Details

Time bar (total: 11.7s)

sample72.0ms

Algorithm
intervals
Results
33.0ms71×body1280valid
12.0ms44×body640valid
11.0ms32×body2560valid
4.0ms25×body320valid
3.0ms71×body80valid
1.0ms13×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

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: 53.2b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.3b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series279.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune153.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New58361
Fresh000
Picked101
Done000
Total59362

Merged error: 0b

Counts
62 → 3

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 272
Calls
1 calls:
69.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series137.0ms

Counts
1 → 3
Calls
1 calls:
137.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify91.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune316.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2750275
Fresh022
Picked011
Done000
Total2753278

Merged error: 0b

Counts
278 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.5b
(+ x (hypot x (sqrt 1.0)))
2.9b
(log (+ x (hypot x (sqrt 1.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log log-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 44
Calls
3 calls:
1.0ms
(hypot x (sqrt 1.0))
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(log (+ x (hypot x (sqrt 1.0))))

series505.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(hypot x (sqrt 1.0))
125.0ms
(+ x (hypot x (sqrt 1.0)))
285.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify92.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune110.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New53053
Fresh011
Picked011
Done011
Total53356

Merged error: 0b

Counts
56 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.1b
(/ 0.125 (pow x 3))
8.0b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
18.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
2802×times-frac
2496×add-sqr-sqrt
1944×*-un-lft-identity
1522×prod-diff
1510×add-cube-cbrt
965×associate--r+
652×unpow-prod-down
339×distribute-rgt-neg-in
330×difference-of-squares
297×distribute-lft-neg-in
272×sqr-pow
149×cube-prod
134×distribute-lft-out--
104×div-inv
99×neg-mul-1
49×cube-mult unpow3
40×fma-neg
19×associate-/r*
15×add-exp-log
13×associate-/l*
12×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 1793
Calls
4 calls:
6.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
97.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
163.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (- 0.0625) (pow x 5))
40.0ms
(/ 0.125 (pow x 3))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
63.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify419.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0500248078

prune6.2s

Filtered
1805 candidates to 1216 candidates (67.4%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New180501805
Fresh000
Picked011
Done022
Total180531808

Merged error: 0b

Counts
1808 → 3

regimes24.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.3b

bsearch95.0ms

Steps
ItersRangePoint
11
3.029362037509861e-19
14.716166499582775
0.000861150922221108
11
-2193661101726697.2
-1.4639597033977343e-08
-0.9978403496791813

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s2305×body1280valid
419.0ms1533×body640valid
274.0ms847×body2560valid
129.0ms780×body320valid
86.0ms2088×body80valid
43.0ms447×body160valid