Details

Time bar (total: 5.7s)

sample62.0ms

Algorithm
intervals
Results
28.0ms61×body1280valid
12.0ms49×body640valid
9.0ms32×body2560valid
3.0ms22×body320valid
2.0ms73×body80valid
1.0ms19×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: 52.0b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
4.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(sqrt (+ (* x x) 1.0))

rewrite22.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series269.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
168.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune184.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

7 alts after pruning (7 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)))

rewrite231.0ms

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:
140.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
71.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series300.0ms

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)))

simplify130.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08882291
147681819
250011795

prune451.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite6.0ms

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))
2.0ms
(+ x (hypot x (sqrt 1.0)))
2.0ms
(log (+ x (hypot x (sqrt 1.0))))

series543.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(hypot x (sqrt 1.0))
134.0ms
(+ x (hypot x (sqrt 1.0)))
294.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify102.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune153.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ x (hypot x (sqrt 1.0)))
1.0b
(+ x (hypot x (sqrt 1.0)))
1.0b
(+ x (hypot x (sqrt 1.0)))
4.0b
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×log-div
24×pow1
15×log-pow
14×associate-*l/
13×*-un-lft-identity
10×add-exp-log add-log-exp
9×fma-def pow1/3 pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×+-commutative rem-log-exp prod-exp sum-log pow-sqr distribute-lft-out
2×pow2
1×log-prod pow3
Counts
4 → 105
Calls
4 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
2.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(+ x (hypot x (sqrt 1.0)))
38.0ms
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

series702.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(+ x (hypot x (sqrt 1.0)))
128.0ms
(+ x (hypot x (sqrt 1.0)))
133.0ms
(+ x (hypot x (sqrt 1.0)))
309.0ms
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

simplify92.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
04121734
19961610
235791407
350021292

prune308.0ms

Filtered
117 candidates to 83 candidates (70.9%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes43.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.1b

bsearch86.0ms

Steps
ItersRangePoint
10
9.558161037350472e-13
0.8818080259852756
0.0010620383232204575
9
-1052513.600169936
-0.041603525395973645
-1.0296783040954165

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.9s

Algorithm
intervals
Results
958.0ms2307×body1280valid
365.0ms1538×body640valid
218.0ms801×body2560valid
111.0ms797×body320valid
67.0ms2130×body80valid
33.0ms427×body160valid