Average Error: 0.0 → 0.0
Time: 6.8s
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. Initial simplification0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  (- (pow x 4) (pow y 4)))

Details

Time bar (total: 4.0s)Debug log

start294.0ms

Algorithm
intervals

setup49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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))

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(- (pow x 4) (pow y 4))

simplify339.0ms

Counts
27 → 31
Calls

27 calls. Slowest were:

25.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (* (pow y 4) 1)))
24.0ms
(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)))))
20.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (* (sqrt (pow y 4)) (sqrt (pow y 4)))))

prune312.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

20.5b
(cbrt (pow x 4))
20.5b
(cbrt (pow x 4))
20.5b
(cbrt (pow x 4))
0.3b
(* (cbrt (pow x 4)) (cbrt (pow x 4)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 69
Calls

4 calls. Slowest were:

5.0ms
(* (cbrt (pow x 4)) (cbrt (pow x 4)))
1.0ms
(cbrt (pow x 4))
0.0ms
(cbrt (pow x 4))

series1.5s

Counts
4 → 12
Calls

4 calls. Slowest were:

677.0ms
(* (cbrt (pow x 4)) (cbrt (pow x 4)))
319.0ms
(cbrt (pow x 4))
255.0ms
(cbrt (pow x 4))
225.0ms
(cbrt (pow x 4))

simplify92.0ms

Counts
41 → 81
Calls

41 calls. Slowest were:

8.0ms
(pow (/ 1 x) -4/3)
4.0ms
(pow (/ 1 x) -4/3)
4.0ms
(pow (/ 1 x) -4/3)

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes207.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms