Details

Time bar (total: 8.7s)

sample65.0ms

Algorithm
intervals
Results
19.0ms246×body160nan
18.0ms511×body80nan
12.0ms256×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: 32.4b

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))))
30.1b
(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))

series313.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(+ x (sqrt (- (* x x) 1.0)))
197.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms
(sqrt (- (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0339436
11140401
25001389

prune157.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))))
0.2b
(/ 0.09375 (pow x 4))

rewrite458.0ms

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)
397.0ms
(+ (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:
24.0ms
(/ (/ 0.25 x) x)
103.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
35.0ms
(/ 0.09375 (pow x 4))

simplify106.0ms

Algorithm
egg-herbie
Counts
538 → 538
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
024538348
150027154

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×add-exp-log
12×unpow-prod-down cube-prod associate-/r*
6×div-exp
5×add-cbrt-cube
4×pow1 cube-mult unpow3 sqr-pow
3×expm1-log1p-u pow-to-exp rec-exp log-prod 1-exp pow-exp log1p-expm1-u associate-/l* add-log-exp
1×cbrt-undiv pow-flip frac-2neg rem-log-exp clear-num log-pow fma-udef div-inv inv-pow
Counts
3 → 99
Calls
3 calls:
0.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
5.0ms
(/ 1 (pow x 3))
1.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))

series282.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
37.0ms
(/ 1 (pow x 3))
161.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0308601
11418481
25001481

prune193.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (log 2) (log (sqrt x)))
0.1b
(/ (/ 0.25 x) x)
0.2b
(/ 0.09375 (pow x 4))
0.3b
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

rewrite619.0ms

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)
4.0ms
(/ 0.09375 (pow x 4))
537.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(+ (log 2) (log (sqrt x)))
24.0ms
(/ (/ 0.25 x) x)
42.0ms
(/ 0.09375 (pow x 4))
109.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify155.0ms

Algorithm
egg-herbie
Counts
684 → 684
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0389912733
1500211675

prune2.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0178
1178

end0.0ms

sample1.9s

Algorithm
intervals
Results
593.0ms16347×body80nan
533.0ms7835×body160nan
398.0ms8000×body80valid