Details

Time bar (total: 4.0s)

sample46.0ms

Algorithm
intervals
Results
12.0ms559×body80nan
11.0ms254×body160nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
32.4b
(sqrt (- (* x x) 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series353.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ x (sqrt (- (* x x) 1.0)))
37.0ms
(- (* x x) 1.0)
195.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms
(sqrt (- (* x x) 1.0))

simplify139.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0327471
11087435
24892422
35001422

prune160.0ms

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

rewrite69.0ms

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:
15.0ms
(- (log x) (/ (/ 0.25 x) x))
4.0ms
(/ 0.09375 (pow x 4))
6.0ms
(/ (/ 0.25 x) x)
37.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(- (log x) (/ (/ 0.25 x) x))
34.0ms
(/ 0.09375 (pow x 4))
30.0ms
(/ (/ 0.25 x) x)
96.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify65.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06821225
126241142
250021115

prune416.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity sqrt-div
9×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- pow-prod-down flip--
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 67
Calls
3 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series606.0ms

Counts
3 → 9
Calls
3 calls:
143.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
270.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
193.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0440941
11553864
25001848

prune207.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b 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
368.0ms16382×body80nan
353.0ms7553×body160nan
228.0ms8000×body80valid