Details

Time bar (total: 49.6s)

analyze3.0ms

Algorithm
search

sample27.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune3.0ms

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)
0.1b
(/ (/ (+ (+ (+ 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))
3.8b
(/ (+ (+ (+ 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:
11.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
18.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
34.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms
(/ (/ (/ (+ (+ (+ 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))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify316.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0149213034
1500212552

prune1.3s

Filtered
281 candidates to 477 candidates (-69.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4689477
Fresh000
Picked101
Done000
Total4699478

Merged error: 1.1b

Counts
478 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
1471×times-frac
1040×*-un-lft-identity
673×add-sqr-sqrt
627×sqrt-prod
590×add-cube-cbrt
258×associate-*r*
225×distribute-lft-out
88×associate-/r/
71×associate-/l*
63×associate-*l*
46×flip3-+ flip-+
44×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
10×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 761
Calls
4 calls:
41.0ms
(/ (sqrt (/ (/ (+ (+ (+ 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))
254.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ 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)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series74.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (sqrt (/ (/ (+ (+ (+ 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))
23.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ 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)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify246.0ms

Algorithm
egg-herbie
Counts
773 → 773
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0195324980
1500124018

prune5.3s

Filtered
494 candidates to 773 candidates (-56.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New7730773
Fresh088
Picked011
Done000
Total7739782

Merged error: 1.1b

Counts
782 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.5b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite760.0ms

Algorithm
rewrite-expression-head
Rules
12132×times-frac
7340×*-un-lft-identity
4744×add-sqr-sqrt add-cube-cbrt
3270×sqrt-prod
1298×distribute-lft-out
784×associate-/l*
298×associate-/r/
284×sqrt-div
150×flip3-+ flip-+
149×div-inv
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 3894
Calls
4 calls:
57.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
162.0ms
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series70.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms
(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
12.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.4s

Algorithm
egg-herbie
Counts
3906 → 3906
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
05001163483

prune37.7s

Filtered
1896 candidates to 3906 candidates (-106.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New390513906
Fresh167
Picked011
Done011
Total390693915

Merged error: 1.1b

Counts
3915 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
16.8b
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
109×add-sqr-sqrt
103×*-un-lft-identity
96×add-cube-cbrt
54×add-exp-log
51×associate-*r*
34×add-cbrt-cube
26×div-exp
22×associate-/r/
19×associate-/l*
15×flip3-+ flip-+
14×cbrt-undiv
12×div-inv
10×pow1 prod-exp associate-/r*
6×cbrt-unprod associate-/l/
5×unswap-sqr
4×frac-times rec-exp 1-exp associate-*l* associate-*l/ add-log-exp
3×frac-2neg clear-num distribute-lft-out
2×pow-flip associate-*r/ inv-pow pow-div
1×pow-prod-down *-commutative
Counts
4 → 235
Calls
4 calls:
6.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
30.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
33.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify61.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09713790
150013267

prune513.0ms

Filtered
164 candidates to 247 candidates (-50.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2461247
Fresh156
Picked101
Done022
Total2488256

Merged error: 1.1b

Counts
256 → 8

regimes150.0ms

Accuracy

51.1% (1.3b remaining)

Error of 2.4b against oracle of 1.1b and baseline of 3.7b

bsearch48.0ms

Steps
ItersRangePoint
8
4.435177733158061e+211
5.782559717516622e+215
9.18785657877642e+211

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05159
15159

end0.0ms

analyze3.0ms

Algorithm
search

sample750.0ms

Algorithm
intervals
Results
481.0ms8000×body80valid
129.0ms8000×pre80true

Profiling

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