Details

Time bar (total: 19.1s)

sample46.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
10.0ms256×pre80true

simplify4.5s

Counts
1 → 1
Iterations
IterNodes
done5004
71738
6803
5457
4220
3107
250
123
09

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
19.6b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-cbrt-cube add-exp-log
5×flip3-+ flip-+
4×add-sqr-sqrt frac-times *-un-lft-identity add-cube-cbrt add-log-exp
3×associate-/r* times-frac flip3-- flip--
2×expm1-log1p-u pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u
1×+-commutative clear-num sum-log fma-def frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
2 → 49
Calls
2 calls:
20.0ms
(+ (* x x) (* y y))
46.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series157.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(+ (* x x) (* y y))
113.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.6s

Counts
55 → 55
Iterations
IterNodes
done5006
21458
1338
097

prune260.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

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)))))
18.8b
(sqrt (+ (* x x) (* y y)))
18.8b
(sqrt (+ (* x x) (* y y)))

rewrite130.0ms

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-cbrt-cube add-exp-log
13×distribute-lft-out
10×sqrt-div
9×unswap-sqr
8×pow1
6×associate-/r* flip3-+ associate-/r/ flip-+ distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 189
Calls
4 calls:
21.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
79.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
13.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
84.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
40.0ms
(sqrt (+ (* x x) (* y y)))
55.0ms
(sqrt (+ (* x x) (* y y)))

simplify2.2s

Counts
201 → 201
Iterations
IterNodes
done5004
22280
1611
0201

prune813.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
61×add-sqr-sqrt
51×times-frac
48×associate-*r*
40×add-cube-cbrt
21×add-cbrt-cube add-exp-log
15×associate-*l*
13×distribute-lft-out
10×pow1
6×frac-times flip3-- associate-*l/ prod-exp cbrt-unprod flip-- unswap-sqr
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×associate-/r* pow-prod-down associate-*r/ *-commutative distribute-lft-out-- difference-of-squares
2×associate-/l/
1×clear-num frac-2neg flip3-+ flip-+
Counts
4 → 168
Calls
4 calls:
15.0ms
(/ (+ x y) (hypot x y))
57.0ms
(* (- x y) (/ (+ x y) (hypot x y)))
55.0ms
(* (- x y) (/ (+ x y) (hypot x y)))
57.0ms
(* (- x y) (/ (+ x y) (hypot x y)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (+ x y) (hypot x y))
133.0ms
(* (- x y) (/ (+ x y) (hypot x y)))
124.0ms
(* (- x y) (/ (+ x y) (hypot x y)))
114.0ms
(* (- x y) (/ (+ x y) (hypot x y)))

simplify1.3s

Counts
180 → 180
Iterations
IterNodes
done5002
21136
1323
0119

prune986.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
0.6b
(cbrt (hypot x y))
0.6b
(cbrt (hypot x y))
0.6b
(cbrt (hypot x y))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
9.0ms
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
1.0ms
(cbrt (hypot x y))
1.0ms
(cbrt (hypot x y))
2.0ms
(cbrt (hypot x y))

series696.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (cbrt (hypot x y)) (cbrt (hypot x y)))
154.0ms
(cbrt (hypot x y))
177.0ms
(cbrt (hypot x y))
163.0ms
(cbrt (hypot x y))

simplify2.8s

Counts
97 → 97
Iterations
IterNodes
done5004
43850
31079
2417
1168
080

prune719.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done14
114
011

end0.0ms

sample1.6s

Algorithm
intervals
Results
716.0ms8000×pre80true
659.0ms8000×body80valid