Details

Time bar (total: 6.9s)

analyze10.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%56.2%43.8%0
0%56.2%43.8%1
0%56.2%43.8%2
42.1%14%43.8%3
42.1%14%43.8%4
52.7%3.5%43.8%5
56.2%0%43.8%6

sample27.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
4.0ms256×pre80true

simplify113.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (111.0ms)

IterNodesCost
0494935
1494935

prune9.0ms

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: 5.1b

Counts
2 → 2

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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite112.0ms

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:
8.0ms
(+ (+ (+ 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)))
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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (+ (+ 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)))
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))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify191.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0497323485
1497323485

prune1.5s

Filtered
288 candidates to 477 candidates (-65.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4716477
Fresh101
Picked011
Done000
Total4727479

Merged error: 0.9b

Counts
479 → 7

localize20.0ms

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)))))
1.9b
(/ (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))))))
4.8b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))
4.8b
(/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (+ alpha (+ beta (* 1.0 2.0))))

rewrite78.0ms

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)))))
30.0ms
(/ (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)))))
26.0ms
(/ (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))))

simplify62.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
053696744

prune762.0ms

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

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2190219
Fresh055
Picked011
Done011
Total2197226

Merged error: 0.9b

Counts
226 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))) (cbrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
5.1b
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
5.1b
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
5.1b
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
772×*-un-lft-identity
592×times-frac
390×cbrt-prod
306×distribute-lft-out
238×add-sqr-sqrt add-cube-cbrt
38×associate-/l*
20×associate-/r/
13×flip3-+ flip-+
10×div-inv
9×add-exp-log
8×cbrt-div associate-/r*
6×add-cbrt-cube
4×pow1 add-log-exp
3×cbrt-undiv pow1/3 div-exp
1×frac-2neg clear-num associate-/l/
Counts
4 → 412
Calls
4 calls:
29.0ms
(/ (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))) (cbrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
6.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
7.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (/ (cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0)))) (+ alpha (+ beta (* 1.0 2.0)))) (cbrt (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
14.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
14.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))
22.0ms
(cbrt (+ alpha (+ beta (+ (* alpha beta) 1.0))))

simplify234.0ms

Algorithm
egg-herbie
Counts
424 → 424
Iterations

Useful iterations: 0 (142.0ms)

IterNodesCost
0492319532
1492319532

prune2.0s

Filtered
181 candidates to 424 candidates (-134.3%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New4240424
Fresh044
Picked011
Done022
Total4247431

Merged error: 0.9b

Counts
431 → 7

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
2.1b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
54×times-frac
32×add-sqr-sqrt
30×add-cube-cbrt
22×associate-/l*
19×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
14×associate-/r/ distribute-lft-out
8×frac-times
7×cbrt-undiv div-exp
5×pow1 associate-*r*
4×associate-*r/ associate-*l* associate-*l/ associate-/r* div-inv
3×prod-exp cbrt-unprod associate-/l/ add-log-exp
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 130
Calls
3 calls:
12.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
28.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series39.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0)))))
21.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ alpha (+ beta (* 1.0 2.0))) (+ alpha (+ beta (+ 1.0 (* 1.0 2.0))))))
11.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
056094301

prune262.0ms

Filtered
101 candidates to 139 candidates (-37.6%)
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New1381139
Fresh123
Picked011
Done033
Total1397146

Merged error: 0.9b

Counts
146 → 7

regimes190.0ms

Accuracy

94.4% (0.1b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 3.7b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
061102
161102

end0.0ms

sample769.0ms

Algorithm
intervals
Results
490.0ms8000×body80valid
133.0ms8000×pre80true

Profiling

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