Average Error: 1.4 → 1.3
Time: 3.4s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{y}{\frac{z - a}{z - t}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{y}{\frac{z - a}{z - t}} + x
double code(double x, double y, double z, double t, double a) {
	return (x + (y * ((z - t) / (z - a))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((y / ((z - a) / (z - t))) + x);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  2. Simplified1.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\]
  3. Using strategy rm

  4. Applied clear-num1.5

    \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{1}{\frac{z - a}{z - t}}}, x\right)\]
  5. Using strategy rm

  6. Applied fma-udef1.5

    \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{z - a}{z - t}} + x}\]

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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