Details

Time bar (total: 1.8m)

sample38.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
11.0ms256×pre80true

simplify328.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
328.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
6×add-cbrt-cube add-exp-log
4×frac-times flip3-+ flip-+
3×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac flip3-- add-cube-cbrt flip--
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/r/
1×pow1 clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 div-inv associate-/l* add-log-exp
Counts
1 → 32
Calls
1 calls:
Slowest
21.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series85.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
85.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify3.4s

Counts
27 → 35
Calls
27 calls:
Slowest
494.0ms
(/ (* (* (* (- x y) (+ x y)) (* (- x y) (+ x y))) (* (- x y) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
397.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
352.0ms
(/ (* (* (* (- x y) (- x y)) (- x y)) (* (* (+ x y) (+ x y)) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
327.0ms
(+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))
292.0ms
(* (- (pow x 3) (pow y 3)) (+ x y))

prune307.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize1.0ms

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

prune8.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
160×*-un-lft-identity
116×add-sqr-sqrt
78×add-cube-cbrt
22×associate-/r* distribute-lft-out
19×distribute-lft-out-- difference-of-squares
15×associate-/r/
9×add-cbrt-cube add-exp-log
8×flip3-+ flip-+ div-inv associate-/l*
4×cbrt-undiv div-exp associate-/l/
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×flip3-- div-sub flip--
Counts
2 → 168
Calls
2 calls:
Slowest
38.0ms
(/ (+ (* x x) (* y y)) (+ x y))
37.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(/ (+ (* x x) (* y y)) (+ x y))
83.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))

simplify22.5s

Counts
251 → 174
Calls
251 calls:
Slowest
685.0ms
(/ (+ (sqrt x) (sqrt y)) (/ (+ (* x x) (* y y)) (+ (pow x 3) (pow y 3))))
498.0ms
(/ (* (cbrt (- x y)) (cbrt (- x y))) (/ (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (* (cbrt (+ x y)) (cbrt (+ x y)))))
391.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (/ (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))) (* (* (+ x y) (+ x y)) (+ x y))))
374.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
364.0ms
(/ (- x y) (/ (cbrt (+ (* x x) (* y y))) (+ x y)))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (+ (* x x) (* y y)))
19.5b
(sqrt (+ (* x x) (* y y)))
0.2b
(* (/ 1 (sqrt (+ (* x x) (* y y)))) (/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
0.0b
(/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
623×times-frac
508×*-un-lft-identity
443×add-sqr-sqrt
246×add-cube-cbrt
160×sqrt-prod
155×associate-*r*
66×distribute-lft-out
61×distribute-lft-out-- difference-of-squares
48×add-exp-log
30×associate-/r* add-cbrt-cube
26×associate-/r/
24×associate-*l*
21×div-exp
20×unswap-sqr
14×flip3-+ flip-+ div-inv
12×cbrt-undiv prod-exp
8×pow1
6×sqrt-div cbrt-unprod
5×associate-/l*
4×insert-posit16 add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 466
Calls
4 calls:
Slowest
88.0ms
(* (/ 1 (sqrt (+ (* x x) (* y y)))) (/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
22.0ms
(/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
6.0ms
(sqrt (+ (* x x) (* y y)))
6.0ms
(sqrt (+ (* x x) (* y y)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y)))
110.0ms
(* (/ 1 (sqrt (+ (* x x) (* y y)))) (/ (- x y) (/ (sqrt (+ (* x x) (* y y))) (+ x y))))
51.0ms
(sqrt (+ (* x x) (* y y)))
50.0ms
(sqrt (+ (* x x) (* y y)))

simplify1.2m

Counts
607 → 478
Calls
607 calls:
Slowest
667.0ms
(/ (- x y) (/ (sqrt (sqrt (+ (* x x) (* y y)))) (+ x y)))
665.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y))))) (/ (* (* (- x y) (- x y)) (- x y)) (/ (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (* (* (+ x y) (+ x y)) (+ x y)))))
615.0ms
(/ (- (sqrt x) (sqrt y)) (/ (sqrt (sqrt (+ (* x x) (* y y)))) (+ x y)))
575.0ms
(* (* (* (/ 1 (sqrt (+ (* x x) (* y y)))) (/ 1 (sqrt (+ (* x x) (* y y))))) (/ 1 (sqrt (+ (* x x) (* y y))))) (/ (* (* (- x y) (- x y)) (- x y)) (/ (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (* (* (+ x y) (+ x y)) (+ x y)))))
519.0ms
(+ (- (log 1) (log (sqrt (+ (* x x) (* y y))))) (- (log (- x y)) (log (/ (sqrt (+ (* x x) (* y y))) (+ x y)))))

prune4.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes99.0ms

Accuracy

76.2% (4.7b remaining)

Error of 5.2b against oracle of 0.5b and baseline of 20.1b

bsearch99.0ms

end0.0ms

sample1.0s

Algorithm
intervals
Results
662.0ms8000×body80valid
218.0ms8000×pre80true