Details

Time bar (total: 4.1s)

sample42.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
6.0ms256×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: 19.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
19.4b
(/ (* (- 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:
2.0ms
(+ (* x x) (* y y))
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series91.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (* x x) (* y y))
64.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify44.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0308388
11848330
25001322

prune126.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

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)))
18.5b
(/ (+ (pow x 2) (pow y 2)) (+ x y))

rewrite87.0ms

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:
10.0ms
(+ (pow x 2) (pow y 2))
32.0ms
(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
30.0ms
(/ (+ (pow x 2) (pow y 2)) (+ x y))

series158.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (pow x 2) (pow y 2))
60.0ms
(/ (- x y) (/ (+ (pow x 2) (pow y 2)) (+ x y)))
64.0ms
(/ (+ (pow x 2) (pow y 2)) (+ x y))

simplify102.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07622924
134152840
250012838

prune410.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y))
0.0b
(/ (- x y) (sqrt (+ (pow x 2) (pow y 2))))
18.4b
(sqrt (+ (pow x 2) (pow y 2)))
18.4b
(sqrt (+ (pow x 2) (pow y 2)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
134×*-un-lft-identity
72×times-frac
66×add-sqr-sqrt
65×sqrt-prod
46×add-cube-cbrt
35×distribute-lft-out
26×unpow-prod-down
13×associate-/l*
12×associate-/r*
9×distribute-lft-out-- difference-of-squares
8×add-exp-log sqrt-div add-cbrt-cube
6×pow1
5×flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
1×flip3-- div-sub flip--
Counts
4 → 164
Calls
4 calls:
29.0ms
(/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y))
22.0ms
(/ (- x y) (sqrt (+ (pow x 2) (pow y 2))))
15.0ms
(sqrt (+ (pow x 2) (pow y 2)))
17.0ms
(sqrt (+ (pow x 2) (pow y 2)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y))
88.0ms
(/ (- x y) (sqrt (+ (pow x 2) (pow y 2))))
41.0ms
(sqrt (+ (pow x 2) (pow y 2)))
35.0ms
(sqrt (+ (pow x 2) (pow y 2)))

simplify50.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
03901663
113581534
250011534

prune386.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3))
0.1b
(pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3)
18.4b
(sqrt (+ (pow x 2) (pow y 2)))
18.4b
(sqrt (+ (pow x 2) (pow y 2)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
212×*-un-lft-identity
128×times-frac
112×unpow-prod-down
90×sqrt-prod
82×cbrt-prod
78×add-sqr-sqrt
76×add-cube-cbrt cube-prod
68×distribute-lft-out
8×associate-/r/
7×pow1 add-exp-log add-cbrt-cube
6×flip3-+ flip-+
4×sqrt-div div-inv add-log-exp
3×pow-unpow
2×cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 pow-exp rem-cube-cbrt sqr-pow
1×cbrt-undiv pow-to-exp cbrt-div pow-pow pow1/3 div-exp rem-cbrt-cube
Counts
4 → 222
Calls
4 calls:
30.0ms
(cbrt (pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3))
25.0ms
(pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3)
15.0ms
(sqrt (+ (pow x 2) (pow y 2)))
18.0ms
(sqrt (+ (pow x 2) (pow y 2)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(cbrt (pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3))
94.0ms
(pow (/ (sqrt (+ (pow x 2) (pow y 2))) (+ x y)) 3)
41.0ms
(sqrt (+ (pow x 2) (pow y 2)))
36.0ms
(sqrt (+ (pow x 2) (pow y 2)))

simplify72.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05452652
122642337
250022265

prune365.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.5b

regimes113.0ms

Accuracy

74.5% (4.9b remaining)

Error of 5.4b against oracle of 0.4b and baseline of 19.8b

bsearch127.0ms

Steps
ItersRangePoint
10
3.421516530565708e-172
2.7311386280172475e-162
2.695424215399706e-162
7
-5.8181467498964894e-154
-1.9534729603997635e-155
-2.31540310639935e-154
7
-4.548114588310593e+155
-8.319542791532245e+153
-1.3348215570452238e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03231
13231

end0.0ms

sample1.1s

Algorithm
intervals
Results
729.0ms8000×body80valid
198.0ms8000×pre80true