Details

Time bar (total: 7.0s)

sample49.0ms

Algorithm
intervals
Results
14.0ms265×body160nan
11.0ms584×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: 33.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x x) 1.0)
0.3b
(log (+ x (sqrt (- (* x x) 1.0))))
31.1b
(sqrt (- (* x x) 1.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u prod-diff add-cbrt-cube log1p-expm1-u
2×log-div flip3-- sqrt-div flip-- difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log rem-log-exp log-pow flip-+ distribute-lft-out
Counts
3 → 54
Calls
3 calls:
3.0ms
(- (* x x) 1.0)
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(sqrt (- (* x x) 1.0))

series283.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(- (* x x) 1.0)
187.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms
(sqrt (- (* x x) 1.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0334411
11188365
25002356

prune148.0ms

Filtered
63 candidates to 49 candidates (77.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
9×associate-*r*
7×pow1 add-cube-cbrt associate-*l*
5×add-exp-log
4×frac-times flip3-+ add-cbrt-cube flip-+ unswap-sqr
3×log-prod flip3-- pow-prod-down flip--
2×expm1-log1p-u log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ log1p-expm1-u add-log-exp difference-of-squares
1×sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 60
Calls
2 calls:
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
29.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series467.0ms

Counts
2 → 6
Calls
2 calls:
271.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
196.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify42.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0417811
11477747
25001733

prune224.0ms

Filtered
66 candidates to 51 candidates (77.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
0.5b
(cbrt (sqrt (+ x (sqrt 1.0))))
0.5b
(cbrt (sqrt (+ x (sqrt 1.0))))
0.5b
(cbrt (sqrt (+ x (sqrt 1.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
34.0ms
(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
4.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))
3.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))
4.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(* (cbrt (sqrt (+ x (sqrt 1.0)))) (cbrt (sqrt (+ x (sqrt 1.0)))))
128.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))
130.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))
125.0ms
(cbrt (sqrt (+ x (sqrt 1.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03831642
113761550
250021444

prune444.0ms

Filtered
140 candidates to 90 candidates (64.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

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))))

rewrite486.0ms

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:
28.0ms
(- (log x) (/ (/ 0.25 x) x))
4.0ms
(/ 0.09375 (pow x 4))
6.0ms
(/ (/ 0.25 x) x)
372.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
525.0ms
(- (log x) (/ (/ 0.25 x) x))
36.0ms
(/ 0.09375 (pow x 4))
30.0ms
(/ (/ 0.25 x) x)
100.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify161.0ms

Algorithm
egg-herbie
Counts
739 → 739
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0264714534
1500211801

prune2.0s

Filtered
739 candidates to 412 candidates (55.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01720
11720

end0.0ms

sample1.2s

Algorithm
intervals
Results
336.0ms7587×body160nan
324.0ms16244×body80nan
220.0ms8000×body80valid