Average Error: 0.3 → 0.1
Time: 3.2s
Precision: binary64
Cost: 576
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{4 \cdot \left(x - z\right)}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{4 \cdot \left(x - z\right)}{y}
(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))
↓
(FPCore (x y z) :precision binary64 (+ 4.0 (/ (* 4.0 (- x z)) y)))
double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}
↓
double code(double x, double y, double z) {
	return 4.0 + ((4.0 * (x - 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

Alternatives

Alternative 1
Error0.2
Cost576
\[4 + \left(x - z\right) \cdot \frac{4}{y}\]
Alternative 2
Error9.3
Cost1041
\[\begin{array}{l} \mathbf{if}\;z \leq -4.382156838142269 \cdot 10^{+145} \lor \neg \left(z \leq -1.8241153054947625 \cdot 10^{+53} \lor \neg \left(z \leq -1955.0358215334759\right) \land z \leq 2.6003811983724558 \cdot 10^{-15}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array}\]
Alternative 3
Error9.3
Cost1041
\[\begin{array}{l} \mathbf{if}\;z \leq -4.382156838142269 \cdot 10^{+145} \lor \neg \left(z \leq -2.682279506997406 \cdot 10^{+53} \lor \neg \left(z \leq -361902.6474953381\right) \land z \leq 4.3415448511141566 \cdot 10^{-10}\right):\\ \;\;\;\;4 + z \cdot \frac{-4}{y}\\ \mathbf{else}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \end{array}\]
Alternative 4
Error18.7
Cost448
\[4 + 4 \cdot \frac{x}{y}\]
Alternative 5
Error58.2
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.3

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.2

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

  4. Applied associate-*l/_binary64_109330.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))