Details

Time bar (total: 4.6s)

sample49.0ms

Algorithm
intervals
Results
11.0ms499×body80nan
11.0ms236×body160nan
10.0ms256×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: 29.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(+ x (sqrt (- (* x x) 1.0)))
27.3b
(sqrt (- (* x x) 1.0))

rewrite50.0ms

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:
19.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
17.0ms
(+ x (sqrt (- (* x x) 1.0)))
13.0ms
(sqrt (- (* x x) 1.0))

series292.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
64.0ms
(+ x (sqrt (- (* x x) 1.0)))
48.0ms
(sqrt (- (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0339436
11140401
25001389

prune149.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
20×sqrt-prod
17×*-un-lft-identity
14×sqrt-div
11×add-cube-cbrt
10×pow1
9×associate-*r*
7×add-exp-log associate-*l*
6×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×expm1-log1p-u frac-times log1p-expm1-u unswap-sqr
3×log-prod flip3-- fma-def sqrt-pow1 pow1/2 pow-prod-down flip--
2×log-div associate-*r/ associate-*l/ hypot-def distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 96
Calls
4 calls:
6.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms
(sqrt (+ x (sqrt 1.0)))
4.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
50.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
61.0ms
(sqrt (+ x (sqrt 1.0)))
262.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
185.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05241160
118471044
250011027

prune296.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
0.6b
(cbrt (sqrt (- x (sqrt 1.0))))
0.6b
(cbrt (sqrt (- x (sqrt 1.0))))
0.6b
(cbrt (sqrt (- x (sqrt 1.0))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
87×cbrt-prod
80×add-sqr-sqrt
67×sqrt-prod
42×*-un-lft-identity
22×add-cube-cbrt
18×cbrt-div sqrt-div swap-sqr difference-of-squares
12×associate-*r* associate-*l*
11×pow1
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 → 142
Calls
4 calls:
53.0ms
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
9.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
6.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
6.0ms
(cbrt (sqrt (- x (sqrt 1.0))))

series892.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(* (cbrt (sqrt (- x (sqrt 1.0)))) (cbrt (sqrt (- x (sqrt 1.0)))))
193.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
193.0ms
(cbrt (sqrt (- x (sqrt 1.0))))
191.0ms
(cbrt (sqrt (- x (sqrt 1.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05021932
118331809
250021681

prune459.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.4s

Algorithm
intervals
Results
354.0ms7752×body160nan
340.0ms16280×body80nan
227.0ms8000×body80valid