Details

Time bar (total: 1.7m)

sample31.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
4.0ms256×pre80true

simplify82.0ms

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

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)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
7.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
21.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms
(/ (/ (/ (+ (+ (+ 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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
135.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify141.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0149213034
1500212552

prune856.0ms

Filtered
477 candidates to 281 candidates (58.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New4716477
Fresh000
Picked101
Done000
Total4726478

Merged error: 0.7b

Counts
478 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b
(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.8b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
3618×times-frac
2167×*-un-lft-identity
1425×add-sqr-sqrt add-cube-cbrt
371×distribute-lft-out
248×associate-/l*
158×associate-/r/
89×div-inv
70×flip3-+ flip-+
64×add-exp-log
44×div-exp
34×add-cbrt-cube
29×associate-/r*
20×cbrt-undiv
6×rec-exp 1-exp
5×pow1
4×frac-2neg clear-num associate-/l/ add-log-exp
1×pow-flip inv-pow
Counts
4 → 1337
Calls
4 calls:
27.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
20.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
64.0ms
(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series458.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
75.0ms
(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
150.0ms
(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
93.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify433.0ms

Algorithm
egg-herbie
Counts
1349 → 1349
Iterations

Useful iterations: 1 (75.0ms)

IterNodesCost
0384442667
1500141446

prune2.3s

Filtered
1349 candidates to 694 candidates (51.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New134811349
Fresh235
Picked011
Done000
Total135051355

Merged error: 0.0b

Counts
1355 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.0b
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.4b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
297×times-frac
216×*-un-lft-identity
161×add-sqr-sqrt
140×add-cube-cbrt
78×associate-*l*
38×distribute-lft-out
37×difference-of-squares
34×add-exp-log add-cbrt-cube
28×associate-/r/
25×associate-/l*
18×associate-*r*
14×cbrt-undiv div-exp div-inv
13×flip3-+ flip-+
11×associate-/r*
6×pow1 prod-exp cbrt-unprod unswap-sqr
5×associate-/l/
4×add-log-exp
3×flip3-- frac-2neg clear-num flip--
1×frac-times div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 308
Calls
4 calls:
58.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
18.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series513.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
42.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
164.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify104.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014177781
150017281

prune798.0ms

Filtered
320 candidates to 240 candidates (75.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3200320
Fresh033
Picked011
Done011
Total3205325

Merged error: 0.0b

Counts
325 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
3.7b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite6.7s

Algorithm
rewrite-expression-head
Rules
150680×times-frac
79598×*-un-lft-identity
53536×add-sqr-sqrt
53534×add-cube-cbrt
24288×sqrt-prod
13032×distribute-lft-out
2778×div-inv
2643×associate-/r/
1284×flip3-+ flip-+
356×associate-/r*
124×add-exp-log
111×div-exp
86×associate-/l*
60×add-cbrt-cube
43×cbrt-undiv
20×1-exp
6×pow1 sqrt-div
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 28450
Calls
4 calls:
14.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
649.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series668.0ms

Counts
4 → 12
Calls
4 calls:
368.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
163.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify15.1s

Algorithm
egg-herbie
Counts
28462 → 28462
Iterations

Useful iterations: 0 (407.0ms)

IterNodesCost
0220391708286

prune1.2m

Filtered
28462 candidates to 13333 candidates (46.8%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New28462028462
Fresh022
Picked011
Done022
Total28462528467

Merged error: 0.0b

Counts
28467 → 5

regimes62.0ms

Accuracy

70.2% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.8b

bsearch77.0ms

Steps
ItersRangePoint
10
6.818549849740831e+152
1.0700860518635087e+163
4.0357355175226436e+156

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03934
13934

end0.0ms

sample649.0ms

Algorithm
intervals
Results
363.0ms8000×body80valid
139.0ms8000×pre80true

Profiling

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