Details

Time bar (total: 1.3m)

sample31.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify79.0ms

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: 3.9b

Counts
2 → 1

localize16.0ms

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite106.0ms

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)))
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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series61.0ms

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

simplify138.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0149213034
1500212552

prune1.3s

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: 1.2b

Counts
478 → 8

localize17.0ms

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)))
0.1b
(/ (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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite381.0ms

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:
243.0ms
(* (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)))
36.0ms
(/ (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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series78.0ms

Counts
4 → 12
Calls
4 calls:
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)))
23.0ms
(/ (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))
19.0ms
(/ (+ (+ (+ 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)))

simplify243.0ms

Algorithm
egg-herbie
Counts
773 → 773
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0195324980
1500124018

prune5.1s

Filtered
773 candidates to 494 candidates (36.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New7730773
Fresh077
Picked011
Done000
Total7738781

Merged error: 1.2b

Counts
781 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.2b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
56×add-sqr-sqrt
46×times-frac
45×sqrt-prod
38×add-cube-cbrt
27×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div distribute-lft-out
8×pow1
7×flip3-+ associate-*l* flip-+ associate-/l*
6×unswap-sqr
4×associate-/r/ add-log-exp
3×associate-/r*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 137
Calls
4 calls:
25.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
13.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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))

series75.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
43.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05362173
122301957
250011889

prune319.0ms

Filtered
149 candidates to 101 candidates (32.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1490149
Fresh066
Picked011
Done011
Total1498157

Merged error: 1.2b

Counts
157 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite658.0ms

Algorithm
rewrite-expression-head
Rules
10146×times-frac
6530×*-un-lft-identity
5526×cbrt-prod
3740×add-sqr-sqrt add-cube-cbrt
1848×sqrt-prod
1395×distribute-lft-out
643×associate-/r/
333×div-inv
313×flip3-+ flip-+
161×associate-/r*
33×associate-/l*
23×cbrt-div
15×add-exp-log
12×add-cbrt-cube
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 3486
Calls
4 calls:
114.0ms
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ 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)))
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)))

series149.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (/ (+ (+ (+ 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)))
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)))

simplify1.5s

Algorithm
egg-herbie
Counts
3498 → 3498
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
05001178697

prune1.1m

Filtered
3498 candidates to 1720 candidates (50.8%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New349803498
Fresh055
Picked011
Done022
Total349883506

Merged error: 1.2b

Counts
3506 → 8

regimes132.0ms

Accuracy

23.7% (1.9b remaining)

Error of 3.0b against oracle of 1.0b and baseline of 3.6b

bsearch17.0ms

Steps
ItersRangePoint
6
3.952203133477583e+60
4.610529988477083e+61
3.3936925540993565e+61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04133
14133

end0.0ms

sample827.0ms

Algorithm
intervals
Results
476.0ms8000×body80valid
139.0ms8000×pre80true

Profiling

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