Average Error: 62.0 → 62.0
Time: 2.2s
Precision: 64
Internal Precision: 128
\[\frac{x - lo}{hi - lo}\]
↓
\[0\]

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Taylor expanded around 0 62.0

    \[\leadsto \color{blue}{0}\]

  3. Final simplification62.0

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))

Details

Time bar (total: 2.0s)Debug log

sample44.0ms

Algorithm
intervals

simplify15.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

15.0ms
(/ (- x lo) (- hi lo))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.0b

localize18.0ms

Local error

Found 1 expressions with local error:

62.0b
(/ (- x lo) (- hi lo))

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 34
Calls

1 calls. Slowest were:

6.0ms
(/ (- x lo) (- hi lo))

series59.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

59.0ms
(/ (- x lo) (- hi lo))

simplify806.0ms

Counts
33 → 37
Calls

33 calls. Slowest were:

505.0ms
(/ (* (* (- x lo) (- x lo)) (- x lo)) (* (* (- hi lo) (- hi lo)) (- hi lo)))
33.0ms
(/ (* (cbrt (- x lo)) (cbrt (- x lo))) 1)
22.0ms
(- (* x x) (* lo lo))

prune288.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.0b

localize1.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune4.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 62.0b

end0.0ms

sample753.0ms

Algorithm
intervals