Details

Time bar (total: 11.2s)

sample64.0ms

Algorithm
intervals
Results
30.0ms71×body1280valid
13.0ms60×body640valid
7.0ms27×body2560valid
3.0ms22×body320valid
2.0ms61×body80valid
1.0ms15×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: 54.5b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(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))

series269.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune164.0ms

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 1 expressions with local error:

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

rewrite78.0ms

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:
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series130.0ms

Counts
1 → 3
Calls
1 calls:
130.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify94.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune313.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2750275
Fresh033
Picked011
Done000
Total2754279

Merged error: 0.0b

Counts
279 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.1b
(/ (- 0.0625) (pow x 5))
13.1b
(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))))

rewrite495.0ms

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:
5.0ms
(/ 0.125 (pow x 3))
7.0ms
(/ (- 0.0625) (pow x 5))
99.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
168.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 0.125 (pow x 3))
52.0ms
(/ (- 0.0625) (pow x 5))
175.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
61.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify428.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500248078

prune6.1s

Filtered
1805 candidates to 1216 candidates (67.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New180501805
Fresh022
Picked011
Done011
Total180541809

Merged error: 0.0b

Counts
1809 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b
(+ x (hypot x (sqrt 1.0)))
3.1b
(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))))

series421.0ms

Counts
2 → 6
Calls
2 calls:
129.0ms
(+ x (hypot x (sqrt 1.0)))
292.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0238284
1786255
23259247
35001245

prune91.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New39140
Fresh101
Picked011
Done022
Total40444

Merged error: 0.0b

Counts
44 → 4

regimes28.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch79.0ms

Steps
ItersRangePoint
9
0.0002199982819353488
137964.03928948785
0.0008937142540349351
9
-30563.43924112807
-0.41295360884021565
-1.0293396280566764

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.9s

Algorithm
intervals
Results
979.0ms2348×body1280valid
376.0ms1567×body640valid
214.0ms756×body2560valid
106.0ms754×body320valid
67.0ms2169×body80valid
31.0ms406×body160valid