Details

Time bar (total: 12.4s)

sample65.0ms

Algorithm
intervals
Results
31.0ms72×body1280valid
15.0ms56×body640valid
5.0ms19×body2560valid
3.0ms25×body320valid
2.0ms71×body80valid
1.0ms13×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.5b
(sqrt (+ (* x x) 1.0))

rewrite46.0ms

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:
20.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series267.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune184.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

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)))

rewrite291.0ms

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:
188.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
84.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series288.0ms

Counts
2 → 6
Calls
2 calls:
151.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
137.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify115.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08882345
148131909
250011888

prune449.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (hypot x (sqrt 1.0)) x)
2.5b
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×add-exp-log
5×pow1 *-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def rem-log-exp
2×expm1-log1p-u log-div flip3-+ associate-*r/ prod-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative log-prod 1-exp pow-prod-down sum-log distribute-lft-out
Counts
2 → 34
Calls
2 calls:
5.0ms
(+ (hypot x (sqrt 1.0)) x)
9.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series399.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(+ (hypot x (sqrt 1.0)) x)
272.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify127.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
0258271
11000244
24895235
35001234

prune100.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite1.0s

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:
10.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
428.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
373.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- 0.0625) (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
174.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
52.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify390.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500248078

prune6.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch76.0ms

Steps
ItersRangePoint
11
1.661404138935296e-22
2.5556453819330236
0.0010417603980457134
7
-5.56536991933885
-0.04331797882383785
-1.0106802036626215

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14625
24625

end0.0ms

sample1.8s

Algorithm
intervals
Results
919.0ms2317×body1280valid
365.0ms1626×body640valid
215.0ms810×body2560valid
98.0ms754×body320valid
63.0ms2091×body80valid
30.0ms402×body160valid