Details

Time bar (total: 5.5s)

sample22.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×pre80true

simplify71.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0236
1526
21176
32406
44786
59476
618446
750016

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
1 → 33
Calls
1 calls:
12.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series65.0ms

Counts
1 → 3
Calls
1 calls:
65.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify44.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0279306
11480261
25001254

prune91.0ms

Filtered
36 candidates to 30 candidates (83.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (/ (hypot x y) (+ x y)))
0.0b
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
0.0b
(/ (hypot x y) (+ x y))
17.3b
(sqrt (+ (* x x) (* y y)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
1794×times-frac
1230×*-un-lft-identity
977×add-sqr-sqrt
686×add-cube-cbrt
291×sqrt-prod
145×distribute-lft-out-- difference-of-squares
127×distribute-lft-out
103×associate-/l*
94×associate-/r/
51×div-inv
44×flip3-+ flip-+
28×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num associate-/l/
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- hypot-def
Counts
4 → 879
Calls
4 calls:
20.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
46.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
8.0ms
(/ (hypot x y) (+ x y))
4.0ms
(sqrt (+ (* x x) (* y y)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
136.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (sqrt (+ (* x x) (* y y))))
96.0ms
(/ (hypot x y) (+ x y))
40.0ms
(sqrt (+ (* x x) (* y y)))

simplify175.0ms

Algorithm
egg-herbie
Counts
891 → 891
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0227216143
1500114520

prune1.6s

Filtered
891 candidates to 460 candidates (51.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
569×times-frac
411×*-un-lft-identity
307×add-sqr-sqrt
197×add-cube-cbrt
103×associate-/l*
55×distribute-lft-out-- difference-of-squares
52×distribute-lft-out
40×add-exp-log
37×associate-/r/
31×add-cbrt-cube
23×associate-/r*
22×div-exp
21×div-inv
17×flip3-+ flip-+
16×cbrt-undiv
6×prod-exp
3×pow1 expm1-log1p-u frac-2neg 1-exp div-sub clear-num cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
1×flip3-- flip--
Counts
3 → 388
Calls
3 calls:
16.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
37.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (* 1 (hypot x y)))
5.0ms
(/ (hypot x y) (+ x y))

series282.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(/ (- x y) (/ (hypot x y) (+ x y)))
94.0ms
(/ (/ (- x y) (/ (hypot x y) (+ x y))) (* 1 (hypot x y)))
97.0ms
(/ (hypot x y) (+ x y))

simplify67.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012354353
150014153

prune782.0ms

Filtered
397 candidates to 258 candidates (65.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt (hypot x y)))
0.3b
(* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))
0.3b
(* (/ 1 (sqrt (hypot x y))) (/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))))
0.4b
(/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log
78×add-sqr-sqrt
76×times-frac
72×*-un-lft-identity
52×add-cube-cbrt add-cbrt-cube
40×associate-*r*
36×sqrt-prod
31×div-exp
28×prod-exp
25×associate-*l*
18×cbrt-undiv
16×cbrt-unprod
10×pow1
8×associate-/l* unswap-sqr
7×associate-/r*
6×distribute-lft-out
5×rec-exp 1-exp div-inv
4×expm1-log1p-u associate-*r/ associate-/r/ log1p-expm1-u add-log-exp
3×pow-flip distribute-lft-out-- difference-of-squares
2×frac-2neg pow-prod-down clear-num *-commutative associate-/l/
1×frac-times flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub associate-*l/ flip-- flip-+ inv-pow
Counts
4 → 207
Calls
4 calls:
3.0ms
(/ 1 (sqrt (hypot x y)))
22.0ms
(* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))
41.0ms
(* (/ 1 (sqrt (hypot x y))) (/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))))
14.0ms
(/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ 1 (sqrt (hypot x y)))
106.0ms
(* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))
96.0ms
(* (/ 1 (sqrt (hypot x y))) (/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y)))))
158.0ms
(/ (- x y) (* (hypot x y) (/ (sqrt (hypot x y)) (+ x y))))

simplify109.0ms

Algorithm
egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08592348
147931886
250011882

prune409.0ms

Filtered
219 candidates to 130 candidates (59.4%)
Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0148
1168
2168

end0.0ms

sample485.0ms

Algorithm
intervals
Results
232.0ms8000×body80valid
108.0ms8000×pre80true