Details

Time bar (total: 6.4s)

sample18.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms88×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize6.0ms

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))))

rewrite22.0ms

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:
10.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series453.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ 1.0 (sqrt (+ x 1.0)))
49.0ms
(sqrt (+ x 1.0))
335.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0460585
11938554
25002551

prune202.0ms

Filtered
70 candidates to 55 candidates (78.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New67370
Fresh000
Picked011
Done000
Total67471

Merged error: 0b

Counts
71 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 106
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
11.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series684.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
68.0ms
(+ 1.0 (sqrt (+ x 1.0)))
235.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
330.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06811007
13263915
25002876

prune263.0ms

Filtered
118 candidates to 74 candidates (62.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1180118
Fresh022
Picked011
Done011
Total1184122

Merged error: 0b

Counts
122 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
0.0b
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
0.2b
(* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
7.0b
(+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
33×frac-add
23×associate-*r/
22×prod-exp
20×add-log-exp
13×add-cbrt-cube
12×div-exp associate-*r*
11×flip3-+ flip-+
10×add-sqr-sqrt *-un-lft-identity sum-log
8×add-cube-cbrt times-frac
7×pow-to-exp pow-exp
6×pow1
4×frac-times associate-*l/ cbrt-unprod
3×+-commutative unpow-prod-down associate-*l*
2×cbrt-undiv
1×associate-+l+ associate-+r+ pow-prod-down *-commutative div-inv distribute-lft-out unpow2 unswap-sqr sqr-pow
Counts
4 → 100
Calls
4 calls:
38.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
11.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
14.0ms
(* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
28.0ms
(+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
504.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
446.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
189.0ms
(* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
459.0ms
(+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09103571
150013450

prune539.0ms

Filtered
112 candidates to 76 candidates (67.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh011
Picked011
Done022
Total1124116

Merged error: 0b

Counts
116 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
244.0ms
(sqrt (+ x 1.0))
73.0ms
(+ 1.0 (sqrt (+ x 1.0)))
596.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
327.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08561494
141691377
250021353

prune342.0ms

Filtered
144 candidates to 92 candidates (63.9%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1440144
Fresh000
Picked011
Done033
Total1444148

Merged error: 0b

Counts
148 → 4

regimes75.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084
184

end0.0ms

sample435.0ms

Algorithm
intervals
Results
207.0ms7999×body80valid
62.0ms2660×body80nan
0.0ms1×body1280valid

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