Details

Time bar (total: 25.4s)

sample29.0ms

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: 2.6b

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))
2.4b
(/ (+ (+ (+ 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)
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
36.0ms
(/ (/ (/ (+ (+ (+ 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))
16.0ms
(/ (+ (+ (+ 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)
25.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
23.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify140.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0149213034
1500212552

prune1.4s

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4716477
Fresh000
Picked011
Done000
Total4717478

Merged error: 1.2b

Counts
478 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
2.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite871.0ms

Algorithm
rewrite-expression-head
Rules
1973×times-frac
1066×*-un-lft-identity
1026×add-sqr-sqrt
779×cbrt-prod
720×add-cube-cbrt
615×associate-*r*
173×distribute-lft-out
97×associate-*l*
84×add-exp-log
74×associate-/r/
63×unswap-sqr
44×cbrt-undiv div-exp
40×flip3-+ add-cbrt-cube flip-+
37×div-inv
24×cbrt-div
20×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 → 861
Calls
4 calls:
754.0ms
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ 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))

series74.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
21.0ms
(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))

simplify335.0ms

Algorithm
egg-herbie
Counts
873 → 873
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0500140853

prune11.4s

Filtered
664 candidates to 873 candidates (-31.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New8730873
Fresh055
Picked011
Done011
Total8737880

Merged error: 1.2b

Counts
880 → 7

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)))
1.1b
(* (/ (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))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite731.0ms

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:
54.0ms
(/ (/ (/ (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)))
487.0ms
(* (/ (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))

series101.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ (/ (/ (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))
10.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify507.0ms

Algorithm
egg-herbie
Counts
1509 → 1509
Iterations

Useful iterations: 1 (69.0ms)

IterNodesCost
0444254041
1500152458

prune8.0s

Filtered
631 candidates to 1509 candidates (-139.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New150901509
Fresh044
Picked011
Done022
Total150971516

Merged error: 1.2b

Counts
1516 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
0.7b
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
24×add-sqr-sqrt add-cube-cbrt times-frac
8×add-exp-log add-cbrt-cube distribute-lft-out associate-/l*
6×cbrt-prod flip3-+ associate-/r* flip-+
4×pow1 cbrt-div associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg pow1/3 div-exp clear-num div-inv
Counts
4 → 96
Calls
4 calls:
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 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)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(cbrt (+ (+ alpha beta) (* 2.0 1.0)))
17.0ms
(cbrt (+ (+ 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)))

simplify52.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03591318
113641228
250011224

prune389.0ms

Filtered
84 candidates to 108 candidates (-28.6%)
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1080108
Fresh033
Picked011
Done033
Total1087115

Merged error: 1.2b

Counts
115 → 7

regimes174.0ms

Accuracy

93.7% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 3.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04050
14050

end0.0ms

sample789.0ms

Algorithm
intervals
Results
470.0ms8000×body80valid
127.0ms8000×pre80true

Profiling

Loading profile data...