Average Error: 1.3 → 1.3
Time: 12.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\mathsf{fma}\left(y, \frac{z}{z - a} - \frac{t}{z - a}, x\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
\mathsf{fma}\left(y, \frac{z}{z - a} - \frac{t}{z - a}, x\right)
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (z - a))))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) fma(y, ((double) (((double) (z / ((double) (z - a)))) - ((double) (t / ((double) (z - a)))))), 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

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Target

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  2. Simplified1.3

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

  4. Applied div-sub1.3

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

  5. Final simplification1.3

    \[\leadsto \mathsf{fma}\left(y, \frac{z}{z - a} - \frac{t}{z - a}, x\right)\]

Reproduce

herbie shell --seed 2020113 +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)))))