Details

Time bar (total: 4.7s)

sample49.0ms

Algorithm
intervals
Results
14.0ms298×body160nan
12.0ms571×body80nan
7.0ms256×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: 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))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod sqrt-prod add-cbrt-cube log1p-expm1-u
3×fma-def prod-diff
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 fma-neg diff-log rem-log-exp sum-log log-pow
Counts
4 → 71
Calls
4 calls:
8.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
7.0ms
(- (* x x) 1.0)
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(sqrt (- (* x x) 1.0))

series360.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
44.0ms
(- (* x x) 1.0)
70.0ms
(+ x (sqrt (- (* x x) 1.0)))
50.0ms
(sqrt (- (* x x) 1.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0384531
11360471
25002457

prune373.0ms

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))))

rewrite34.0ms

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))))

series619.0ms

Counts
3 → 9
Calls
3 calls:
284.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
145.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
189.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify50.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04671012
11665907
25001894

prune246.0ms

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)))))

rewrite112.0ms

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×expm1-log1p-u rem-sqrt-square prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- add-log-exp
3×sqrt-unprod
2×*-commutative
1×distribute-lft-out
Counts
4 → 159
Calls
4 calls:
6.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
7.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
59.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
30.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

series858.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
192.0ms
(sqrt (sqrt (- x (sqrt 1.0))))
200.0ms
(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0))))) (sqrt (sqrt (- x (sqrt 1.0)))))
278.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (sqrt (- x (sqrt 1.0)))))

simplify89.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07992370
130292159
250022098

prune543.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01615
11615

end0.0ms

sample1.3s

Algorithm
intervals
Results
351.0ms7553×body160nan
328.0ms15697×body80nan
241.0ms8000×body80valid