Details

Time bar (total: 12.0s)

sample63.0ms

Algorithm
intervals
Results
28.0ms71×body1280valid
13.0ms47×body640valid
7.0ms27×body2560valid
4.0ms26×body320valid
2.0ms74×body80valid
1.0ms11×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
1.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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

series279.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
178.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune184.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

3 alts after pruning (3 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)))

rewrite88.0ms

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:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series303.0ms

Counts
2 → 6
Calls
2 calls:
161.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
141.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
08882291
147681819
250011795

prune462.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.2b
(+ (hypot x (sqrt 1.0)) x)
1.9b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite8.0ms

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:
1.0ms
(hypot x (sqrt 1.0))
3.0ms
(+ (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))
125.0ms
(+ (hypot x (sqrt 1.0)) x)
290.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify85.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune136.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.4b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.5b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite499.0ms

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:
7.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
95.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
170.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
60.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify432.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500248078

prune6.4s

Filtered
1805 candidates to 1216 candidates (67.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.3b

bsearch94.0ms

Steps
ItersRangePoint
10
9.598072339636849e-08
814.2255113159289
0.000831272214997279
11
-402.67606408878214
-1.1015269942960052e-19
-1.030140799834648

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04136
14136

end0.0ms

sample1.9s

Algorithm
intervals
Results
978.0ms2374×body1280valid
371.0ms1550×body640valid
210.0ms780×body2560valid
109.0ms763×body320valid
66.0ms2157×body80valid
29.0ms376×body160valid