Average Error: 0.2 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} + -0.5\right)\]
\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

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

Derivation

  1. Initial program 0.2

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

  3. Applied *-un-lft-identity_binary640.2

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

  4. Applied times-frac_binary640.0

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020224 
(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))