Details

Time bar (total: 4.3s)

sample46.0ms

Algorithm
intervals
Results
11.0ms244×body160nan
11.0ms256×body80valid
10.0ms490×body80nan

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: 30.6b

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)))
28.5b
(sqrt (- (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
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 → 43
Calls
3 calls:
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series328.0ms

Counts
3 → 9
Calls
3 calls:
204.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
66.0ms
(+ x (sqrt (- (* x x) 1.0)))
57.0ms
(sqrt (- (* x x) 1.0))

simplify134.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
0316408
11042379
24663366
35002365

prune129.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b
(+ 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
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
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
6.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series650.0ms

Counts
3 → 9
Calls
3 calls:
289.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
155.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0440941
11553864
25001848

prune201.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (sqrt 1.0))))
0.1b
(sqrt (sqrt (+ x (sqrt 1.0))))
0.3b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.3b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-div
62×sqrt-prod
36×add-sqr-sqrt
32×frac-times
26×*-un-lft-identity
23×flip3-+ flip-+
20×pow1 associate-*l*
16×add-cube-cbrt associate-*r/
13×sqrt-pow1
12×flip3-- flip--
11×add-exp-log add-cbrt-cube
10×associate-*r* pow-prod-down associate-*l/
9×pow1/2
6×unswap-sqr
4×rem-sqrt-square prod-exp cbrt-unprod distribute-lft-out add-log-exp
3×sqrt-unprod
2×*-commutative difference-of-squares
1×distribute-lft-out--
Counts
4 → 145
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
5.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
19.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
17.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series828.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
132.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
207.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
352.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify80.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07812232
130142047
250022008

prune501.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

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

sample1.2s

Algorithm
intervals
Results
345.0ms7745×body160nan
330.0ms16329×body80nan
220.0ms8000×body80valid