Average Error: 0.1 → 0.0
Time: 4.6s
Precision: binary64
Cost: 576
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} + -0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} + -0.5\right)
(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))
↓
(FPCore (x y z) :precision binary64 (* 4.0 (+ (/ (- x y) z) -0.5)))
double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}
↓
double code(double x, double y, double z) {
	return 4.0 * (((x - y) / z) + -0.5);
}

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

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Alternatives

Alternative 1
Error8.8
Cost776
\[\begin{array}{l} \mathbf{if}\;y \leq -9.140876239196955 \cdot 10^{-13} \lor \neg \left(y \leq 5.225395937530882 \cdot 10^{-13}\right):\\ \;\;\;\;-4 \cdot \left(0.5 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \end{array}\]
Alternative 2
Error11.9
Cost1418
\[\begin{array}{l} \mathbf{if}\;y \leq -4.817469173696096 \cdot 10^{+107}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.153247720109581 \cdot 10^{+90}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq -3714210517111.7705 \lor \neg \left(y \leq 5.425539066150178 \cdot 10^{+41}\right):\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + 4 \cdot \frac{x}{z}\\ \end{array}\]
Alternative 3
Error15.6
Cost1090
\[\begin{array}{l} \mathbf{if}\;z \leq -6.402395957328198 \cdot 10^{+130}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 8.29131568575834 \cdot 10^{+118}:\\ \;\;\;\;4 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array}\]
Alternative 4
Error15.7
Cost1090
\[\begin{array}{l} \mathbf{if}\;z \leq -6.128557572857904 \cdot 10^{+130}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 5.092970192101209 \cdot 10^{+119}:\\ \;\;\;\;\frac{4}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array}\]
Alternative 5
Error31.0
Cost2246
\[\begin{array}{l} \mathbf{if}\;y \leq -7.489653913156995 \cdot 10^{+107}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.7876441181788666 \cdot 10^{+90}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq -32908857192073.652:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -6.194459076610972 \cdot 10^{-216}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 7.378536101424116 \cdot 10^{-235}:\\ \;\;\;\;4 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.1666383717936055 \cdot 10^{+41}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \end{array}\]
Alternative 6
Error29.7
Cost913
\[\begin{array}{l} \mathbf{if}\;y \leq -4.6932667729394494 \cdot 10^{+107} \lor \neg \left(y \leq -2.153247720109581 \cdot 10^{+90} \lor \neg \left(y \leq -11964302598769.615\right) \land y \leq 5.46615876729591 \cdot 10^{+40}\right):\\ \;\;\;\;-4 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array}\]
Alternative 7
Error36.7
Cost64
\[-2\]
Alternative 8
Error57.7
Cost64
\[-1\]
Alternative 9
Error62.4
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity_binary64_184920.1

    \[\leadsto \frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{\color{blue}{1 \cdot z}}\]

  4. Applied times-frac_binary64_184980.0

    \[\leadsto \color{blue}{\frac{4}{1} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{4} \cdot \frac{\left(x - y\right) - z \cdot 0.5}{z}\]

  6. Simplified0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x - y}{z} + -0.5\right)}\]

  7. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} + -0.5\right)}\]

  8. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x - y}{z} + -0.5\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))