Details

Time bar (total: 4.0s)

analyze261.0ms

Algorithm
search

sample62.0ms

Algorithm
intervals
Results
18.0ms98×body2560nan
15.0ms99×body1280nan
10.0ms256×body80valid
6.0ms53×body640nan
2.0ms18×body320nan
1.0ms13×body160nan
0.0ms8×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.1b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
27.1b
(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series21.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
12.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

simplify157.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (152.0ms)

IterNodesCost
0316408
11042379
24663366
35002365

prune86.0ms

Filtered
43 candidates to 52 candidates (-20.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New50252
Fresh000
Picked011
Done000
Total50353

Merged error: 0.0b

Counts
53 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×add-exp-log associate-*l*
6×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
2×log-div associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
15.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series36.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
8.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
11.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05121068
11971999
25002986

prune215.0ms

Filtered
73 candidates to 95 candidates (-30.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New95095
Fresh011
Picked011
Done011
Total95398

Merged error: 0.0b

Counts
98 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log x) (/ (/ 0.25 x) x))
0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b
(/ 0.09375 (pow x 4))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
88×*-un-lft-identity
74×add-sqr-sqrt
65×add-cube-cbrt
16×associate-/l*
14×add-exp-log
12×unpow-prod-down distribute-lft-out--
11×pow1 associate--l+ add-cbrt-cube
10×associate-/r* add-log-exp
9×log-prod
8×distribute-lft-out
7×associate-+r+ log-pow
6×div-exp div-inv
4×cbrt-undiv diff-log sqr-pow
3×sub-neg associate-+l+ sum-log difference-of-squares
2×frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ pow-exp flip-- flip-+ associate-/l/
Counts
4 → 167
Calls
4 calls:
15.0ms
(- (log x) (/ (/ 0.25 x) x))
6.0ms
(/ (/ 0.25 x) x)
33.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series42.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(- (log x) (/ (/ 0.25 x) x))
3.0ms
(/ (/ 0.25 x) x)
13.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

simplify62.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06941225
125461106
250011095

prune256.0ms

Filtered
119 candidates to 179 candidates (-50.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1781179
Fresh000
Picked101
Done022
Total1793182

Merged error: 0b

Counts
182 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b
(/ 0.09375 (pow x 4))
0.5b
(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
0.8b
(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
128×*-un-lft-identity
50×distribute-lft-out--
40×distribute-lft-out
35×pow1
34×unpow-prod-down
30×log-pow
28×cbrt-prod add-sqr-sqrt add-cube-cbrt
22×cube-prod
21×times-frac
10×add-exp-log
9×add-log-exp
8×associate--l+
7×associate-+r+ associate-/r* add-cbrt-cube
6×log-prod sqr-pow
4×cube-div
3×pow-unpow associate-+l+ flip3-+ diff-log div-exp sum-log flip-+ associate-/l*
2×cube-mult pow-to-exp sub-neg cbrt-div unpow3 pow-exp
1×cbrt-undiv +-commutative associate-+r- pow-pow frac-2neg pow1/3 clear-num rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 157
Calls
4 calls:
30.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))
34.0ms
(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
31.0ms
(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

series44.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
3.0ms
(/ 0.09375 (pow x 4))
9.0ms
(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
22.0ms
(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

simplify107.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09802067
144451969
250011940

prune261.0ms

Filtered
81 candidates to 169 candidates (-108.6%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1690169
Fresh000
Picked011
Done022
Total1693172

Merged error: 0b

Counts
172 → 3

regimes91.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

analyze257.0ms

Algorithm
search

sample1.7s

Algorithm
intervals
Results
538.0ms2918×body2560nan
394.0ms2577×body1280nan
304.0ms8000×body80valid
143.0ms1205×body640nan
56.0ms617×body320nan
22.0ms334×body160nan
10.0ms281×body80nan

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