Details

Time bar (total: 12.2s)

sample42.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
9.0ms256×pre80true

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5000
71661
6583
5348
4190
398
248
122
09

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

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×pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/r/ insert-posit16
1×+-commutative clear-num sum-log frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
2 → 44
Calls
2 calls:
7.0ms
(+ (* x x) (* y y))
45.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series139.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(+ (* x x) (* y y))
103.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.3s

Counts
50 → 50
Iterations
IterNodes
done5001
21553
1323
093

prune258.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

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)))

rewrite144.0ms

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×prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 179
Calls
4 calls:
19.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
103.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
12.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
99.0ms
(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
56.0ms
(sqrt (+ (* x x) (* y y)))
41.0ms
(sqrt (+ (* x x) (* y y)))

simplify2.2s

Counts
191 → 191
Iterations
IterNodes
done5002
22319
1596
0195

prune712.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
18×exp-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×log-pow
9×times-frac add-cbrt-cube add-exp-log
8×associate-/l/
7×flip3-+ flip-+ add-log-exp
6×associate-/r/
5×pow1
4×frac-times insert-posit16
3×log-prod associate-/r* flip3-- div-inv flip--
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×+-commutative clear-num sum-log frac-2neg rem-log-exp prod-exp cbrt-unprod associate-/l* rem-exp-log
Counts
4 → 84
Calls
4 calls:
28.0ms
(exp (/ (* (- x y) (+ y x)) (+ (* x x) (* y y))))
7.0ms
(+ (* x x) (* y y))
43.0ms
(log (exp (/ (* (- x y) (+ y x)) (+ (* x x) (* y y)))))
22.0ms
(/ (* (- x y) (+ y x)) (+ (* x x) (* y y)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(exp (/ (* (- x y) (+ y x)) (+ (* x x) (* y y))))
49.0ms
(+ (* x x) (* y y))
99.0ms
(log (exp (/ (* (- x y) (+ y x)) (+ (* x x) (* y y)))))
120.0ms
(/ (* (- x y) (+ y x)) (+ (* x x) (* y y)))

simplify1.4s

Counts
96 → 96
Iterations
IterNodes
done5001
21690
1380
0136

prune488.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes151.0ms

Accuracy

72.8% (5.2b remaining)

Error of 5.7b against oracle of 0.4b and baseline of 19.7b

bsearch194.0ms

Steps
ItersRangePoint
5
1.2654350453177412e-202
4.88616549423691e-202
1.2966442305400266e-202
9
1.5708857102523663e-223
3.0247758926628463e-218
2.9860065638011237e-218
8
-3.8298708653240857e-159
-3.406854034464677e-163
-1.2013518175407308e-161
9
-1.854306054422796e+154
-6.720912415933141e+146
-1.3691694056010857e+154

simplify13.0ms

Iterations
IterNodes
done36
236
135
030

end0.0ms

sample1.5s

Algorithm
intervals
Results
859.0ms8000×body80valid
377.0ms8000×pre80true