127.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (- (* (fma 1.0 2.0 (+ alpha beta)) (fma 1.0 2.0 (+ alpha beta))) (* 1.0 1.0)))

simplify46.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08502105
150012008

prune415.0ms

Filtered
123 candidates to 96 candidates (78.0%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1221123
Fresh134
Picked011
Done022
Total1237130

Merged error: 0.2b

Counts
130 → 7

regimes83.0ms

Accuracy

72.2% (0.9b remaining)

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

bsearch181.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04227
14227

end0.0ms

sample523.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
96.0ms8000×pre80true