Details

Time bar (total: 2.0s)

analyze4.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
62.5%12.5%25%4
68.7%6.2%25%5
71.8%3.1%25%6
73.4%1.6%25%7
74.2%0.8%25%8
74.6%0.4%25%9
74.8%0.2%25%10
74.9%0.1%25%11
74.9%0%25%12
74.9%0%25%13
74.9%0%25%14

sample22.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
088
188

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
9.0ms
(+ 1.0 (sqrt (+ x 1.0)))
6.0ms
(sqrt (+ x 1.0))
12.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series40.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ 1.0 (sqrt (+ x 1.0)))
6.0ms
(sqrt (+ x 1.0))
27.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
053111021

prune152.0ms

Filtered
52 candidates to 70 candidates (-34.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New67370
Fresh000
Picked101
Done000
Total68371

Merged error: 0b

Counts
71 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
7.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series57.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
34.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
6.0ms
(cbrt (+ x 1.0))
6.0ms
(cbrt (+ x 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052571713

prune250.0ms

Filtered
79 candidates to 98 candidates (-24.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh022
Picked011
Done000
Total983101

Merged error: 0b

Counts
101 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
8.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
25.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify38.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
054092323

prune183.0ms

Filtered
91 candidates to 144 candidates (-58.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1440144
Fresh011
Picked011
Done011
Total1443147

Merged error: 0b

Counts
147 → 3

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))
0.0b
(+ (* 1/8 (/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))) (- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2))))))
9.0b
(- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2)))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×prod-exp
19×associate-*r/
15×div-exp
12×times-frac add-cbrt-cube associate-/l*
10×add-log-exp
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp pow-exp
6×unpow-prod-down cube-prod frac-sub
5×frac-add
3×pow1 cbrt-undiv cbrt-unprod
2×cube-mult frac-times sub-neg flip3-- diff-log unpow3 associate-*l/ sum-log flip-- sqr-pow
1×+-commutative associate-+r- associate-+r+ frac-2neg flip3-+ clear-num associate-/r* flip-+ div-inv
Counts
3 → 86
Calls
3 calls:
14.0ms
(/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))
24.0ms
(+ (* 1/8 (/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))) (- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2))))))
12.0ms
(- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2)))))

series130.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))
68.0ms
(+ (* 1/8 (/ (pow x 3) (* 1.0 (* (sqrt 1.0) (pow (+ 1.0 (sqrt 1.0)) 2))))) (- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2))))))
42.0ms
(- (* 1/4 (/ (pow x 3) (* 1.0 (pow (+ 1.0 (sqrt 1.0)) 3)))) (* 1/2 (* (/ x (sqrt 1.0)) (/ x (pow (+ 1.0 (sqrt 1.0)) 2)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
057392923

prune371.0ms

Filtered
58 candidates to 95 candidates (-63.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New95095
Fresh000
Picked011
Done022
Total95398

Merged error: 0b

Counts
98 → 3

regimes32.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11215

end0.0ms

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
62.5%12.5%25%4
68.7%6.2%25%5
71.8%3.1%25%6
73.4%1.6%25%7
74.2%0.8%25%8
74.6%0.4%25%9
74.8%0.2%25%10
74.9%0.1%25%11
74.9%0%25%12
74.9%0%25%13
74.9%0%25%14

sample301.0ms

Algorithm
intervals
Results
216.0ms7999×body80valid
0.0ms1×body1280valid

Profiling

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