Details

Time bar (total: 1.4s)

analyze5.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
25%0%75%13
25%0%75%14

sample19.0ms (1.3%)

Algorithm
intervals
Results
13.0ms256×body80valid

simplify153.0ms (10.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (151.0ms)

IterNodesCost
0489211
1489211

prune7.0ms (0.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.0b

Counts
2 → 1

localize8.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
24×add-sqr-sqrt times-frac
22×add-cube-cbrt
16×log-prod
add-exp-log
distribute-lft-out
pow1 add-cbrt-cube add-log-exp
sqrt-prod associate-/l*
associate-/r*
flip3-+ sqrt-div div-exp rem-log-exp flip-+ div-inv associate-/l/
cbrt-undiv +-commutative rem-sqrt-square log-div flip3-- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log log-pow flip-- difference-of-squares
Counts
4 → 88
Calls

4 calls:

7.0ms
(/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x)
6.0ms
(log (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
5.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
3.0ms
(sqrt (- 1.0 (* x x)))

series29.0ms (2%)

Counts
4 → 12
Calls

4 calls:

15.0ms
(log (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
6.0ms
(/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x)
4.0ms
(sqrt (- 1.0 (* x x)))
4.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))

simplify28.0ms (2%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
049951479
149951479

prune204.0ms (14.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New991100
Fresh000
Picked101
Done000
Total1001101

Merged error: 0b

Counts
101 → 1

localize11.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(sqrt (- 1.0 (* x x)))
0.1b
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
0.1b
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))

rewrite21.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
34×*-un-lft-identity
32×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
pow1
rem-sqrt-square sqrt-div distribute-lft-out
add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
flip3-- flip-- div-inv difference-of-squares
Counts
4 → 88
Calls

4 calls:

7.0ms
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
7.0ms
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
3.0ms
(sqrt (- 1.0 (* x x)))
3.0ms
(sqrt (- 1.0 (* x x)))

series29.0ms (2%)

Counts
4 → 12
Calls

4 calls:

10.0ms
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
10.0ms
(sqrt (/ (+ 1.0 (sqrt (- 1.0 (* x x)))) x))
5.0ms
(sqrt (- 1.0 (* x x)))
4.0ms
(sqrt (- 1.0 (* x x)))

simplify61.0ms (4.2%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049711564
149711564

prune346.0ms (24%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh000
Picked011
Done000
Total1001101

Merged error: 0b

Counts
101 → 1

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02925
12925

end0.0ms (0%)

sample495.0ms (34.3%)

Algorithm
intervals
Results
403.0ms8000×body80valid
0.0msbody80nan

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