Details

Time bar (total: 1.2m)

sample64.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
14.0ms256×pre80true

simplify182.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
181.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize36.0ms

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))

rewrite82.0ms

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×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
1×distribute-rgt-in +-commutative clear-num sum-log fma-def 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 → 83
Calls
3 calls:
Slowest
44.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
25.0ms
(* (- x y) (+ x y))
12.0ms
(+ (* x x) (* y y))

series169.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
71.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
60.0ms
(* (- x y) (+ x y))
38.0ms
(+ (* x x) (* y y))

simplify7.6s

Counts
60 → 92
Calls
60 calls:
Slowest
696.0ms
(/ (* (* (* (- x y) (+ x y)) (* (- x y) (+ x y))) (* (- x y) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
515.0ms
(/ (* (* (* (- x y) (- x y)) (- x y)) (* (* (+ x y) (+ x y)) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
515.0ms
(+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))
500.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
499.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))

prune766.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize24.0ms

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))

rewrite82.0ms

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×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×clear-num frac-2neg
1×+-commutative sum-log fma-def flip3-- div-sub flip--
Counts
3 → 187
Calls
3 calls:
Slowest
42.0ms
(/ (+ (* x x) (* y y)) (+ x y))
29.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
7.0ms
(+ (* x x) (* y y))

series209.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
81.0ms
(/ (+ (* x x) (* y y)) (+ x y))
79.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
48.0ms
(+ (* x x) (* y y))

simplify21.1s

Counts
255 → 196
Calls
255 calls:
Slowest
486.0ms
(/ (+ (sqrt x) (sqrt y)) (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
484.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
439.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
432.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (/ (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))) (* (* (+ x y) (+ x y)) (+ x y))))
412.0ms
(/ (+ (sqrt x) (sqrt y)) (/ (+ (* x x) (* y y)) (+ (pow x 3) (pow y 3))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize54.0ms

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)))))

rewrite101.0ms

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×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 hypot-def
Counts
4 → 327
Calls
4 calls:
Slowest
35.0ms
(/ (sqrt (+ (* x x) (* y y))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
29.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(/ (+ x y) (sqrt (+ (* x x) (* y y))))
84.0ms
(/ (sqrt (+ (* x x) (* y y))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
45.0ms
(sqrt (+ (* x x) (* y y)))
45.0ms
(sqrt (+ (* x x) (* y y)))

simplify27.6s

Counts
490 → 339
Calls
490 calls:
Slowest
514.0ms
(/ (* (* (+ x y) (+ x y)) (+ x y)) (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))))
418.0ms
(/ 1 (/ (+ x y) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3)))))
416.0ms
(/ (* (* (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))))))
381.0ms
(/ (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (/ (+ x y) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y))))))
366.0ms
(/ 1 (/ (+ x y) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y))))))

prune3.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
32×add-sqr-sqrt
30×times-frac
23×add-cube-cbrt
19×add-cbrt-cube add-exp-log
18×associate-*r*
8×associate-/l*
7×distribute-lft-out
6×cbrt-undiv div-exp
5×pow1 associate-/r* associate-/r/
4×prod-exp cbrt-unprod
3×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg flip3-+ associate-*r/ flip-+ distribute-lft-out-- difference-of-squares unswap-sqr associate-/l/
1×flip3-- div-sub pow-prod-down *-commutative flip--
Counts
3 → 110
Calls
3 calls:
Slowest
26.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
25.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
12.0ms
(/ (hypot x y) (+ x y))

series363.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
122.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
121.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
120.0ms
(/ (hypot x y) (+ x y))

simplify4.0s

Counts
97 → 119
Calls
97 calls:
Slowest
425.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (* (* (* (hypot x y) (hypot x y)) (hypot x y)) (/ (* (* (hypot x y) (hypot x y)) (hypot x y)) (* (* (+ x y) (+ x y)) (+ x y)))))
372.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (* (* (* (hypot x y) (hypot x y)) (hypot x y)) (* (* (/ (hypot x y) (+ x y)) (/ (hypot x y) (+ x y))) (/ (hypot x y) (+ x y)))))
317.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (* (* (* (hypot x y) (/ (hypot x y) (+ x y))) (* (hypot x y) (/ (hypot x y) (+ x y)))) (* (hypot x y) (/ (hypot x y) (+ x y)))))
309.0ms
(/ (* (* (hypot x y) (hypot x y)) (hypot x y)) (* (* (+ x y) (+ x y)) (+ x y)))
218.0ms
(* (* (* (hypot x y) (hypot x y)) (hypot x y)) (* (* (/ (hypot x y) (+ x y)) (/ (hypot x y) (+ x y))) (/ (hypot x y) (+ x y))))

prune960.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes491.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
909.0ms8000×body80valid
353.0ms8000×pre80true