Details

Time bar (total: 3.7s)

sample19.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×pre80true

simplify61.0ms

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: 22.4b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
10×add-exp-log add-cbrt-cube
8×frac-times flip3-+ flip-+ associate-/l/
7×add-cube-cbrt
6×flip3-- flip--
5×pow1 associate-*l* add-log-exp
4×associate-*r/ associate-*r* associate-*l/
3×times-frac associate-/r*
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 73
Calls
3 calls:
16.0ms
(* (- x y) (+ x y))
3.0ms
(+ (* x x) (* y y))
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series133.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (- x y) (+ x y))
26.0ms
(+ (* x x) (* y y))
64.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify63.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0419577
12448504
25003497

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x y) (+ x y))
0.0b
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
0.0b
(+ (* x x) (* y y))
22.1b
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
41×associate-/r/
36×add-sqr-sqrt *-un-lft-identity
32×add-exp-log add-cube-cbrt
24×frac-times
20×flip3-+ add-cbrt-cube flip-+
18×flip3-- flip--
16×associate-/r*
14×div-exp
12×associate-*r/ associate-*l/
7×pow1 cbrt-undiv
6×div-inv associate-/l* add-log-exp
5×associate-*l* prod-exp
4×associate-*r*
3×rec-exp 1-exp cbrt-unprod
2×frac-2neg clear-num associate-/l/
1×+-commutative distribute-rgt-in pow-flip distribute-lft-in pow-prod-down sum-log *-commutative distribute-lft-out distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 161
Calls
4 calls:
17.0ms
(* (- x y) (+ x y))
22.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
3.0ms
(+ (* x x) (* y y))
14.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (- x y) (+ x y))
64.0ms
(/ 1 (/ (+ (* x x) (* y y)) (* (- x y) (+ x y))))
27.0ms
(+ (* x x) (* y y))
65.0ms
(/ (+ (* x x) (* y y)) (* (- x y) (+ x y)))

simplify103.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06561830
139641623
250011542

prune309.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

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)))))
21.7b
(sqrt (+ (* x x) (* y y)))
21.7b
(sqrt (+ (* x x) (* y y)))

rewrite88.0ms

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:
12.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
62.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
3.0ms
(sqrt (+ (* x x) (* y y)))
4.0ms
(sqrt (+ (* x x) (* y y)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
65.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
35.0ms
(sqrt (+ (* x x) (* y y)))
40.0ms
(sqrt (+ (* x x) (* y y)))

simplify71.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05792358
124292169
250012080

prune392.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.2b
(/ 1 (+ (* x x) (* y y)))
0.2b
(/ 1 (* (- x y) (+ x y)))
23.0b
(/ (/ 1 (+ (* x x) (* y y))) (/ 1 (* (- x y) (+ x y))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
429×times-frac
171×associate-/r/
158×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
102×add-exp-log
69×flip3-+ flip-+
68×frac-times
64×div-exp
51×flip3-- flip--
35×div-inv
34×associate-*r/ associate-*l/
32×add-cbrt-cube
21×associate-/l*
19×associate-/r*
18×rec-exp 1-exp
16×cbrt-undiv
15×prod-exp
8×pow1
6×add-log-exp
3×pow-flip frac-2neg clear-num cbrt-unprod
2×inv-pow
1×+-commutative pow-prod-down sum-log associate-/l/
Counts
4 → 381
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
5.0ms
(/ 1 (+ (* x x) (* y y)))
16.0ms
(/ 1 (* (- x y) (+ x y)))
28.0ms
(/ (/ 1 (+ (* x x) (* y y))) (/ 1 (* (- x y) (+ x y))))

series181.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* x x) (* y y))
42.0ms
(/ 1 (+ (* x x) (* y y)))
45.0ms
(/ 1 (* (- x y) (+ x y)))
67.0ms
(/ (/ 1 (+ (* x x) (* y y))) (/ 1 (* (- x y) (+ x y))))

simplify94.0ms

Algorithm
egg-herbie
Counts
393 → 393
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
018336360
150035972

prune744.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

77% (4.6b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 20.3b

bsearch96.0ms

Steps
ItersRangePoint
7
5.6616189558876546e-164
4.661455184122338e-162
1.576932748768084e-162
9
-3.09395538785007e-162
-1.0666593843843787e-169
-2.8249914759998345e-162
11
-5.6048539391173195e+159
-9.416010498651701e+134
-9.748168832064247e+142

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02916
12916

end0.0ms

sample468.0ms

Algorithm
intervals
Results
225.0ms8000×body80valid
106.0ms8000×pre80true