Details

Time bar (total: 6.0s)

sample79.0ms

Algorithm
intervals
Results
35.0ms71×body1280valid
17.0ms60×body640valid
10.0ms27×body2560valid
4.0ms22×body320valid
3.0ms61×body80valid
2.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize6.0ms

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))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series294.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(+ x (sqrt (+ (* x x) 1.0)))
184.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify136.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune142.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite86.0ms

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 associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
68.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series140.0ms

Counts
1 → 3
Calls
1 calls:
140.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify83.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
07251757
138321368
250021368

prune357.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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))))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
4.0ms
(/ 0.125 (pow x 3))
7.0ms
(/ (- 0.0625) (pow x 5))
177.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
187.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 0.125 (pow x 3))
48.0ms
(/ (- 0.0625) (pow x 5))
191.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
55.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify97.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08371970
138171891
250021883

prune577.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube distribute-lft-out
5×pow1 difference-of-squares sqr-pow
4×cube-mult unpow3 distribute-lft-out--
3×flip3-+ div-exp flip-+ associate-/l*
2×log-div diff-log sum-log frac-sub
1×cbrt-undiv +-commutative pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow flip-- div-inv
Counts
4 → 117
Calls
4 calls:
6.0ms
(+ x (/ 0.5 x))
65.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))
110.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ x (/ 0.5 x))
37.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
42.0ms
(/ 0.125 (pow x 3))
154.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0478840
12195800
25001800

prune240.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch93.0ms

Steps
ItersRangePoint
9
0.0002199982819353488
137964.03928948785
0.885438759469176
9
-30563.43924112807
-0.41295360884021565
-1.0293396280566764

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s2348×body1280valid
478.0ms1567×body640valid
278.0ms756×body2560valid
141.0ms754×body320valid
112.0ms2169×body80valid
46.0ms406×body160valid