Details

Time bar (total: 3.2s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
3.0ms256×pre80true

simplify60.0ms

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: 16.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
16.3b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite39.0ms

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:
11.0ms
(+ (* x x) (* y y))
27.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series86.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x x) (* y y))
57.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify45.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0308388
11848330
25001322

prune124.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

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)))))
15.6b
(sqrt (+ (* x x) (* y y)))
15.6b
(sqrt (+ (* x x) (* y y)))

rewrite153.0ms

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:
25.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
103.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
7.0ms
(sqrt (+ (* x x) (* y y)))
8.0ms
(sqrt (+ (* x x) (* y y)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
60.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
33.0ms
(sqrt (+ (* x x) (* y y)))
37.0ms
(sqrt (+ (* x x) (* y y)))

simplify66.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05792358
124292169
250012080

prune390.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
16.3b
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
41×associate-/r/
29×add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×frac-times
17×flip3-+ add-cbrt-cube flip-+
16×associate-/r*
15×flip3-- flip--
14×div-exp
10×associate-*r/ associate-*l/
7×cbrt-undiv
6×div-inv associate-/l*
5×add-log-exp
4×pow1 prod-exp
3×rec-exp 1-exp
2×frac-2neg clear-num cbrt-unprod associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
3 → 130
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
38.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
37.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series146.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(+ (* x x) (* y y))
61.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
60.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify88.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06041641
139131448
250011367

prune257.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (exp (log (sqrt (+ (* x x) (* y y)))))))
5.3b
(exp (log (sqrt (+ (* x x) (* y y)))))
15.6b
(sqrt (+ (* x x) (* y y)))
15.6b
(sqrt (+ (* x x) (* y y)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
103×add-sqr-sqrt
83×times-frac
78×*-un-lft-identity
48×add-cube-cbrt
43×sqrt-prod
42×associate-*r*
36×log-prod associate-*l* exp-sum
16×add-cbrt-cube
14×add-exp-log
12×unswap-sqr
10×pow1 sqrt-div
9×distribute-lft-out
6×exp-prod distribute-lft-out-- difference-of-squares
5×flip3-+ flip-+
4×cbrt-undiv log-div exp-diff div-exp prod-exp associate-/r/ cbrt-unprod add-log-exp
3×sqrt-pow1 pow1/2 log-pow
2×rem-sqrt-square div-inv
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative rem-exp-log
Counts
4 → 162
Calls
4 calls:
127.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (exp (log (sqrt (+ (* x x) (* y y)))))))
10.0ms
(exp (log (sqrt (+ (* x x) (* y y)))))
8.0ms
(sqrt (+ (* x x) (* y y)))
8.0ms
(sqrt (+ (* x x) (* y y)))

series161.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (exp (log (sqrt (+ (* x x) (* y y)))))))
38.0ms
(exp (log (sqrt (+ (* x x) (* y y)))))
33.0ms
(sqrt (+ (* x x) (* y y)))
33.0ms
(sqrt (+ (* x x) (* y y)))

simplify70.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06682282
125382093
250021996

prune384.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes69.0ms

Accuracy

76.5% (4.7b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 20.3b

bsearch81.0ms

Steps
ItersRangePoint
6
4.3811697035537754e-170
3.106715750607624e-169
3.047723682413627e-169
9
-3.283662621146742e-162
-1.0074491365266925e-168
-1.558923983411082e-162
10
-8.37881605524702e+155
-3.72436965410306e+139
-1.7855327738146168e+140

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03221
13221

end0.0ms

sample496.0ms

Algorithm
intervals
Results
227.0ms8000×body80valid
95.0ms8000×pre80true