Details

Time bar (total: 12.6s)

sample59.0ms

Algorithm
intervals
Results
27.0ms75×body1280valid
10.0ms46×body640valid
6.0ms24×body2560valid
4.0ms29×body320valid
2.0ms61×body80valid
2.0ms21×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: 54.8b

localize10.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ x (sqrt (+ (* x x) 1.0)))
4.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

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:
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series277.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
179.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0331422
11127385
25002366

prune192.0ms

Pruning

3 alts after pruning (3 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)))

rewrite98.0ms

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:
78.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series139.0ms

Counts
1 → 3
Calls
1 calls:
139.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify86.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07291769
138381380
250031380

prune421.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.5b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite1.1s

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:
6.0ms
(/ (- 0.0625) (pow x 5))
6.0ms
(/ 0.125 (pow x 3))
273.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
540.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (- 0.0625) (pow x 5))
40.0ms
(/ 0.125 (pow x 3))
180.0ms
(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))))

simplify407.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500248078

prune6.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.3b
(+ (hypot x (sqrt 1.0)) x)
4.0b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite11.0ms

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))
7.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series513.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(hypot x (sqrt 1.0))
132.0ms
(+ (hypot x (sqrt 1.0)) x)
283.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune144.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.6b

bsearch84.0ms

Steps
ItersRangePoint
10
4.555257425893614e-05
47183757994.54101
0.0009520350065117032
9
-13600.963204601821
-0.00047371797307045637
-1.020862079458779

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.8s

Algorithm
intervals
Results
902.0ms2309×body1280valid
372.0ms1601×body640valid
207.0ms769×body2560valid
98.0ms742×body320valid
64.0ms2176×body80valid
30.0ms403×body160valid