Details

Time bar (total: 6.0s)

sample61.0ms

Algorithm
intervals
Results
26.0ms65×body1280valid
12.0ms48×body640valid
8.0ms29×body2560valid
4.0ms30×body320valid
2.0ms71×body80valid
1.0ms13×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: 52.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b
(sqrt (+ (* x x) 1.0))

rewrite22.0ms

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))

series274.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
168.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (139.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune146.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize15.0ms

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)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
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×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
120.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series299.0ms

Counts
2 → 6
Calls
2 calls:
155.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
144.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify112.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08542143
146871747
250011747

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
10.0b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube distribute-lft-out--
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult diff-log unpow3
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×sub-neg log-div associate--l+ frac-sub
1×cbrt-undiv +-commutative pow-to-exp associate-+r- flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 125
Calls
4 calls:
131.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
68.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
4.0ms
(/ 0.125 (pow x 3))
113.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
36.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
41.0ms
(/ 0.125 (pow x 3))
152.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0505968
12345912
25002912

prune249.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.4b
(/ 0.125 (pow x 3))
12.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
18.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite397.0ms

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:
6.0ms
(/ (- 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
182.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
195.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (- 0.0625) (pow x 5))
40.0ms
(/ 0.125 (pow x 3))
179.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
59.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify100.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08371970
138171891
250021883

prune566.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes66.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.1b

bsearch78.0ms

Steps
ItersRangePoint
7
0.4954286465087044
15.365363555117188
0.8863596176122291
10
-1.7081313977704333
-1.7977825652338532e-10
-1.0118201374548368

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
966.0ms2338×body1280valid
359.0ms1552×body640valid
223.0ms843×body2560valid
101.0ms771×body320valid
65.0ms2124×body80valid
28.0ms372×body160valid