Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
Internal Precision: 128
\[{x}^{4} - {y}^{4}\]
↓
\[{x}^{4} - {y}^{4}\]

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[{x}^{4} - {y}^{4}\]

  2. Final simplification0.0

    \[\leadsto {x}^{4} - {y}^{4}\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  (- (pow x 4) (pow y 4)))

Details

Time bar (total: 5.7s)Debug log

sample129.0ms

Algorithm
intervals

simplify10.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

10.0ms
(- (pow x 4) (pow y 4))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (pow x 4) (pow y 4))

rewrite13.0ms

Algorithm
rewrite-expression-head
Counts
1 → 28
Calls

1 calls. Slowest were:

10.0ms
(- (pow x 4) (pow y 4))

series71.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

71.0ms
(- (pow x 4) (pow y 4))

simplify433.0ms

Counts
27 → 31
Calls

27 calls. Slowest were:

34.0ms
(fma 1 (pow x 4) (- (* (pow y 4) 1)))
33.0ms
(fma (- (cbrt (pow y 4))) (* (cbrt (pow y 4)) (cbrt (pow y 4))) (* (cbrt (pow y 4)) (* (cbrt (pow y 4)) (cbrt (pow y 4)))))
29.0ms
(fma (* (cbrt (pow x 4)) (cbrt (pow x 4))) (cbrt (pow x 4)) (- (* (cbrt (pow y 4)) (* (cbrt (pow y 4)) (cbrt (pow y 4))))))

prune279.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

25.5b
(cbrt (pow x 4))
25.5b
(cbrt (pow x 4))
25.5b
(cbrt (pow x 4))
0.2b
(* (cbrt (pow x 4)) (cbrt (pow x 4)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

8.0ms
(* (cbrt (pow x 4)) (cbrt (pow x 4)))
0.0ms
(cbrt (pow x 4))
0.0ms
(cbrt (pow x 4))

series1.1s

Counts
4 → 12
Calls

4 calls. Slowest were:

315.0ms
(cbrt (pow x 4))
266.0ms
(cbrt (pow x 4))
240.0ms
(cbrt (pow x 4))
239.0ms
(* (cbrt (pow x 4)) (cbrt (pow x 4)))

simplify53.0ms

Counts
41 → 81
Calls

41 calls. Slowest were:

2.0ms
(+ (log (cbrt (pow x 4))) (log (cbrt (pow x 4))))
2.0ms
(cbrt (cbrt (pow x 4)))
2.0ms
(sqrt (cbrt (pow x 4)))

prune951.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes172.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals