Details

Time bar (total: 3.0s)

analyze265.0ms (8.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%50%25%4
25%37.5%37.5%5
25%31.2%43.8%6
25%28.1%46.9%7
25%26.5%48.5%8
25%25.8%49.2%9
25%25.4%49.6%10
25%25.2%49.8%11
25%25.1%49.9%12
25%25%50%13
25%25%50%14

sample52.0ms (1.7%)

Algorithm
intervals
Results
16.0ms92×body2560nan
10.0ms256×body80valid
9.0ms59×body1280nan
5.0ms41×body640nan
2.0ms23×body320nan
1.0msbody160nan
0.0msbody80nan

simplify61.0ms (2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
052579

prune7.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.6b

Counts
2 → 1

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
29.4b
(sqrt (- (* x x) 1.0))

rewrite18.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity
add-sqr-sqrt
pow1 add-cube-cbrt add-log-exp
add-exp-log log-prod sqrt-prod
add-cbrt-cube
log-div flip3-+ sqrt-div flip-+ distribute-lft-out
+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls

3 calls:

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

series19.0ms (0.6%)

Counts
3 → 9
Calls

3 calls:

9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(sqrt (- (* x x) 1.0))

simplify41.0ms (1.4%)

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05188615

prune99.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New50252
Fresh000
Picked101
Done000
Total51253

Merged error: 0b

Counts
53 → 2

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
0.1b
(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
0.2b
(/ 0.25 (* x x))
0.4b
(/ 0.09375 (pow x 4))

rewrite54.0ms (1.8%)

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
24×add-sqr-sqrt add-cube-cbrt times-frac
15×distribute-lft-out
14×add-exp-log
13×pow1
12×unpow-prod-down
11×add-cbrt-cube
10×add-log-exp
log-pow
associate-/r* distribute-lft-out--
log-prod associate-/l*
div-exp sum-log
associate-+r+ sqr-pow
cbrt-undiv associate-+l+ associate--l+
+-commutative frac-2neg flip3-+ diff-log clear-num flip-+ div-inv
pow-to-exp associate-+r- sub-neg frac-add pow-exp prod-exp cbrt-unprod
Counts
4 → 110
Calls

4 calls:

23.0ms
(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
18.0ms
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
5.0ms
(/ 0.25 (* x x))
5.0ms
(/ 0.09375 (pow x 4))

series26.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

10.0ms
(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
8.0ms
(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
4.0ms
(/ 0.09375 (pow x 4))
3.0ms
(/ 0.25 (* x x))

simplify47.0ms (1.6%)

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049781427
149781427

prune240.0ms (8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1220122
Fresh011
Picked011
Done000
Total1222124

Merged error: 0b

Counts
124 → 2

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite20.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity sqrt-div
associate-*r*
pow1 add-cube-cbrt
associate-*l*
add-exp-log
flip3-+ add-cbrt-cube flip-+ add-log-exp
frac-times unswap-sqr
log-prod flip3-- pow-prod-down flip--
log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
+-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:

13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

series33.0ms (1.1%)

Counts
3 → 9
Calls

3 calls:

13.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
8.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))

simplify40.0ms (1.3%)

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049631255
149631255

prune199.0ms (6.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New76076
Fresh000
Picked011
Done011
Total76278

Merged error: 0b

Counts
78 → 2

regimes26.0ms (0.9%)

Accuracy

Total 0.3b remaining (99.3%)

Threshold costs 0.3b (99.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05617
15617

end0.0ms (0%)

sample1.7s (57.4%)

Algorithm
intervals
Results
578.0ms3053×body2560nan
395.0ms2514×body1280nan
308.0ms8000×body80valid
152.0ms1250×body640nan
57.0ms615×body320nan
21.0ms324×body160nan
10.0ms317×body80nan

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