Details

Time bar (total: 16.5s)

sample31.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune3.0ms

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: 4.4b

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))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite110.0ms

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:
6.0ms
(+ (+ alpha beta) (* beta alpha))
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms
(/ (/ (/ (+ (+ (+ 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:
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) (* 2.0 1.0)) 1.0))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0151213008
1500112540

prune1.4s

Filtered
475 candidates to 280 candidates (41.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4678475
Fresh000
Picked101
Done000
Total4688476

Merged error: 1.2b

Counts
476 → 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)))) (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))
0.3b
(* (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)))))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
484×times-frac
370×*-un-lft-identity
302×sqrt-prod
284×add-sqr-sqrt
224×add-cube-cbrt
83×swap-sqr
64×distribute-lft-out
63×associate-*r* associate-*l*
38×associate-/r/
21×flip3-+ flip-+
19×pow1 div-inv
16×unswap-sqr
15×add-exp-log add-cbrt-cube
10×associate-/r*
9×associate-/l*
8×sqrt-pow1 pow1/2 sqrt-div
7×associate-/l/
5×pow-prod-up
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg pow-prod-down clear-num pow-sqr
2×frac-times associate-*r/ associate-*l/ prod-exp cbrt-unprod
1×pow2 pow-plus sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 351
Calls
4 calls:
56.0ms
(/ (* (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))
102.0ms
(* (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)))))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
17.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series74.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (* (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))
21.0ms
(* (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)))))
18.0ms
(/ (+ (+ (+ 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)))

simplify112.0ms

Algorithm
egg-herbie
Counts
363 → 363
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010438596
150018202

prune1.2s

Filtered
363 candidates to 233 candidates (35.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3630363
Fresh077
Picked011
Done000
Total3638371

Merged error: 1.2b

Counts
371 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.4b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
603×times-frac
424×*-un-lft-identity
375×add-sqr-sqrt
279×cbrt-prod
244×add-cube-cbrt
194×associate-*l*
114×associate-*r*
90×distribute-lft-out
40×add-exp-log
28×add-cbrt-cube unswap-sqr
25×associate-/r/
20×cbrt-div
18×cbrt-undiv div-exp
15×flip3-+ flip-+
13×div-inv
9×prod-exp cbrt-unprod
6×pow1
4×add-log-exp
3×pow1/3
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 408
Calls
4 calls:
313.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 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))

series71.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify142.0ms

Algorithm
egg-herbie
Counts
420 → 420
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0177713550
1500113120

prune2.3s

Filtered
420 candidates to 315 candidates (25.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4200420
Fresh066
Picked011
Done011
Total4208428

Merged error: 1.2b

Counts
428 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.5b
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ 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))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite756.0ms

Algorithm
rewrite-expression-head
Rules
3553×times-frac
2088×*-un-lft-identity
1654×add-sqr-sqrt
1436×add-cube-cbrt
1370×sqrt-prod
615×associate-*r*
326×distribute-lft-out
126×associate-/r/
87×associate-/l*
65×flip3-+ flip-+
63×div-inv
55×associate-*l*
45×add-exp-log add-cbrt-cube unswap-sqr
22×cbrt-undiv div-exp
10×sqrt-div
8×pow1 prod-exp cbrt-unprod
7×associate-/r*
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1497
Calls
4 calls:
55.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
521.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ 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))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series102.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
23.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ (+ 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))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify507.0ms

Algorithm
egg-herbie
Counts
1509 → 1509
Iterations

Useful iterations: 1 (76.0ms)

IterNodesCost
0444254041
1500152458

prune7.7s

Filtered
1509 candidates to 631 candidates (58.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New150901509
Fresh055
Picked011
Done022
Total150981517

Merged error: 1.2b

Counts
1517 → 8

regimes138.0ms

Accuracy

55.7% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch24.0ms

Steps
ItersRangePoint
9
4.1572337400485617e+164
2.9546957391849226e+171
1.6951903778370228e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04248
14248

end0.0ms

sample822.0ms

Algorithm
intervals
Results
484.0ms8000×body80valid
122.0ms8000×pre80true

Profiling

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