Details

Time bar (total: 8.8s)

analyze1.8s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14

sample140.0ms

Algorithm
intervals
Results
39.0ms48×body1280valid
24.0ms43×body640valid
18.0ms132×body80valid
7.0ms18×body320valid
4.0ms15×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
0550124

prune14.0ms

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: 20.9b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.8b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
14.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series125.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
31.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify32.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
052741735

prune261.0ms

Filtered
72 candidates to 102 candidates (-41.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New957102
Fresh011
Picked011
Done000
Total959104

Merged error: 15.1b

Counts
104 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* J (* 2.0 (cos (/ K 2.0)))))
0.2b
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
8.8b
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
10.8b
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
18×add-cbrt-cube
13×*-un-lft-identity
12×add-sqr-sqrt
11×pow1 add-cube-cbrt
9×prod-exp
7×unpow-prod-down
6×times-frac div-exp cbrt-unprod
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×cbrt-undiv pow-unpow associate-*l* pow-prod-down associate-/l*
2×flip3-+ flip-+ div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r* clear-num associate-/r* *-commutative distribute-lft-out sqr-pow
Counts
4 → 83
Calls
4 calls:
6.0ms
(/ U (* J (* 2.0 (cos (/ K 2.0)))))
7.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
15.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

series123.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ U (* J (* 2.0 (cos (/ K 2.0)))))
31.0ms
(pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)
42.0ms
(* J (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* J (* 2.0 (cos (/ K 2.0))))) 2.0)))

simplify38.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
050831532

prune247.0ms

Filtered
66 candidates to 95 candidates (-43.9%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New90595
Fresh167
Picked011
Done101
Total9212104

Merged error: 15.1b

Counts
104 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
10.8b
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
10.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series186.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
59.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0))))
33.0ms
(sqrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
37.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049041580
149041580

prune347.0ms

Filtered
62 candidates to 88 candidates (-41.9%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New87188
Fresh01010
Picked011
Done011
Total8713100

Merged error: 15.1b

Counts
100 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

3.2b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
3.3b
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
16.7b
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
16.7b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log cbrt-prod add-cbrt-cube
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*r* *-commutative
Counts
4 → 70
Calls
4 calls:
8.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
7.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
37.0ms
(* J (* -2.0 (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))))))
58.0ms
(cbrt (+ 1.0 (pow (/ U (* 2.0 (* J (cos (/ K 2.0))))) 2.0)))
60.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051081766

prune296.0ms

Filtered
64 candidates to 82 candidates (-28.1%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New81182
Fresh1910
Picked011
Done022
Total821395

Merged error: 15.1b

Counts
95 → 13

regimes578.0ms

Accuracy

-33.6% (7.4b remaining)

Error of 20.2b against oracle of 12.7b and baseline of 18.3b

bsearch136.0ms

Steps
ItersRangePoint
7
1.4685322249737117e-118
2.7288955576927585e-116
1.4979404704575452e-118
8
-3.0804600931006826e-204
-3.0206576009870166e-207
-1.8154118417069826e-206

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04853
14853

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s1476×body1280valid
706.0ms1284×body640valid
472.0ms4331×body80valid
231.0ms596×body320valid
81.0ms313×body160valid

Profiling

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