Details

Time bar (total: 25.2s)

sample31.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.8b

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))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite114.0ms

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)
18.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms
(/ (/ (/ (+ (+ (+ 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)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (+ (+ 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)))
22.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify144.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0149213034
1500212552

prune4.0s

Filtered
477 candidates to 281 candidates (41.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4698477
Fresh000
Picked101
Done000
Total4708478

Merged error: 0.4b

Counts
478 → 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)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
828×*-un-lft-identity
383×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
33×flip3-+ flip-+
31×div-inv
20×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 524
Calls
4 calls:
5.0ms
(+ (+ alpha beta) (* beta alpha))
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 3.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify150.0ms

Algorithm
egg-herbie
Counts
536 → 536
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0152713829
1500113288

prune4.3s

Filtered
536 candidates to 279 candidates (47.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5333536
Fresh347
Picked011
Done000
Total5368544

Merged error: 0.4b

Counts
544 → 8

localize14.0ms

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)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite366.0ms

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:
35.0ms
(/ (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))
236.0ms
(* (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)))
13.0ms
(/ (+ (+ (+ 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)))

series78.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (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)))
21.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify251.0ms

Algorithm
egg-herbie
Counts
773 → 773
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0195324980
1500124018

prune13.2s

Filtered
773 candidates to 493 candidates (36.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New7730773
Fresh066
Picked011
Done011
Total7738781

Merged error: 0.4b

Counts
781 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
30×cbrt-div
27×associate-*r*
26×add-sqr-sqrt
25×cbrt-prod
23×times-frac
21×add-cube-cbrt
16×add-exp-log frac-times flip3-+ flip-+
12×associate-*l/
10×add-cbrt-cube
9×pow1
6×prod-exp cbrt-unprod distribute-lft-out
5×associate-*r/
4×add-log-exp
3×pow1/3 pow-prod-down unswap-sqr
2×cbrt-undiv div-exp associate-/r/
1×associate-*l* *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
32.0ms
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
6.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series60.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
19.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06572450
126832223
250012130

prune1.0s

Filtered
120 candidates to 92 candidates (23.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1200120
Fresh055
Picked011
Done022
Total1208128

Merged error: 0.4b

Counts
128 → 8

regimes137.0ms

Accuracy

53.9% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 4.0b

bsearch62.0ms

Steps
ItersRangePoint
7
4.196129009894779e+185
8.107185202951957e+186
8.919474576974323e+185

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
12815

end0.0ms

sample694.0ms

Algorithm
intervals
Results
348.0ms8000×body80valid
115.0ms8000×pre80true

Profiling

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