Details

Time bar (total: 1.6s)

analyze13.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%18.7%81.3%0
0%18.7%81.3%1
0%18.7%81.3%2
0%18.7%81.3%3
0%18.7%81.3%4
4.7%14%81.3%5
5.3%13.5%81.3%6
18.1%0.6%81.3%7
18.1%0.6%81.3%8
18.6%0.1%81.3%9
18.6%0.1%81.3%10
18.7%0%81.3%11
18.7%0%81.3%12
18.7%0%81.3%13
18.7%0%81.3%14

sample21.0ms (1.3%)

Algorithm
1×intervals
Results
9.0ms256×body80valid
5.0ms256×pre80true

simplify120.0ms (7.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (118.0ms)

IterNodesCost
0489715
1489715

prune8.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 20.5b

Counts
2 → 2

localize8.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
20.6b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite21.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
8×associate-/l/
7×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times add-cube-cbrt *-un-lft-identity add-log-exp
3×flip3-- times-frac associate-/r* flip--
2×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×+-commutative frac-2neg prod-exp clear-num sum-log cbrt-unprod div-inv associate-/l*
Counts
2 → 42
Calls

2 calls:

16.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
4.0ms
(+ (* x x) (* y y))

series16.0ms (1%)

Counts
2 → 6
Calls

2 calls:

11.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
6.0ms
(+ (* x x) (* y y))

simplify20.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
05103655

prune71.0ms (4.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New45348
Fresh011
Picked011
Done000
Total45550

Merged error: 0.5b

Counts
50 → 5

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune8.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New000
Fresh033
Picked011
Done011
Total055

Merged error: 0.5b

Counts
5 → 5

localize12.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ x y))
19.8b
(sqrt (+ (* x x) (* y y)))
19.8b
(sqrt (+ (* x x) (* y y)))

rewrite43.0ms (2.7%)

Algorithm
1×rewrite-expression-head
Rules
79×add-sqr-sqrt
71×*-un-lft-identity
62×times-frac
43×add-cube-cbrt
40×sqrt-prod
36×associate-*l*
13×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×pow1 sqrt-div
6×flip3-+ associate-/r* flip-+
5×associate-/l*
4×associate-*r* associate-/r/ add-log-exp
3×unswap-sqr
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-sub pow-prod-down associate-*l/ clear-num *-commutative flip-- distribute-lft-out
Counts
4 → 151
Calls

4 calls:

19.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ x y))
9.0ms
(/ (- x y) (sqrt (+ (* x x) (* y y))))
4.0ms
(sqrt (+ (* x x) (* y y)))
4.0ms
(sqrt (+ (* x x) (* y y)))

series39.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ x y))
12.0ms
(/ (- x y) (sqrt (+ (* x x) (* y y))))
7.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

simplify54.0ms (3.3%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
058812655

prune175.0ms (10.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1630163
Fresh022
Picked011
Done022
Total1635168

Merged error: 0.5b

Counts
168 → 5

localize10.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
20.0b
(/ (+ x y) (+ (* x x) (* y y)))

rewrite29.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×flip3-+ associate-/r/ flip-+ associate-/l*
3×associate-/r*
2×cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 89
Calls

3 calls:

14.0ms
(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
8.0ms
(/ (+ x y) (+ (* x x) (* y y)))
4.0ms
(+ (* x x) (* y y))

series24.0ms (1.5%)

Counts
3 → 9
Calls

3 calls:

11.0ms
(* (- x y) (/ (+ x y) (+ (* x x) (* y y))))
8.0ms
(/ (+ x y) (+ (* x x) (* y y)))
5.0ms
(+ (* x x) (* y y))

simplify40.0ms (2.5%)

Algorithm
1×egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
053171452

prune98.0ms (6.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New98098
Fresh011
Picked011
Done033
Total985103

Merged error: 0.5b

Counts
103 → 5

regimes145.0ms (9%)

Accuracy

Total 4.5b remaining (89.4%)

Threshold costs 0b (0%)

bsearch45.0ms (2.8%)

Steps
ItersRangePoint
10
4.915073955433892e-170
5.148523267551369e-157
1.5574783314889873e-162
9
-9.759662152981248e-157
-5.648508456451283e-165
-1.5570222608799464e-162
9
-3.239675390048663e+155
-6.414788358883296e+148
-1.3557348503118228e+154

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03530
13530

end0.0ms (0%)

sample584.0ms (36.3%)

Algorithm
1×intervals
Results
293.0ms8000×body80valid
153.0ms8000×pre80true

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