Details

Time bar (total: 6.0s)

sample52.0ms

Algorithm
intervals
Results
15.0ms254×body160nan
13.0ms559×body80nan
7.0ms256×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: 34.9b

localize8.0ms

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))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod sqrt-prod add-cbrt-cube log1p-expm1-u
3×fma-def prod-diff
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 fma-neg diff-log rem-log-exp sum-log log-pow
Counts
4 → 71
Calls
4 calls:
7.0ms
(+ x (sqrt (- (* x x) 1.0)))
5.0ms
(- (* x x) 1.0)
7.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series368.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ x (sqrt (- (* x x) 1.0)))
46.0ms
(- (* x x) 1.0)
195.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
58.0ms
(sqrt (- (* x x) 1.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0384531
11360471
25002457

prune192.0ms

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))))

rewrite201.0ms

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:
21.0ms
(- (log x) (/ (/ 0.25 x) x))
5.0ms
(/ 0.09375 (pow x 4))
7.0ms
(/ (/ 0.25 x) x)
93.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series648.0ms

Counts
4 → 12
Calls
4 calls:
487.0ms
(- (log x) (/ (/ 0.25 x) x))
34.0ms
(/ 0.09375 (pow x 4))
28.0ms
(/ (/ 0.25 x) x)
98.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify147.0ms

Algorithm
egg-herbie
Counts
739 → 739
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0264714534
1500211801

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

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))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
9×add-cube-cbrt associate-*r*
8×pow1
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- fma-def pow-prod-down flip-- log1p-expm1-u
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 → 76
Calls
3 calls:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
3.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
14.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series648.0ms

Counts
3 → 9
Calls
3 calls:
154.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
296.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
197.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify49.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04671012
11665907
25001894

prune250.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes16.0ms

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

sample1.4s

Algorithm
intervals
Results
379.0ms16382×body80nan
354.0ms7553×body160nan
231.0ms8000×body80valid