Details

Time bar (total: 13.0s)

sample86.0ms

Algorithm
intervals
Results
42.0ms76×body1280valid
12.0ms37×body640valid
12.0ms30×body2560valid
5.0ms31×body320valid
3.0ms68×body80valid
2.0ms14×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.3b
(log (+ x (sqrt (+ (* x x) 1.0))))
18.3b
(sqrt (+ (* x x) 1.0))

rewrite47.0ms

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:
18.0ms
(+ x (sqrt (+ (* x x) 1.0)))
17.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series285.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ x (sqrt (+ (* x x) 1.0)))
176.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0331422
11127385
25002366

prune195.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite306.0ms

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:
197.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
88.0ms
(* 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)))

simplify113.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08882345
148131909
250011888

prune473.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
10.7b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
15.6b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite944.0ms

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:
11.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
293.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
395.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (- 0.0625) (pow x 5))
37.0ms
(/ 0.125 (pow x 3))
193.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
54.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify382.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500248078

prune6.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.7b
(+ (hypot x (sqrt 1.0)) x)
3.3b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log log-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
6.0ms
(+ (hypot x (sqrt 1.0)) x)
5.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series516.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(hypot x (sqrt 1.0))
126.0ms
(+ (hypot x (sqrt 1.0)) x)
290.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify88.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune136.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch64.0ms

Steps
ItersRangePoint
5
0.0004221944073348045
0.001242113813128165
0.0009563381925855175
9
-1873866393.190807
-0.5149414008252181
-0.995006844885953

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04131
14131

end0.0ms

sample1.9s

Algorithm
intervals
Results
958.0ms2398×body1280valid
373.0ms1584×body640valid
209.0ms788×body2560valid
106.0ms765×body320valid
63.0ms2084×body80valid
29.0ms381×body160valid