Details

Time bar (total: 4.4s)

sample47.0ms

Algorithm
intervals
Results
12.0ms248×body160nan
10.0ms256×body80valid
10.0ms463×body80nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
28.9b
(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
8.0ms
(+ x (sqrt (- (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series325.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(+ x (sqrt (- (* x x) 1.0)))
197.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms
(sqrt (- (* x x) 1.0))

simplify137.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (132.0ms)

IterNodesCost
0316408
11042379
24663366
35003365

prune140.0ms

Filtered
52 candidates to 43 candidates (82.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log x) (/ (/ 0.25 x) x))
0.2b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b
(/ 0.09375 (pow x 4))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
88×*-un-lft-identity
74×add-sqr-sqrt
65×add-cube-cbrt
16×associate-/l*
14×add-exp-log
12×unpow-prod-down distribute-lft-out--
11×pow1 associate--l+ add-cbrt-cube
10×associate-/r* add-log-exp
9×log-prod
8×distribute-lft-out
7×associate-+r+ log-pow
6×div-exp div-inv
4×cbrt-undiv diff-log sqr-pow
3×sub-neg associate-+l+ sum-log difference-of-squares
2×frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ pow-exp flip-- flip-+ associate-/l/
Counts
4 → 167
Calls
4 calls:
17.0ms
(- (log x) (/ (/ 0.25 x) x))
6.0ms
(/ (/ 0.25 x) x)
304.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
8.0ms
(/ 0.09375 (pow x 4))

series464.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(- (log x) (/ (/ 0.25 x) x))
24.0ms
(/ (/ 0.25 x) x)
94.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
38.0ms
(/ 0.09375 (pow x 4))

simplify61.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06831218
124921094
250011089

prune467.0ms

Filtered
179 candidates to 117 candidates (65.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (- 0.5) x) (/ 0.125 (pow x 3)))
0.2b
(log (+ (* 2 x) (- (/ (- 0.5) x) (/ 0.125 (pow x 3)))))
0.5b
(/ 0.125 (pow x 3))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×times-frac
39×*-un-lft-identity
29×add-cube-cbrt
14×unpow-prod-down cube-prod
12×associate-/r*
10×difference-of-squares
9×add-exp-log
6×sqr-pow
5×add-cbrt-cube add-log-exp
4×pow1 cube-mult unpow3
3×log-prod div-exp associate-/l* distribute-lft-out--
2×log-div
1×cbrt-undiv associate--l- neg-sub0 pow-to-exp sub-neg flip3-- distribute-rgt-neg-in frac-2neg flip3-+ diff-log div-sub rem-log-exp pow-exp clear-num log-pow frac-sub flip-- flip-+ div-inv
Counts
3 → 106
Calls
3 calls:
244.0ms
(- (/ (- 0.5) x) (/ 0.125 (pow x 3)))
187.0ms
(log (+ (* 2 x) (- (/ (- 0.5) x) (/ 0.125 (pow x 3)))))
12.0ms
(/ 0.125 (pow x 3))

series278.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(- (/ (- 0.5) x) (/ 0.125 (pow x 3)))
155.0ms
(log (+ (* 2 x) (- (/ (- 0.5) x) (/ 0.125 (pow x 3)))))
39.0ms
(/ 0.125 (pow x 3))

simplify57.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0457837
12002799
25001799

prune236.0ms

Filtered
115 candidates to 71 candidates (61.7%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159
1159

end0.0ms

sample1.3s

Algorithm
intervals
Results
359.0ms7606×body160nan
343.0ms16200×body80nan
235.0ms8000×body80valid