Details

Time bar (total: 1.1m)

sample42.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
8.0ms256×pre80true

simplify370.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
370.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize30.0ms

Local error

Found 3 expressions with local error:

20.1b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
0.0b
(+ (* x x) (* y y))
0.0b
(* (- x y) (+ x y))

rewrite514.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
10×add-cbrt-cube add-exp-log
8×frac-times flip3-+ flip-+ associate-/l/
7×add-cube-cbrt
6×flip3-- flip--
5×pow1 associate-*l* add-log-exp
4×associate-*r* associate-*l/ associate-*r/
3×associate-/r* times-frac insert-posit16
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
1×distribute-rgt-in +-commutative clear-num sum-log frac-2neg distribute-lft-in pow-prod-down *-commutative div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 76
Calls
3 calls:
Slowest
453.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
45.0ms
(* (- x y) (+ x y))
14.0ms
(+ (* x x) (* y y))

series192.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
95.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
59.0ms
(* (- x y) (+ x y))
38.0ms
(+ (* x x) (* y y))

simplify6.5s

Counts
60 → 85
Calls
60 calls:
Slowest
648.0ms
(/ (* (* (* (- x y) (+ x y)) (* (- x y) (+ x y))) (* (- x y) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
503.0ms
(/ (* (* (* (- x y) (- x y)) (- x y)) (* (* (+ x y) (+ x y)) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
484.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
465.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
346.0ms
(+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))

prune685.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 3 expressions with local error:

19.7b
(/ (+ (* x x) (* y y)) (+ x y))
0.0b
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
0.0b
(+ (* x x) (* y y))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
161×*-un-lft-identity
117×add-sqr-sqrt
79×add-cube-cbrt
22×associate-/r* distribute-lft-out
19×distribute-lft-out-- difference-of-squares
15×associate-/r/
10×add-cbrt-cube add-exp-log
9×flip3-+ flip-+
8×div-inv associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1 insert-posit16
2×clear-num frac-2neg
1×+-commutative sum-log flip3-- div-sub flip--
Counts
3 → 180
Calls
3 calls:
Slowest
46.0ms
(/ (+ (* x x) (* y y)) (+ x y))
20.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
11.0ms
(+ (* x x) (* y y))

series228.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
88.0ms
(/ (+ (* x x) (* y y)) (+ x y))
41.0ms
(+ (* x x) (* y y))

simplify23.4s

Counts
255 → 189
Calls
255 calls:
Slowest
480.0ms
(/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (* (cbrt (+ x y)) (cbrt (+ x y)))))
454.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
399.0ms
(/ (+ (sqrt x) (sqrt y)) (/ (+ (* x x) (* y y)) (+ (pow x 3) (pow y 3))))
392.0ms
(/ (- (sqrt x) (sqrt y)) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
372.0ms
(/ (+ (sqrt x) (sqrt y)) (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
372×times-frac
288×*-un-lft-identity
198×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
49×distribute-lft-out
36×associate-/r*
22×sqrt-div
17×associate-/r/
12×flip3-+ flip-+
11×add-cbrt-cube add-exp-log
10×associate-/l*
9×div-inv
6×pow1
4×cbrt-undiv div-exp insert-posit16 add-log-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 317
Calls
4 calls:
Slowest
43.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
32.0ms
(/ (sqrt (+ (* x x) (* y y))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
12.0ms
(sqrt (+ (* x x) (* y y)))
11.0ms
(sqrt (+ (* x x) (* y y)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
91.0ms
(/ (sqrt (+ (* x x) (* y y))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
66.0ms
(sqrt (+ (* x x) (* y y)))
61.0ms
(sqrt (+ (* x x) (* y y)))

simplify28.9s

Counts
490 → 329
Calls
490 calls:
Slowest
681.0ms
(sqrt (+ (pow (* x x) 3) (pow (* y y) 3)))
373.0ms
(/ (sqrt (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y))))) (/ (+ x y) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y))))))
368.0ms
(/ (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (* (* (/ (+ x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y))))) (/ (+ x y) (sqrt (+ (* x x) (* y y))))))
352.0ms
(/ (sqrt (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3)))))
348.0ms
(/ (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (/ (+ x y) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3)))))

prune3.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize0.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes129.0ms

Accuracy

76.3% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 20.4b

bsearch147.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.4s8000×body80valid
302.0ms8000×pre80true