Average Error: 0.0 → 0.0
Time: 3.8s
Precision: binary64
Cost: 704
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{y}{z - y}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{y}{z - y}
(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))
↓
(FPCore (x y z) :precision binary64 (- (/ x (- z y)) (/ y (- z y))))
double code(double x, double y, double z) {
	return (x - y) / (z - y);
}
↓
double code(double x, double y, double z) {
	return (x / (z - y)) - (y / (z - y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{z - y} - \frac{y}{z - y}\]

Alternatives

Alternative 1
Error0.0
Cost448
\[\frac{x - y}{z - y}\]
Alternative 2
Error15.3
Cost913
\[\begin{array}{l} \mathbf{if}\;z \leq -4.133134180066263 \cdot 10^{+35} \lor \neg \left(z \leq -4.819508152852456 \cdot 10^{-16} \lor \neg \left(z \leq -1.9402093974087821 \cdot 10^{-60}\right) \land z \leq 9.292040657424431 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array}\]
Alternative 3
Error19.9
Cost1604
\[\begin{array}{l} \mathbf{if}\;y \leq -3.4107792422265796 \cdot 10^{+143}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.996952577100625 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq -8.208324847786021 \cdot 10^{-88}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.3935216354259882 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 4
Error20.2
Cost962
\[\begin{array}{l} \mathbf{if}\;y \leq -3.1439123524935136 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6224067416569235 \cdot 10^{+44}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 5
Error25.5
Cost834
\[\begin{array}{l} \mathbf{if}\;y \leq -2.2350121376181807 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.0451244861208155 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 6
Error39.6
Cost706
\[\begin{array}{l} \mathbf{if}\;y \leq -9.636344527118387 \cdot 10^{-136}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.270219332102459 \cdot 10^{-104}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 7
Error41.2
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{z - y}\]
  2. Using strategy rm

  3. Applied div-sub_binary64_178150.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \frac{x}{z - y} - \frac{y}{z - y}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))