Details

Time bar (total: 4.7s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize12.0ms

Local error

Found 1 expressions with local error:

17.9b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
6×add-exp-log add-cbrt-cube
4×frac-times flip3-+ flip-+
3×add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity times-frac associate-/r* flip--
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×pow1 frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l* add-log-exp
Counts
1 → 31
Calls
1 calls:
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series60.0ms

Counts
1 → 3
Calls
1 calls:
60.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify43.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0270311
11434265
25001261

prune85.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
17.9b
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
41×associate-/r/
28×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×frac-times
16×flip3-+ associate-/r* add-cbrt-cube flip-+
15×flip3-- flip--
14×div-exp
10×associate-*r/ associate-*l/
7×cbrt-undiv
6×div-inv associate-/l*
4×prod-exp
3×pow1 rec-exp 1-exp
2×frac-2neg clear-num cbrt-unprod associate-/l/ add-log-exp
1×pow-flip inv-pow
Counts
2 → 119
Calls
2 calls:
21.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
13.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series124.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
60.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify82.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05621563
134291382
250011301

prune204.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
0.0b
(/ (sqrt (+ (* x x) (* y y))) (+ x y))
17.6b
(sqrt (+ (* x x) (* y y)))
17.6b
(sqrt (+ (* x x) (* y y)))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
2922×times-frac
1935×*-un-lft-identity
1479×add-sqr-sqrt
1105×add-cube-cbrt
930×sqrt-prod
229×distribute-lft-out
186×distribute-lft-out-- difference-of-squares
139×associate-/r/
72×flip3-+ flip-+
70×div-inv
68×sqrt-div
42×associate-/l*
34×associate-/r*
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×pow1
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub clear-num
Counts
4 → 1247
Calls
4 calls:
53.0ms
(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
10.0ms
(/ (sqrt (+ (* x x) (* y y))) (+ x y))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
82.0ms
(/ (sqrt (+ (* x x) (* y y))) (+ x y))
36.0ms
(sqrt (+ (* x x) (* y y)))
45.0ms
(sqrt (+ (* x x) (* y y)))

simplify318.0ms

Algorithm
egg-herbie
Counts
1259 → 1259
Iterations

Useful iterations: 1 (55.0ms)

IterNodesCost
0345434019
1500333011

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (+ (* x x) (* y y)))
17.6b
(sqrt (+ (* x x) (* y y)))
17.6b
(sqrt (+ (* x x) (* y y)))
17.6b
(/ (* (- x y) (- x y)) (+ (* x x) (* y y)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity sqrt-prod add-cbrt-cube
8×associate-/l/
7×pow1
6×flip3-- sqrt-div flip--
4×frac-times flip3-+ flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/r*
2×cbrt-undiv associate-*r/ div-exp associate-*l/ associate-/r/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))
3.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(/ (* (- x y) (- x y)) (+ (* x x) (* y y)))

series181.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ (* x x) (* y y)))
41.0ms
(sqrt (+ (* x x) (* y y)))
35.0ms
(sqrt (+ (* x x) (* y y)))
69.0ms
(/ (* (- x y) (- x y)) (+ (* x x) (* y y)))

simplify41.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0279615
11286557
25001552

prune307.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes80.0ms

Accuracy

76.5% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 20.4b

bsearch109.0ms

Steps
ItersRangePoint
10
5.733635285122226e-170
3.4471621288568952e-158
8.648162569416419e-160
10
-2.2852977508774913e-159
-1.6322255024892554e-169
-1.7364647816785135e-159
10
-2.771665303262814e+161
-1.6259263967015282e+146
-1.592424023249112e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03116
13216
23216

end0.0ms

sample487.0ms

Algorithm
intervals
Results
231.0ms8000×body80valid
116.0ms8000×pre80true