Details

Time bar (total: 2.2s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
5.0ms256×pre80true

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1487
21047
31967
43597
56867
613557
750017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
22.1b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite16.0ms

Algorithm
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:
3.0ms
(+ (* x x) (* y y))
11.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series88.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(+ (* x x) (* y y))
62.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0308388
11848330
25001322

prune100.0ms

Filtered
48 candidates to 39 candidates (81.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New44448
Fresh000
Picked011
Done000
Total44549

Merged error: 0.2b

Counts
49 → 5

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune5.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New000
Fresh033
Picked011
Done011
Total055

Merged error: 0.2b

Counts
5 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
21.8b
(sqrt (+ (* x x) (* y y)))
21.8b
(sqrt (+ (* x x) (* y y)))
21.8b
(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
72×sqrt-prod
59×add-sqr-sqrt
57×add-cube-cbrt *-un-lft-identity
22×sqrt-div
18×add-exp-log associate-/r/ add-cbrt-cube
14×flip3-+ flip-+
13×associate-/l*
12×associate-/r*
9×div-inv associate-/l/
7×cbrt-undiv div-exp
6×pow1
4×frac-times add-log-exp
3×flip3-- flip--
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
Counts
4 → 176
Calls
4 calls:
16.0ms
(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
3.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

series215.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))
37.0ms
(sqrt (+ (* x x) (* y y)))
36.0ms
(sqrt (+ (* x x) (* y y)))
81.0ms
(/ (* (- x y) (+ x y)) (sqrt (+ (* x x) (* y y))))

simplify85.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06122996
129972693
250022692

prune318.0ms

Filtered
188 candidates to 119 candidates (63.3%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1880188
Fresh022
Picked011
Done022
Total1885193

Merged error: 0.2b

Counts
193 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (pow y 2))
0.2b
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
21.9b
(/ (+ x y) (+ (pow x 2) (pow y 2)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
41×times-frac
32×add-sqr-sqrt
31×distribute-lft-out
26×associate-*r*
25×add-cube-cbrt
20×unpow-prod-down
10×add-exp-log add-cbrt-cube
5×pow1 associate-*l* associate-/r* add-log-exp
4×flip3-+ associate-/r/ flip-+ associate-/l*
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 → 109
Calls
3 calls:
7.0ms
(+ (pow x 2) (pow y 2))
24.0ms
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
17.0ms
(/ (+ x y) (+ (pow x 2) (pow y 2)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (pow x 2) (pow y 2))
61.0ms
(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
51.0ms
(/ (+ x y) (+ (pow x 2) (pow y 2)))

simplify57.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0390902
11953823
25001822

prune184.0ms

Filtered
118 candidates to 69 candidates (58.5%)
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1180118
Fresh011
Picked011
Done033
Total1185123

Merged error: 0.2b

Counts
123 → 5

regimes78.0ms

Accuracy

78% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 21.5b

bsearch102.0ms

Steps
ItersRangePoint
8
2.8873402050864073e-176
3.1124934180468344e-173
3.0806017080940076e-173
7
-6.985971265089402e-192
-2.1074608720573333e-193
-6.916531533579351e-192
8
-2.55267597913346e-155
-8.668710857002485e-158
-8.785060401238793e-158
7
-1.6711135734881002e+155
-1.8783855919608248e+153
-2.594815085473371e+153

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample584.0ms

Algorithm
intervals
Results
290.0ms8000×body80valid
151.0ms8000×pre80true