Details

Time bar (total: 2.4s)

analyze49.0ms (2.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
50%50%0.1%5
62.4%37.5%0.1%6
74.9%25%0.1%7
81.2%18.7%0.1%8
87.4%12.5%0.1%9
90.5%9.4%0.1%10
93.7%6.2%0.1%11
95.2%4.7%0.1%12
96.8%3.1%0.1%13
97.6%2.3%0.1%14

sample14.0ms (0.6%)

Algorithm
1×intervals
Results
8.0ms256×body80valid

simplify205.0ms (8.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (204.0ms)

IterNodesCost
0264111
1264111

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
0.0b
(/ (* x y) 2.0)
7.6b
(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite24.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
16×times-frac
14×add-cube-cbrt
10×add-exp-log add-cbrt-cube
7×associate-/r*
5×add-log-exp
4×distribute-lft-out associate-/l*
3×pow1 cbrt-undiv div-exp
2×frac-2neg clear-num associate-/r/ div-inv difference-of-squares
1×sub-neg flip3-- flip3-+ diff-log prod-exp flip-- cbrt-unprod flip-+ distribute-lft-out--
Counts
3 → 68
Calls

3 calls:

12.0ms
(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.0ms
(/ y (+ 1.0 (/ (* x y) 2.0)))
4.0ms
(/ (* x y) 2.0)

series22.0ms (0.9%)

Counts
3 → 9
Calls

3 calls:

11.0ms
(/ y (+ 1.0 (/ (* x y) 2.0)))
7.0ms
(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
3.0ms
(/ (* x y) 2.0)

simplify61.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04981946
14981946

prune118.0ms (5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New74377
Fresh000
Picked101
Done000
Total75378

Merged error: 0b

Counts
78 → 3

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(- x (/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y)))
0.0b
(/ (* y x) 2.0)
0.1b
(/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y))
7.5b
(/ (+ 1.0 (/ (* y x) 2.0)) y)

rewrite42.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
117×times-frac
101×*-un-lft-identity
78×add-sqr-sqrt
64×add-cube-cbrt
22×add-exp-log associate-/r*
16×add-cbrt-cube distribute-lft-out
10×div-exp
8×div-inv associate-/l*
6×cbrt-undiv add-log-exp
5×pow1 difference-of-squares
3×frac-2neg clear-num
2×rec-exp 1-exp associate-/l/ distribute-lft-out--
1×sub-neg flip3-- pow-flip flip3-+ diff-log prod-exp associate-/r/ flip-- cbrt-unprod flip-+ inv-pow
Counts
4 → 160
Calls

4 calls:

17.0ms
(- x (/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y)))
8.0ms
(/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y))
6.0ms
(/ (+ 1.0 (/ (* y x) 2.0)) y)
4.0ms
(/ (* y x) 2.0)

series28.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

11.0ms
(/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y))
7.0ms
(- x (/ 1 (/ (+ 1.0 (/ (* y x) 2.0)) y)))
6.0ms
(/ (+ 1.0 (/ (* y x) 2.0)) y)
3.0ms
(/ (* y x) 2.0)

simplify62.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049862527
149862527

prune256.0ms (10.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1720172
Fresh022
Picked011
Done000
Total1723175

Merged error: 0b

Counts
175 → 3

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))
0.5b
(/ x (sqrt 2.0))
0.5b
(/ y (sqrt 2.0))
7.6b
(/ y (+ 1.0 (* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))))

rewrite35.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Rules
98×add-sqr-sqrt
93×times-frac
68×add-cube-cbrt *-un-lft-identity
48×sqrt-prod
22×add-exp-log associate-*r* associate-*l* add-cbrt-cube
15×associate-/r*
9×associate-/l* unswap-sqr
7×cbrt-undiv div-exp
6×pow1
5×div-inv
4×prod-exp cbrt-unprod add-log-exp
3×frac-2neg clear-num
2×associate-/r/
1×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 180
Calls

4 calls:

15.0ms
(* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))
6.0ms
(/ y (+ 1.0 (* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))))
4.0ms
(/ y (sqrt 2.0))
4.0ms
(/ x (sqrt 2.0))

series55.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

30.0ms
(/ y (+ 1.0 (* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))))
12.0ms
(* (/ x (sqrt 2.0)) (/ y (sqrt 2.0)))
8.0ms
(/ x (sqrt 2.0))
5.0ms
(/ y (sqrt 2.0))

simplify55.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050431843

prune379.0ms (16%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1920192
Fresh011
Picked011
Done011
Total1923195

Merged error: 0b

Counts
195 → 3

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b
(/ (* y x) 2.0)
0.2b
(* (/ (* y x) 2.0) (/ (* y x) 2.0))
5.0b
(/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0))))
13.2b
(* (/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

rewrite38.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
41×add-sqr-sqrt
40×times-frac
34×*-un-lft-identity
32×add-cube-cbrt
25×associate-*l*
18×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
13×pow1
12×associate-*r*
8×difference-of-squares
7×swap-sqr associate-/r* div-inv
4×flip3-- associate-/r/ flip-- associate-/l* add-log-exp
3×frac-times associate-*r/ unswap-sqr
2×sub-neg frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-sqr pow-prod-up distribute-lft-out--
Counts
4 → 155
Calls

4 calls:

14.0ms
(* (/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0)))) (- 1.0 (/ (* x y) 2.0)))
9.0ms
(* (/ (* y x) 2.0) (/ (* y x) 2.0))
6.0ms
(/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0))))
4.0ms
(/ (* y x) 2.0)

series52.0ms (2.2%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(* (/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0)))) (- 1.0 (/ (* x y) 2.0)))
17.0ms
(/ y (- (* 1.0 1.0) (* (/ (* y x) 2.0) (/ (* y x) 2.0))))
7.0ms
(* (/ (* y x) 2.0) (/ (* y x) 2.0))
3.0ms
(/ (* y x) 2.0)

simplify41.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
049682257
149682257

prune339.0ms (14.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1670167
Fresh000
Picked011
Done022
Total1673170

Merged error: 0b

Counts
170 → 3

regimes69.0ms (2.9%)

Accuracy

Total 0.0b remaining (80.6%)

Threshold costs 0.0b (80.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
13413

end0.0ms (0%)

sample378.0ms (15.9%)

Algorithm
1×intervals
Results
256.0ms7998×body80valid
0.0ms1×body2560valid
0.0ms1×body1280valid

Profiling

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