Average Error: 0.0 → 0.0
Time: 1.3min
Precision: binary64
Cost: 448
\[x \cdot y - z \cdot t\]
↓
\[x \cdot y - z \cdot t\]
x \cdot y - z \cdot t
↓
x \cdot y - z \cdot t
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
↓
(FPCore (x y z t) :precision binary64 (- (* x y) (* z t)))
double code(double x, double y, double z, double t) {
	return (x * y) - (z * t);
}
↓
double code(double x, double y, double z, double t) {
	return (x * y) - (z * t);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error16.2
Cost1361
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.6469980270730156 \cdot 10^{+53} \lor \neg \left(x \cdot y \leq -1.1236814514435829 \cdot 10^{-103} \lor \neg \left(x \cdot y \leq -3.941334016551552 \cdot 10^{-128}\right) \land x \cdot y \leq 2.2242411706673505 \cdot 10^{-26}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-z \cdot t\\ \end{array}\]
Alternative 2
Error30.8
Cost192
\[x \cdot y\]
Alternative 3
Error61.1
Cost64
\[0\]
Alternative 4
Error61.7
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 0.0

    \[x \cdot y - z \cdot t\]
  2. Using strategy rm

  3. Applied flip--_binary64_823727.3

    \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{x \cdot y + z \cdot t}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary64_826227.3

    \[\leadsto \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{\color{blue}{1 \cdot \left(x \cdot y + z \cdot t\right)}}\]

  6. Applied *-un-lft-identity_binary64_826227.3

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)\right)}}{1 \cdot \left(x \cdot y + z \cdot t\right)}\]

  7. Applied times-frac_binary64_826827.3

    \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{x \cdot y + z \cdot t}}\]

  8. Simplified27.3

    \[\leadsto \color{blue}{1} \cdot \frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{x \cdot y + z \cdot t}\]

  9. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\left(1 \cdot \left(x \cdot y - z \cdot t\right)\right)}\]
  10. Using strategy rm

  11. Applied pow1_binary64_83230.0

    \[\leadsto 1 \cdot \left(1 \cdot \color{blue}{{\left(x \cdot y - z \cdot t\right)}^{1}}\right)\]

  12. Simplified0.0

    \[\leadsto \color{blue}{x \cdot y - z \cdot t}\]

  13. Final simplification0.0

    \[\leadsto x \cdot y - z \cdot t\]

Reproduce

herbie shell --seed 2021040 
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))