Average Error: 10.4 → 1.3
Time: 5.8s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a} \]
↓
\[y \cdot \frac{z - t}{z - a} + x \]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
y \cdot \frac{z - t}{z - a} + x

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a) :precision binary64 (+ (* y (/ (- z t) (- z a))) 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 - t) / (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

Enter valid numbers for all inputs

Target

Original10.4
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

  1. Initial program 10.4

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

  2. Simplified1.3

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

  3. Applied fma-udef_binary641.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2022081 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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