Details

Time bar (total: 5.0s)

sample85.0ms

Algorithm
intervals
Results
27.0ms533×body80nan
25.0ms250×body160nan
16.0ms256×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: 33.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
31.2b
(sqrt (- (* x x) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×add-cube-cbrt sqrt-prod add-log-exp
3×pow1 fma-def
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ distribute-lft-out difference-of-squares
Counts
2 → 35
Calls
2 calls:
11.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(sqrt (- (* x x) 1.0))

series116.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ x (sqrt (- (* x x) 1.0)))
51.0ms
(sqrt (- (* x x) 1.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0235239
1739223
22858218
35001216

prune105.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.4b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×sqrt-prod
12×sqrt-div
11×*-un-lft-identity
9×associate-*r*
7×add-cube-cbrt associate-*l*
6×pow1
4×add-exp-log frac-times flip3-+ add-cbrt-cube flip-+ add-log-exp unswap-sqr
3×flip3-- fma-def pow-prod-down flip--
2×expm1-log1p-u sqrt-pow1 pow1/2 associate-*r/ associate-*l/ log1p-expm1-u difference-of-squares
1×+-commutative sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 60
Calls
2 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
31.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series334.0ms

Counts
2 → 6
Calls
2 calls:
143.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
190.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify42.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0382708
11369643
25002629

prune182.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.4b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.4b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b
(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
51×sqrt-prod
38×sqrt-div
29×*-un-lft-identity
28×pow1
24×associate-*r*
21×add-cube-cbrt
20×associate-*l*
13×sqrt-pow1 flip3-+ pow1/2 flip-+
12×frac-times unswap-sqr
10×add-exp-log add-cbrt-cube
9×pow-prod-down
8×swap-sqr
6×flip3-- associate-*r/ associate-*l/ flip--
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×sqrt-unprod prod-exp pow-sqr *-commutative cbrt-unprod
2×distribute-lft-out distribute-lft-out--
1×pow2 rem-sqrt-square pow-plus rem-square-sqrt
Counts
4 → 164
Calls
4 calls:
3.0ms
(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
32.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
29.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
16.0ms
(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

series729.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
193.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
191.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
148.0ms
(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05102330
120112096
250022044

prune523.0ms

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
01520
11520

end0.0ms

sample2.5s

Algorithm
intervals
Results
848.0ms16296×body80nan
762.0ms7673×body160nan
519.0ms8000×body80valid