Average Error: 2.2 → 2.2
Time: 3.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\frac{z - t}{\frac{y}{x}} + t\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\frac{z - t}{\frac{y}{x}} + t
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (z - t)) / ((double) (y / x)))) + 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

Target

Original2.2
Target2.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.2

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

  3. Applied clear-num2.4

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

  4. Applied associate-*l/2.2

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

  5. Simplified2.2

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

  6. Final simplification2.2

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

Reproduce

herbie shell --seed 2020113 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))