Details

Time bar (total: 5.4s)

sample30.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify122.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (120.0ms)

IterNodesCost
0494935
1494935

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.8b

Counts
2 → 2

localize16.0ms

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

rewrite107.0ms

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))
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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
24.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
21.0ms
(/ (/ (/ (+ (+ (+ 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))
11.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify157.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0504823442

prune1.7s

Filtered
286 candidates to 475 candidates (-66.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4678475
Fresh101
Picked101
Done000
Total4698477

Merged error: 0.8b

Counts
477 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
68×times-frac
65×sqrt-prod
62×add-sqr-sqrt
53×distribute-lft-out
44×add-cube-cbrt
38×associate-*r*
11×add-exp-log add-cbrt-cube
10×sqrt-div
8×pow1 associate-*l* associate-/l*
7×flip3-+ flip-+
6×unswap-sqr
4×associate-/r* associate-/r/ add-log-exp
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 → 164
Calls
4 calls:
15.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
28.0ms
(* (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
6.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series75.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
12.0ms
(* (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (/ (sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
9.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
9.0ms
(sqrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify60.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
050634026

prune327.0ms

Filtered
100 candidates to 176 candidates (-76.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1760176
Fresh077
Picked011
Done000
Total1768184

Merged error: 0.8b

Counts
184 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
2.7b
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
3.6b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
3.6b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
192×*-un-lft-identity
109×times-frac
80×distribute-lft-out
57×sqrt-prod
55×add-sqr-sqrt
51×add-cube-cbrt
39×associate-/l*
18×flip3-+ flip-+
16×associate-/r/
15×add-exp-log add-cbrt-cube
13×sqrt-div
9×associate-/r*
8×frac-times
7×associate-*l*
6×pow1
5×associate-*r* div-inv associate-/l/
4×cbrt-undiv associate-*r/ div-exp associate-*l/ add-log-exp
3×frac-2neg clear-num
2×prod-exp cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 207
Calls
4 calls:
13.0ms
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
28.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
13.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
25.0ms
(/ (sqrt (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))) (* (sqrt (+ alpha (+ beta (* 1.0 2.0)))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
11.0ms
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
052446744

prune771.0ms

Filtered
136 candidates to 219 candidates (-61.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2190219
Fresh066
Picked011
Done011
Total2198227

Merged error: 0.8b

Counts
227 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
0.0b
(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
0.5b
(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
3.6b
(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
68×distribute-lft-out
54×add-exp-log times-frac
36×add-sqr-sqrt
35×associate-*l*
34×frac-times add-cbrt-cube
31×add-cube-cbrt
29×flip3-+ flip-+
24×associate-*r/
22×prod-exp
21×associate-/r/
17×pow1
14×div-exp
12×cbrt-unprod
11×associate-*l/
8×cbrt-undiv associate-/l*
7×pow-prod-down
6×associate-/r*
5×distribute-rgt-in distribute-lft-in associate-*r*
4×rec-exp 1-exp add-log-exp
3×pow-flip div-inv
2×frac-2neg clear-num *-commutative associate-/l/ unswap-sqr
1×inv-pow
Counts
4 → 204
Calls
4 calls:
24.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
21.0ms
(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
28.0ms
(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
15.0ms
(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series100.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))))
20.0ms
(* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))
25.0ms
(/ 1 (* (+ alpha (+ beta (* 1.0 2.0))) (* (/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0))))))
16.0ms
(/ (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))) (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify69.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
054456876

prune362.0ms

Filtered
128 candidates to 216 candidates (-68.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2142216
Fresh325
Picked101
Done022
Total2186224

Merged error: 0.1b

Counts
224 → 6

regimes109.0ms

Accuracy

67.5% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 3.5b

bsearch19.0ms

Steps
ItersRangePoint
8
4.091623635391055e+156
9.307022402011123e+159
4.763269870250496e+156

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04570
14570

end0.0ms

sample815.0ms

Algorithm
intervals
Results
477.0ms8000×body80valid
122.0ms8000×pre80true

Profiling

Loading profile data...