Details

Time bar (total: 2.5s)

sample21.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
4.0ms256×pre80true

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1487
21047
31967
43597
56867
613557
750017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
20.9b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite15.0ms

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:
2.0ms
(+ (* x x) (* y y))
11.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series90.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(+ (* x x) (* y y))
64.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify46.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0308388
11848330
25001322

prune114.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

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

prune6.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

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) (sqrt (+ (* x x) (* y y)))))
20.0b
(sqrt (+ (* x x) (* y y)))
20.0b
(sqrt (+ (* x x) (* y y)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
93×*-un-lft-identity
90×times-frac
55×add-cube-cbrt
54×sqrt-prod
36×associate-*l*
30×associate-*r*
18×add-exp-log add-cbrt-cube
13×distribute-lft-out
10×sqrt-div
9×unswap-sqr
8×pow1
6×flip3-+ associate-/r* associate-/r/ flip-+ distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 175
Calls
4 calls:
11.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
59.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
63.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
36.0ms
(sqrt (+ (* x x) (* y y)))
42.0ms
(sqrt (+ (* x x) (* y y)))

simplify67.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05792358
124292169
250012080

prune356.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) (pow y 2))
0.0b
(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
20.1b
(/ (+ (pow x 2) (pow y 2)) (+ x y))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
347×*-un-lft-identity
270×times-frac
155×add-sqr-sqrt
101×add-cube-cbrt
96×distribute-lft-out
60×unpow-prod-down
30×associate-/r*
27×distribute-lft-out-- difference-of-squares
15×associate-/r/
10×add-exp-log add-cbrt-cube associate-/l*
9×flip3-+ flip-+
8×div-inv
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1
2×frac-2neg clear-num
1×+-commutative flip3-- div-sub sum-log flip--
Counts
3 → 237
Calls
3 calls:
9.0ms
(+ (pow x 2) (pow y 2))
31.0ms
(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
29.0ms
(/ (+ (pow x 2) (pow y 2)) (+ x y))

series154.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (pow x 2) (pow y 2))
63.0ms
(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
64.0ms
(/ (+ (pow x 2) (pow y 2)) (+ x y))

simplify98.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07622924
134152840
250012838

prune404.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes60.0ms

Accuracy

77.2% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 21.1b

bsearch82.0ms

Steps
ItersRangePoint
10
3.909725892130977e-164
3.330093741458529e-151
6.5645559431747094e-161
2
-4.0776446823299444e-161
-3.628943090963693e-161
-4.021556983409163e-161
11
-3.136281992538668e+161
-5.608408056123679e+141
-1.332286012289778e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03223
13223

end0.0ms

sample498.0ms

Algorithm
intervals
Results
238.0ms8000×body80valid
116.0ms8000×pre80true