Details

Time bar (total: 4.4s)

sample52.0ms

Algorithm
intervals
Results
14.0ms298×body160nan
13.0ms571×body80nan
10.0ms256×body80valid

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: 31.4b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(- (* x x) 1.0)
0.0b
(+ x (sqrt (- (* x x) 1.0)))
29.2b
(sqrt (- (* x x) 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
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 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(- (* x x) 1.0)
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

series357.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
38.0ms
(- (* x x) 1.0)
67.0ms
(+ x (sqrt (- (* x x) 1.0)))
54.0ms
(sqrt (- (* x x) 1.0))

simplify140.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0327471
11087435
24892422
35001422

prune164.0ms

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))))

rewrite19.0ms

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))))))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series632.0ms

Counts
3 → 9
Calls
3 calls:
290.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
149.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
193.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0440941
11553864
25001848

prune217.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
116×sqrt-div
79×sqrt-prod
48×add-sqr-sqrt
32×frac-times
26×*-un-lft-identity
24×associate-*r*
23×flip3-- flip--
20×pow1
16×add-cube-cbrt associate-*l/
13×sqrt-pow1
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×associate-*r/ pow-prod-down
9×pow1/2
8×associate-*l* difference-of-squares
6×unswap-sqr
4×rem-sqrt-square prod-exp cbrt-unprod distribute-lft-out-- add-log-exp
3×sqrt-unprod
2×*-commutative
1×distribute-lft-out
Counts
4 → 151
Calls
4 calls:
5.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
5.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
22.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
15.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
193.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
196.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
295.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

simplify82.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07682304
129192103
250012052

prune508.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01615
11615

end0.0ms

sample1.2s

Algorithm
intervals
Results
347.0ms15697×body80nan
342.0ms7553×body160nan
220.0ms8000×body80valid