Details

Time bar (total: 36.6s)

sample62.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
13.0ms256×pre80true

simplify191.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
191.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize41.0ms

Local error

Found 2 expressions with local error:

20.8b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
0.0b
(+ (* x x) (* y y))

rewrite64.0ms

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×expm1-log1p-u pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u
1×+-commutative clear-num sum-log fma-def frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
Counts
2 → 49
Calls
2 calls:
Slowest
47.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
15.0ms
(+ (* x x) (* y y))

series139.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
42.0ms
(+ (* x x) (* y y))

simplify4.5s

Counts
31 → 55
Calls
31 calls:
Slowest
597.0ms
(/ (* (* (* (- x y) (+ x y)) (* (- x y) (+ x y))) (* (- x y) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
539.0ms
(/ (* (* (* (- 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
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
493.0ms
(+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))
346.0ms
(* (- (pow x 3) (pow y 3)) (+ x y))

prune462.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

20.8b
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
0.3b
(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
0.0b
(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0b
(+ (* x x) (* y y))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×associate-/l/
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
5×flip3-+ flip-+ log1p-expm1-u
4×expm1-log1p-u frac-times pow1 insert-posit16
3×associate-/r* times-frac flip3-- flip--
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/r/
1×+-commutative log1p-udef expm1-log1p clear-num sum-log fma-def frac-2neg prod-exp log1p-expm1 cbrt-unprod div-inv associate-/l* expm1-udef
Counts
4 → 73
Calls
4 calls:
Slowest
43.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
15.0ms
(+ (* x x) (* y y))
1.0ms
(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
0.0ms
(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(log1p (expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
152.0ms
(expm1 (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
100.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
32.0ms
(+ (* x x) (* y y))

simplify4.5s

Counts
39 → 85
Calls
39 calls:
Slowest
619.0ms
(/ (* (* (* (- x y) (+ x y)) (* (- x y) (+ x y))) (* (- x y) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
550.0ms
(/ (* (* (* (- x y) (- x y)) (- x y)) (* (* (+ x y) (+ x y)) (+ x y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))))
429.0ms
(* (- (pow x 3) (pow y 3)) (- (* x x) (* y y)))
428.0ms
(+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))
324.0ms
(* (- x y) (+ (pow x 3) (pow y 3)))

prune844.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

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

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 3 expressions with local error:

20.9b
(/ (+ (* x x) (* y y)) (+ x y))
0.0b
(+ (* x x) (* y y))
0.0b
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))

rewrite90.0ms

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
39.0ms
(/ (+ (* x x) (* y y)) (+ x y))
36.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
8.0ms
(+ (* x x) (* y y))

series238.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
99.0ms
(/ (- x y) (/ (+ (* x x) (* y y)) (+ x y)))
91.0ms
(/ (+ (* x x) (* y y)) (+ x y))
48.0ms
(+ (* x x) (* y y))

simplify21.2s

Counts
255 → 196
Calls
255 calls:
Slowest
599.0ms
(/ 1 (/ (+ (* x x) (* y y)) (+ (pow x 3) (pow y 3))))
507.0ms
(/ (* (* (- x y) (- x y)) (- x y)) (/ (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))) (* (* (+ x y) (+ x y)) (+ x y))))
477.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
412.0ms
(/ 1 (/ (+ (* x x) (* y y)) (- (* x x) (* y y))))
355.0ms
(/ 1 (/ (+ (* x x) (* y y)) (+ (pow x 3) (pow y 3))))

prune1.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes167.0ms

Accuracy

77.2% (4.4b remaining)

Error of 5.0b against oracle of 0.5b and baseline of 20.0b

bsearch172.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
994.0ms8000×body80valid
364.0ms8000×pre80true