Details

Time bar (total: 16.5s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify84.0ms

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: 2.9b

Counts
2 → 1

localize17.0ms

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) (* 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
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
10.0ms
(+ (+ alpha beta) (* beta alpha))
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
38.0ms
(/ (/ (/ (+ (+ (+ 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)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* beta alpha))
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (/ (/ (+ (+ (+ 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))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0151213008
1500112540

prune920.0ms

Filtered
475 candidates to 280 candidates (58.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4678475
Fresh000
Picked101
Done000
Total4688476

Merged error: 0.7b

Counts
476 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (+ (+ (+ 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))
0.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.0s

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:
66.0ms
(/ (/ (/ (+ (+ (+ 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)))
164.0ms
(/ (/ (/ (/ (+ (+ (+ 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))
31.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (/ (/ (+ (+ (+ 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)))
155.0ms
(/ (/ (/ (/ (+ (+ (+ 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))
75.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
116.0ms
(/ (+ (+ (+ 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 (48.0ms)

IterNodesCost
05001163483

prune8.0s

Filtered
3906 candidates to 1896 candidates (48.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New390513906
Fresh077
Picked011
Done000
Total390593914

Merged error: 0.7b

Counts
3914 → 9

localize21.0ms

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))))
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))
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)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
819×times-frac
601×*-un-lft-identity
360×sqrt-prod
355×add-sqr-sqrt
349×add-cube-cbrt
126×distribute-lft-out
71×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
10×add-exp-log associate-/r* add-cbrt-cube
5×pow1 associate-/l/
4×add-log-exp
3×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
2×sqrt-div
1×sqrt-pow1 pow1/2
Counts
4 → 477
Calls
4 calls:
24.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
38.0ms
(/ (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))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series702.0ms

Counts
4 → 12
Calls
4 calls:
375.0ms
(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
165.0ms
(/ (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))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify199.0ms

Algorithm
egg-herbie
Counts
489 → 489
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0121214264
1379513729
2500113477

prune1.2s

Filtered
489 candidates to 292 candidates (59.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4890489
Fresh077
Picked011
Done011
Total4899498

Merged error: 0.7b

Counts
498 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (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))

rewrite64.0ms

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:
39.0ms
(* (* (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))))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series266.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (* (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))))
64.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
59.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06602414
126772184
250012091

prune348.0ms

Filtered
120 candidates to 92 candidates (76.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1191120
Fresh156
Picked101
Done022
Total1218129

Merged error: 0.7b

Counts
129 → 8

regimes84.0ms

Accuracy

31.6% (1.6b remaining)

Error of 2.8b against oracle of 1.2b and baseline of 3.6b

bsearch71.0ms

Steps
ItersRangePoint
8
2.8403760274559314e+198
9.039145030578486e+200
8.940011015916639e+200

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

sample638.0ms

Algorithm
intervals
Results
367.0ms8000×body80valid
124.0ms8000×pre80true

Profiling

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