Details

Time bar (total: 5.7s)

sample64.0ms

Algorithm
intervals
Results
29.0ms60×body1280valid
12.0ms53×body640valid
9.0ms35×body2560valid
3.0ms26×body320valid
2.0ms70×body80valid
1.0ms12×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: 53.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.8b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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))

series271.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ x (sqrt (+ (* x x) 1.0)))
171.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune175.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

5 alts after pruning (5 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))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite257.0ms

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:
169.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
69.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series303.0ms

Counts
2 → 6
Calls
2 calls:
165.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08882291
147681819
250011795

prune437.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

6 alts after pruning (5 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))
0.7b
(+ (hypot x (sqrt 1.0)) x)
2.8b
(log (+ (hypot x (sqrt 1.0)) x))

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

series523.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(hypot x (sqrt 1.0))
139.0ms
(+ (hypot x (sqrt 1.0)) x)
279.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune137.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (hypot x (sqrt 1.0)) x)
0.7b
(+ (hypot x (sqrt 1.0)) x)
2.8b
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))
2.8b
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×add-exp-log fma-def log-pow
4×expm1-log1p-u log-div flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×+-commutative sqrt-pow1 pow1/2 rem-log-exp sum-log
Counts
4 → 78
Calls
4 calls:
2.0ms
(+ (hypot x (sqrt 1.0)) x)
2.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))
3.0ms
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))

series845.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(+ (hypot x (sqrt 1.0)) x)
131.0ms
(+ (hypot x (sqrt 1.0)) x)
297.0ms
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))
291.0ms
(log (sqrt (+ (hypot x (sqrt 1.0)) x)))

simplify104.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0285728
1887662
24009634
35001624

prune294.0ms

Filtered
90 candidates to 76 candidates (84.4%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.7b

bsearch81.0ms

Steps
ItersRangePoint
9
0.0004320794088804456
4086.0217424804537
0.0007191932868410093
9
-1117730599.3323822
-0.37949367736095085
-1.0263991806084458

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.8s

Algorithm
intervals
Results
943.0ms2339×body1280valid
359.0ms1544×body640valid
221.0ms828×body2560valid
103.0ms755×body320valid
63.0ms2111×body80valid
33.0ms423×body160valid