Details

Time bar (total: 5.7s)

sample80.0ms

Algorithm
intervals
Results
39.0ms83×body1280valid
15.0ms53×body640valid
10.0ms24×body2560valid
4.0ms26×body320valid
3.0ms61×body80valid
1.0ms9×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 53.9b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b
(sqrt (+ (* x x) 1.0))

rewrite16.0ms

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))

series262.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ x (sqrt (+ (* x x) 1.0)))
163.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0331422
11127385
25002366

prune151.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New57461
Fresh000
Picked101
Done000
Total58462

Merged error: 0.0b

Counts
62 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
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*
184×add-sqr-sqrt
140×unpow-prod-down cube-prod
126×*-un-lft-identity
120×add-cube-cbrt
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow1 pow-to-exp pow-exp add-log-exp
5×fma-neg prod-diff
4×distribute-lft-out
3×associate-*r/ associate-*l*
2×expm1-log1p-u diff-log log-pow frac-sub cbrt-unprod log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 300
Calls
2 calls:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
52.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series289.0ms

Counts
2 → 6
Calls
2 calls:
158.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
131.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify128.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08882291
147681819
250011795

prune397.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3060306
Fresh033
Picked011
Done000
Total3064310

Merged error: 0.0b

Counts
310 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ x (hypot x (sqrt 1.0)))
2.7b
(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(log (+ x (hypot x (sqrt 1.0))))

series406.0ms

Counts
2 → 6
Calls
2 calls:
126.0ms
(+ x (hypot x (sqrt 1.0)))
280.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0238284
1786255
23259247
35001245

prune85.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New39140
Fresh112
Picked101
Done011
Total41344

Merged error: 0.0b

Counts
44 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ x (hypot x (sqrt 1.0)))
0.3b
(+ x (hypot x (sqrt 1.0)))
2.8b
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
2.8b
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×add-exp-log fma-def log-pow
4×expm1-log1p-u log-div flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×+-commutative sqrt-pow1 pow1/2 rem-log-exp sum-log
Counts
4 → 78
Calls
4 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(+ x (hypot x (sqrt 1.0)))
4.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
4.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

series858.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(+ x (hypot x (sqrt 1.0)))
132.0ms
(+ x (hypot x (sqrt 1.0)))
294.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
300.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify121.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0285724
1883658
23992630
35001624

prune307.0ms

Filtered
90 candidates to 76 candidates (84.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh011
Picked101
Done011
Total90393

Merged error: 0.0b

Counts
93 → 3

regimes43.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.1b

bsearch127.0ms

Steps
ItersRangePoint
10
0.0002141056345597589
3206628.0142593775
0.0009508569049847261
11
-4.816760182774211e+16
-0.0014803844373699059
-1.0270036336868176

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04631
14631

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2340×body1280valid
436.0ms1585×body640valid
266.0ms801×body2560valid
135.0ms790×body320valid
96.0ms2081×body80valid
40.0ms403×body160valid