Details

Time bar (total: 9.2s)

sample74.0ms

Algorithm
intervals
Results
23.0ms538×body80nan
21.0ms219×body160nan
13.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

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))))
30.6b
(sqrt (- (* x x) 1.0))

rewrite25.0ms

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:
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(sqrt (- (* x x) 1.0))

series326.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ x (sqrt (- (* x x) 1.0)))
199.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
57.0ms
(sqrt (- (* x x) 1.0))

simplify32.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0339436
11140401
25001389

prune159.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b
(/ 0.09375 (pow x 4))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
609×add-sqr-sqrt
603×times-frac
479×*-un-lft-identity
384×add-cube-cbrt
379×associate-+r+
372×prod-diff
180×associate--l+
84×unpow-prod-down
78×pow1
75×log-pow difference-of-squares
60×distribute-lft-out--
30×div-inv
28×sqr-pow
16×associate-/l*
13×add-exp-log
10×associate-/r* add-cbrt-cube
8×distribute-lft-out add-log-exp
6×log-prod div-exp
4×cbrt-undiv fma-def
3×expm1-log1p-u associate-+l+ diff-log sum-log log1p-expm1-u
2×sub-neg frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp flip-+ associate-/l/
Counts
3 → 529
Calls
3 calls:
6.0ms
(/ (/ 0.25 x) x)
372.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series162.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (/ 0.25 x) x)
96.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
36.0ms
(/ 0.09375 (pow x 4))

simplify106.0ms

Algorithm
egg-herbie
Counts
538 → 538
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
024538348
150027154

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (log 2) (log (sqrt x)))
0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b
(/ 0.09375 (pow x 4))

rewrite565.0ms

Algorithm
rewrite-expression-head
Rules
735×times-frac
684×add-sqr-sqrt
602×*-un-lft-identity
474×associate-+r+
459×add-cube-cbrt
458×prod-diff
272×associate--l+
184×log-pow
145×pow1
84×unpow-prod-down
75×distribute-lft-out-- difference-of-squares
44×distribute-lft-out
43×sqrt-pow1 pow1/2
38×div-inv
28×sqr-pow
17×add-log-exp
16×associate-/l*
15×log-prod
14×add-exp-log
11×fma-def add-cbrt-cube
10×associate-/r* sum-log
8×frac-add
6×flip3-+ diff-log div-exp sqrt-prod flip-+
4×cbrt-undiv expm1-log1p-u associate-+l+ flip3-- frac-sub flip-- log1p-expm1-u
2×+-commutative sub-neg frac-2neg clear-num
1×pow-to-exp associate-+r- pow-exp associate-/l/
Counts
4 → 672
Calls
4 calls:
6.0ms
(+ (log 2) (log (sqrt x)))
6.0ms
(/ (/ 0.25 x) x)
480.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series267.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (log 2) (log (sqrt x)))
25.0ms
(/ (/ 0.25 x) x)
109.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
46.0ms
(/ 0.09375 (pow x 4))

simplify155.0ms

Algorithm
egg-herbie
Counts
684 → 684
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0389912733
1500111675

prune2.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
0.0b
(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
0.2b
(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
0.3b
(/ 0.125 (pow x 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
37×add-sqr-sqrt add-cube-cbrt
36×times-frac
12×unpow-prod-down cube-prod associate-/r*
11×associate-+r+
10×add-exp-log
9×prod-diff add-log-exp
6×add-cbrt-cube
5×pow1 log-prod
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u distribute-lft-out sqr-pow
3×fma-def div-exp associate-/l*
2×log-div flip3-+ sum-log flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative pow-to-exp associate-+r- sub-neg frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow fma-udef div-inv
Counts
4 → 126
Calls
4 calls:
9.0ms
(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
0.0ms
(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
7.0ms
(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
4.0ms
(/ 0.125 (pow x 3))

series334.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
82.0ms
(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
162.0ms
(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
40.0ms
(/ 0.125 (pow x 3))

simplify64.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0447911
12048786
25002785

prune296.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

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
01813
11813

end0.0ms

sample2.2s

Algorithm
intervals
Results
701.0ms16341×body80nan
646.0ms7683×body160nan
412.0ms8000×body80valid