Average Error: 0.0 → 0.0
Time: 4.8s
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 2019002 +o rules:numerics
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  (- (pow x 4) (pow y 4)))

Details

Time bar (total: 4.1s)Debug log

sample186.0ms

Algorithm
intervals

simplify16.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

15.0ms
(- (pow x 4) (pow y 4))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
1 → 28
Calls

1 calls. Slowest were:

6.0ms
(- (pow x 4) (pow y 4))

series56.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

56.0ms
(- (pow x 4) (pow y 4))

simplify350.0ms

Counts
27 → 31
Calls

27 calls. Slowest were:

41.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (* (sqrt (pow y 4)) (sqrt (pow y 4)))))
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))))))

prune349.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

12.4b
(sqrt (pow x 4))
12.4b
(sqrt (pow x 4))
0.2b
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (pow y 4)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
3 → 38
Calls

3 calls. Slowest were:

1.0ms
(sqrt (pow x 4))
1.0ms
(sqrt (pow x 4))
0.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (pow y 4)))

series73.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

41.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (pow y 4)))
16.0ms
(sqrt (pow x 4))
16.0ms
(sqrt (pow x 4))

simplify41.0ms

Counts
17 → 47
Calls

17 calls. Slowest were:

14.0ms
(- (pow x 4) (pow y 4))
7.0ms
(- (pow x 4) (pow y 4))
2.0ms
(sqrt (* (cbrt (pow x 4)) (cbrt (pow x 4))))

prune532.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes186.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm
intervals