Average Error: 0.0 → 0.0
Time: 5.5s
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 2018362 +o rules:numerics
(FPCore (x y)
  :name "Radioactive exchange between two surfaces"
  (- (pow x 4) (pow y 4)))

Details

Time bar (total: 2.8s)Debug log

start553.0ms

Algorithm
intervals

setup71.0ms

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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
1 → 28
Calls

1 calls. Slowest were:

9.0ms
(- (pow x 4) (pow y 4))

series45.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

45.0ms
(- (pow x 4) (pow y 4))

simplify454.0ms

Counts
27 → 31
Calls

27 calls. Slowest were:

45.0ms
(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)))))
35.0ms
(fma (sqrt (pow x 4)) (sqrt (pow x 4)) (- (* (sqrt (pow y 4)) (sqrt (pow y 4)))))
32.0ms
(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)))))

prune374.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

13.3b
(sqrt (pow y 4))
13.3b
(sqrt (pow y 4))
13.1b
(sqrt (pow x 4))
13.1b
(sqrt (pow x 4))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
4 → 56
Calls

4 calls. Slowest were:

2.0ms
(sqrt (pow y 4))
2.0ms
(sqrt (pow y 4))
2.0ms
(sqrt (pow x 4))

series67.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

17.0ms
(sqrt (pow y 4))
17.0ms
(sqrt (pow x 4))
17.0ms
(sqrt (pow x 4))
17.0ms
(sqrt (pow y 4))

simplify48.0ms

Counts
28 → 68
Calls

28 calls. Slowest were:

5.0ms
(sqrt (* (cbrt (pow x 4)) (cbrt (pow x 4))))
4.0ms
(sqrt (* (cbrt (pow y 4)) (cbrt (pow y 4))))
4.0ms
(sqrt (* (cbrt (pow y 4)) (cbrt (pow y 4))))

prune900.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes200.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms