Details

Time bar (total: 6.0s)

sample46.0ms

Algorithm
intervals
Results
14.0ms248×body160nan
10.0ms463×body80nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

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))

rewrite24.0ms

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 sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
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 → 52
Calls
3 calls:
8.0ms
(+ x (sqrt (- (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(sqrt (- (* x x) 1.0))

series318.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ x (sqrt (- (* x x) 1.0)))
191.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
56.0ms
(sqrt (- (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0339436
11140401
25001389

prune161.0ms

Filtered
61 candidates to 53 candidates (86.9%)
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))

rewrite477.0ms

Algorithm
rewrite-expression-head
Rules
870×times-frac
804×add-sqr-sqrt
668×*-un-lft-identity
570×add-cube-cbrt
544×prod-diff
379×associate-+r+
183×associate--l+
124×pow1
120×log-pow
84×unpow-prod-down
78×difference-of-squares
62×distribute-lft-out--
46×div-inv
28×sqr-pow
16×associate-/l*
14×add-exp-log
11×add-cbrt-cube
10×associate-/r* add-log-exp
9×log-prod
8×distribute-lft-out
6×div-exp
4×cbrt-undiv expm1-log1p-u fma-def fma-neg diff-log log1p-expm1-u
3×sub-neg associate-+l+ sum-log
2×frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ pow-exp flip-- flip-+ associate-/l/
Counts
4 → 727
Calls
4 calls:
25.0ms
(- (log x) (/ (/ 0.25 x) x))
6.0ms
(/ (/ 0.25 x) x)
373.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series486.0ms

Counts
4 → 12
Calls
4 calls:
320.0ms
(- (log x) (/ (/ 0.25 x) x))
24.0ms
(/ (/ 0.25 x) x)
98.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
43.0ms
(/ 0.09375 (pow x 4))

simplify148.0ms

Algorithm
egg-herbie
Counts
739 → 739
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0264714534
1500211801

prune2.2s

Filtered
739 candidates to 412 candidates (55.8%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.125 (/ 1 (pow x 3)))
0.0b
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
0.2b
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
0.6b
(/ 1 (pow x 3))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
73×add-sqr-sqrt
57×*-un-lft-identity
53×add-cube-cbrt
40×associate-*r*
34×add-exp-log
23×unpow-prod-down cube-prod
12×div-exp associate-/r*
11×add-cbrt-cube
10×prod-exp
9×unswap-sqr sqr-pow
7×pow1 cube-mult unpow3
6×pow-to-exp rec-exp 1-exp pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod associate-*l* associate-/l*
2×cbrt-undiv cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ rem-log-exp pow-prod-down clear-num log-pow un-div-inv *-commutative fma-udef inv-pow
Counts
4 → 176
Calls
4 calls:
18.0ms
(* 0.125 (/ 1 (pow x 3)))
0.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
1.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
5.0ms
(/ 1 (pow x 3))

series299.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* 0.125 (/ 1 (pow x 3)))
79.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
150.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
34.0ms
(/ 1 (pow x 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0487963
12398726
25002725

prune342.0ms

Filtered
188 candidates to 95 candidates (50.5%)
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
361.0ms7606×body160nan
345.0ms16200×body80nan
239.0ms8000×body80valid