Details

Time bar (total: 5.5s)

sample44.0ms

Algorithm
intervals
Results
11.0ms244×body160nan
10.0ms490×body80nan
8.0ms256×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: 30.6b

localize8.0ms

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))

rewrite28.0ms

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:
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
12.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(sqrt (- (* x x) 1.0))

series324.0ms

Counts
3 → 9
Calls
3 calls:
203.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
70.0ms
(+ x (sqrt (- (* x x) 1.0)))
51.0ms
(sqrt (- (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0339436
11140401
25001389

prune160.0ms

Filtered
61 candidates to 53 candidates (86.9%)
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))))

rewrite35.0ms

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:
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
28.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series653.0ms

Counts
3 → 9
Calls
3 calls:
298.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
148.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify51.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04671012
11665907
25001894

prune263.0ms

Filtered
85 candidates to 69 candidates (81.2%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (sqrt 1.0))))
0.5b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.5b
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.5b
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
484×sqrt-div
144×frac-times
102×sqrt-prod
89×pow1
84×sqrt-pow1
64×add-sqr-sqrt
63×pow-prod-down
61×flip3-+ flip-+
60×flip3-- flip--
48×associate-*r/ associate-*l/
42×pow1/2
28×*-un-lft-identity
25×associate-*r*
21×associate-*l*
20×add-exp-log add-cbrt-cube
18×add-cube-cbrt unswap-sqr
12×pow-prod-up
10×prod-exp cbrt-unprod
8×pow-sqr
7×sqrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×*-commutative distribute-lft-out
2×rem-sqrt-square pow-plus distribute-lft-out--
1×pow2 swap-sqr rem-square-sqrt
Counts
4 → 272
Calls
4 calls:
7.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
35.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
37.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
98.0ms
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
141.0ms
(sqrt (sqrt (+ x (sqrt 1.0))))
565.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
374.0ms
(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
205.0ms
(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

simplify152.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
011975677
146074909
250014901

prune865.0ms

Filtered
284 candidates to 159 candidates (56.0%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

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

sample1.3s

Algorithm
intervals
Results
365.0ms7745×body160nan
349.0ms16329×body80nan
232.0ms8000×body80valid