Details

Time bar (total: 2.8s)

sample17.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms82×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize5.0ms

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))))

rewrite16.0ms

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:
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series24.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
16.0ms
(/ 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

prune134.0ms

Filtered
70 candidates to 55 candidates (21.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New67370
Fresh000
Picked101
Done000
Total68371

Merged error: 0b

Counts
71 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 317
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
20.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series70.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
10.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
20.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
30.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
011265984
146445345
250015337

prune576.0ms

Filtered
329 candidates to 147 candidates (55.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3290329
Fresh022
Picked011
Done000
Total3293332

Merged error: 0b

Counts
332 → 3

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)))))

rewrite37.0ms

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)))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify97.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08561494
141691377
250021353

prune206.0ms

Filtered
144 candidates to 94 candidates (34.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1440144
Fresh011
Picked011
Done011
Total1443147

Merged error: 0b

Counts
147 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -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
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
8.2b
(+ (* (/ 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)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
31×prod-exp
24×div-exp
18×add-cbrt-cube
16×times-frac
14×add-sqr-sqrt pow-to-exp pow-exp
12×add-cube-cbrt *-un-lft-identity associate-*r*
9×unpow-prod-down
8×associate-/l* add-log-exp
6×pow1 associate-*r/
5×cbrt-unprod
4×cbrt-undiv frac-add
3×associate-*l* unpow2 sqr-pow
2×+-commutative flip3-+ sum-log flip-+ div-inv
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
4 → 109
Calls
4 calls:
14.0ms
(* -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
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
25.0ms
(+ (* (/ 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)))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* -1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
46.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
18.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
47.0ms
(+ (* (/ 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)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
05671483
129941325
250021318

prune469.0ms

Filtered
121 candidates to 70 candidates (42.1%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1210121
Fresh000
Picked011
Done022
Total1213124

Merged error: 0b

Counts
124 → 3

regimes34.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01010
11010

end0.0ms

sample451.0ms

Algorithm
intervals
Results
222.0ms7997×body80valid
67.0ms2640×body80nan
0.0ms3×body1280valid

Profiling

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