Details

Time bar (total: 15.5s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×pre80true

simplify5.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
0915
12314
25114
39714
420614
540214
673314
7125814
8335314
done500014

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.0b

localize8.0ms

Local error

Found 1 expressions with local error:

21.1b
(/ (* (- 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 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)))

series64.0ms

Counts
1 → 3
Calls
1 calls:
64.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify735.0ms

Counts
36 → 36
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
081692
1279613
21179519
done5001519

prune93.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
20×add-exp-log add-cbrt-cube
19×associate-*l*
16×associate-*r*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp unswap-sqr
2×frac-2neg clear-num
1×frac-times hypot-udef flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 146
Calls
4 calls:
0.0ms
(hypot x y)
10.0ms
(/ (+ x y) (hypot x y))
28.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
8.0ms
(/ (- x y) (hypot x y))

series310.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(hypot x y)
88.0ms
(/ (+ x y) (hypot x y))
89.0ms
(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
88.0ms
(/ (- x y) (hypot x y))

simplify1.0s

Counts
158 → 158
Iterations

Useful iterations: 2 (332.0ms)

IterNodesCost
01722247
14892185
216931971
done50011971

prune327.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
55×*-un-lft-identity
54×add-exp-log
49×times-frac
39×add-cube-cbrt
34×add-cbrt-cube
22×prod-exp
20×associate-*l*
17×associate-*r*
14×div-exp
12×pow1 cbrt-unprod
11×frac-times
8×cbrt-undiv associate-*l/ associate-/l*
7×associate-*r/ distribute-lft-out-- difference-of-squares
6×flip3-+ associate-/r* flip-+
4×expm1-log1p-u rec-exp 1-exp pow-prod-down log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num *-commutative associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- pow-flip distribute-lft-in div-sub un-div-inv flip-- distribute-lft-out inv-pow
Counts
4 → 176
Calls
4 calls:
2.0ms
(/ 1 (hypot x y))
22.0ms
(* (/ (- x y) (hypot x y)) (+ x y))
8.0ms
(/ (- x y) (hypot x y))
33.0ms
(* (* (/ (- x y) (hypot x y)) (+ x y)) (/ 1 (hypot x y)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (hypot x y))
86.0ms
(* (/ (- x y) (hypot x y)) (+ x y))
89.0ms
(/ (- x y) (hypot x y))
91.0ms
(* (* (/ (- x y) (hypot x y)) (+ x y)) (/ 1 (hypot x y)))

simplify1.7s

Counts
188 → 188
Iterations

Useful iterations: 2 (576.0ms)

IterNodesCost
02252827
17162619
225732243
done50002243

prune348.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x y) (hypot x y))
0.0b
(* (/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y))) (/ (+ x y) (hypot x y)))
0.0b
(/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y)))
0.5b
(/ (- x y) (sqrt (hypot x y)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
879×times-frac
625×add-sqr-sqrt
584×*-un-lft-identity
430×sqrt-prod
400×add-cube-cbrt
208×associate-*l*
85×distribute-lft-out-- difference-of-squares
43×associate-/l*
34×add-exp-log add-cbrt-cube
18×div-inv
16×associate-*r*
15×associate-/r*
14×cbrt-undiv div-exp unswap-sqr
7×distribute-lft-out
6×pow1 prod-exp cbrt-unprod
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg div-sub clear-num
1×frac-times flip3-- flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 619
Calls
4 calls:
7.0ms
(/ (+ x y) (hypot x y))
113.0ms
(* (/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y))) (/ (+ x y) (hypot x y)))
18.0ms
(/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y)))
9.0ms
(/ (- x y) (sqrt (hypot x y)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(/ (+ x y) (hypot x y))
88.0ms
(* (/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y))) (/ (+ x y) (hypot x y)))
87.0ms
(/ (/ (- x y) (sqrt (hypot x y))) (sqrt (hypot x y)))
95.0ms
(/ (- x y) (sqrt (hypot x y)))

simplify2.6s

Counts
631 → 631
Iterations

Useful iterations: 2 (1.8s)

IterNodesCost
050715552
1148714158
2487312866
done500012866

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11015
done1015

end0.0ms

sample479.0ms

Algorithm
intervals
Results
226.0ms8000×body80valid
107.0ms8000×pre80true