Details

Time bar (total: 6.1s)

sample77.0ms

Algorithm
intervals
Results
36.0ms76×body1280valid
14.0ms53×body640valid
8.0ms25×body2560valid
5.0ms30×body320valid
5.0ms57×body80valid
1.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

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: 54.9b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.5b
(+ x (sqrt (+ (* x x) 1.0)))
3.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.1b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series276.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
174.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (139.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune135.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0.0b

Counts
52 → 5

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)))

rewrite84.0ms

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:
15.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
51.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series303.0ms

Counts
2 → 6
Calls
2 calls:
160.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
143.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify113.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146891648
250021648

prune376.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2911292
Fresh044
Picked011
Done000
Total2916297

Merged error: 0.0b

Counts
297 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.9b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.6b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite169.0ms

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))
5.0ms
(/ 0.125 (pow x 3))
71.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
77.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (- 0.0625) (pow x 5))
42.0ms
(/ 0.125 (pow x 3))
184.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
58.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify110.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
08371970
138171891
250021883

prune537.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh044
Picked011
Done011
Total2356241

Merged error: 0.0b

Counts
241 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- x (sqrt (+ (* x x) 1.0)))
0.0b
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
3.6b
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
14.1b
(sqrt (+ (* x x) 1.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
105×add-sqr-sqrt
80×*-un-lft-identity
60×times-frac
37×difference-of-squares
36×log-prod
30×add-cube-cbrt
25×distribute-lft-out--
15×sqrt-prod
9×add-exp-log
6×pow1 associate-/r* add-cbrt-cube add-log-exp
5×associate-/l*
4×flip3-- associate-/r/ flip--
2×sqrt-div div-exp rem-log-exp div-inv associate-/l/
1×cbrt-undiv sub-neg rem-sqrt-square log-div frac-2neg sqrt-pow1 flip3-+ sub0-neg pow1/2 diff-log div-sub distribute-frac-neg clear-num log-pow flip-+
Counts
4 → 136
Calls
4 calls:
6.0ms
(- x (sqrt (+ (* x x) 1.0)))
11.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
14.0ms
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
4.0ms
(sqrt (+ (* x x) 1.0))

series652.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- x (sqrt (+ (* x x) 1.0)))
117.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
420.0ms
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06271716
123681646
250011641

prune283.0ms

Filtered
148 candidates to 100 candidates (67.6%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1480148
Fresh033
Picked011
Done022
Total1486154

Merged error: 0.0b

Counts
154 → 6

regimes75.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 32.0b

bsearch76.0ms

Steps
ItersRangePoint
7
0.06291072096871789
1.2997713508729505
0.889945842865035
9
-5.855776674212404
-7.74497267090904e-05
-1.0125513793407366

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2327×body1280valid
440.0ms1553×body640valid
278.0ms797×body2560valid
144.0ms824×body320valid
87.0ms2097×body80valid
40.0ms402×body160valid