Details

Time bar (total: 10.2s)

sample57.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
8.0ms256×pre80true

simplify2.6s

Counts
1 → 1
Iterations
IterNodes
done5000
73699
6840
5403
4208
3103
248
122
09

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
15.7b
(/ (* x x) (+ (* x x) (* y y)))
28.2b
(/ (* y y) (+ (* x x) (* y y)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
10×times-frac
9×*-un-lft-identity
8×associate-/r/
7×add-cube-cbrt
6×associate-/r*
5×add-log-exp
4×cbrt-undiv flip3-+ div-exp flip-+ div-inv difference-of-squares
3×pow1 distribute-rgt-out--
2×clear-num frac-2neg prod-exp cbrt-unprod associate-/l*
1×sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
3 → 68
Calls
3 calls:
96.0ms
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
22.0ms
(/ (* x x) (+ (* x x) (* y y)))
14.0ms
(/ (* y y) (+ (* x x) (* y y)))

series246.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
82.0ms
(/ (* x x) (+ (* x x) (* y y)))
50.0ms
(/ (* y y) (+ (* x x) (* y y)))

simplify2.0s

Counts
77 → 77
Iterations
IterNodes
done5002
22706
1373
0117

prune415.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
15.7b
(/ (* x x) (+ (* x x) (* y y)))
21.3b
(sqrt (+ (* x x) (* y y)))
21.3b
(sqrt (+ (* x x) (* y y)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
99×times-frac
64×*-un-lft-identity add-cube-cbrt
54×sqrt-prod
30×swap-sqr
24×associate-*r* associate-*l*
21×add-cbrt-cube add-exp-log
13×pow1
12×sqrt-div
10×associate-/r/
9×unswap-sqr
7×flip3-+ flip-+
6×cbrt-undiv div-exp
5×prod-exp cbrt-unprod div-inv
4×add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times clear-num frac-2neg pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l*
Counts
4 → 164
Calls
4 calls:
68.0ms
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
20.0ms
(/ (* x x) (+ (* x x) (* y y)))
10.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
54.0ms
(/ (* x x) (+ (* x x) (* y y)))
49.0ms
(sqrt (+ (* x x) (* y y)))
65.0ms
(sqrt (+ (* x x) (* y y)))

simplify1.1s

Counts
176 → 176
Iterations
IterNodes
done5000
1721
0207

prune734.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune11.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 1 expressions with local error:

22.3b
(/ (- (* x x) (* y y)) (+ (* x x) (* y y)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-/l* difference-of-squares
3×associate-/r* add-cbrt-cube add-exp-log
2×associate-/r/ associate-/l/
1×pow1 cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp flip-+ div-inv flip-- add-log-exp
Counts
1 → 36
Calls
1 calls:
23.0ms
(/ (- (* x x) (* y y)) (+ (* x x) (* y y)))

series61.0ms

Counts
1 → 3
Calls
1 calls:
61.0ms
(/ (- (* x x) (* y y)) (+ (* x x) (* y y)))

simplify1.2s

Counts
39 → 39
Iterations
IterNodes
done5001
2982
1216
078

prune211.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.9b

regimes104.0ms

Accuracy

61.3% (7.5b remaining)

Error of 8.0b against oracle of 0.5b and baseline of 19.9b

bsearch58.0ms

Steps
ItersRangePoint
7
2.42011835416667e-163
8.820107011884713e-162
5.816163962969592e-162
8
-2.975188198181845e-134
-1.2050796968657376e-137
-2.9269037547224618e-134

simplify4.0ms

Iterations
IterNodes
done18
118
015

end0.0ms

sample863.0ms

Algorithm
intervals
Results
418.0ms8000×body80valid
260.0ms8000×pre80true