Details

Time bar (total: 3.9s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1

sample37.0ms

Algorithm
intervals
Results
15.0ms61×body1280valid
7.0ms40×body640valid
4.0ms124×body80valid
2.0ms17×body320valid
1.0ms14×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0479710
1479710

prune10.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 30.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 59
Calls
3 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify59.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05248834

prune138.0ms

Filtered
53 candidates to 68 candidates (-28.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh000
Picked101
Done000
Total66369

Merged error: 0.0b

Counts
69 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
0.1b
(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube add-log-exp unswap-sqr
3×associate-*r* prod-exp
2×pow1 distribute-rgt-in distribute-lft-in associate-*r/ associate--r+ sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- flip3-+ diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod flip-+
Counts
2 → 48
Calls
2 calls:
3.0ms
(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
8.0ms
(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

series13.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
8.0ms
(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

simplify35.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05219694

prune74.0ms

Filtered
38 candidates to 54 candidates (-42.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New54054
Fresh022
Picked011
Done000
Total54357

Merged error: 0.0b

Counts
57 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
0.0b
(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
0.0b
(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
3.6b
(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
298×add-sqr-sqrt
175×times-frac
138×*-un-lft-identity
120×difference-of-squares
108×unpow-prod-down cube-prod
68×add-cube-cbrt
51×sqr-pow
36×associate-/l*
25×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×distribute-lft-out
8×associate-/r/
7×associate-/r*
6×add-log-exp
5×pow1 difference-cubes
4×flip3-+ flip-+ div-inv
3×cbrt-undiv pow-unpow div-exp
2×flip3-- frac-2neg pow-exp clear-num flip-- associate-/l/ rem-cube-cbrt
1×cube-div cube-mult pow-to-exp sub-neg pow-pow diff-log unpow3 div-sub
Counts
4 → 282
Calls
4 calls:
6.0ms
(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
44.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
8.0ms
(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
32.0ms
(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

series98.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
55.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3)) (+ (* 1.0 1.0) (* (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
11.0ms
(pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3)
24.0ms
(- (pow (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 3) (pow 1.0 3))

simplify125.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0529112395

prune1.1s

Filtered
147 candidates to 294 candidates (-100.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2922294
Fresh101
Picked101
Done011
Total2943297

Merged error: 0.0b

Counts
297 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (+ 1.0 (pow (exp -2.0) x)) 3)
0.0b
(pow (+ 1.0 (pow (exp -2.0) x)) 2)
0.0b
(/ (- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0) (+ 1.0 (+ (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (/ 4.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)))))
3.6b
(- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
116×add-sqr-sqrt
95×*-un-lft-identity
73×times-frac
35×difference-of-squares
33×distribute-lft-out
25×add-cube-cbrt
15×unpow-prod-down
11×cube-prod
9×associate-/l* sqr-pow
8×add-exp-log
7×add-cbrt-cube distribute-lft-out--
6×pow1 pow-unpow add-log-exp
5×associate-/r*
2×cube-div pow-to-exp flip3-- pow-pow flip3-+ pow-exp associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv cube-mult sub-neg frac-2neg diff-log unpow3 div-sub div-exp clear-num div-inv unpow2 rem-cube-cbrt
Counts
4 → 139
Calls
4 calls:
6.0ms
(pow (+ 1.0 (pow (exp -2.0) x)) 3)
6.0ms
(pow (+ 1.0 (pow (exp -2.0) x)) 2)
62.0ms
(/ (- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0) (+ 1.0 (+ (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (/ 4.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)))))
20.0ms
(- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0)

series88.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (+ 1.0 (pow (exp -2.0) x)) 3)
6.0ms
(pow (+ 1.0 (pow (exp -2.0) x)) 2)
58.0ms
(/ (- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0) (+ 1.0 (+ (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) (/ 4.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2)))))
18.0ms
(- (/ 8.0 (pow (+ 1.0 (pow (exp -2.0) x)) 3)) 1.0)

simplify71.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
051094900

prune443.0ms

Filtered
81 candidates to 151 candidates (-86.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1501151
Fresh011
Picked101
Done011
Total1513154

Merged error: 0.0b

Counts
154 → 3

regimes153.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch60.0ms

Steps
ItersRangePoint
5
0.0008199449608619843
0.0032579644775507983
0.0008654656792303772
10
-1802018.0487007513
-6.1737052062143345e-12
-0.000966599909477714

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048144
148144

end0.0ms

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1

sample1.0s

Algorithm
intervals
Results
443.0ms1718×body1280valid
211.0ms1228×body640valid
142.0ms4074×body80valid
76.0ms655×body320valid
25.0ms325×body160valid

Profiling

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