Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
↓
\[\mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y \cdot z, -0.5, t\right)\right) \]
\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t
↓
\mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y \cdot z, -0.5, t\right)\right)

(FPCore (x y z t)
 :precision binary64
 (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))
↓
(FPCore (x y z t) :precision binary64 (fma 0.125 x (fma (* y z) -0.5 t)))
double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}
↓
double code(double x, double y, double z, double t) {
	return fma(0.125, x, fma((y * z), -0.5, t));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y \]

Derivation

  1. Initial program 0.0

    \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot z, -0.5, \mathsf{fma}\left(0.125, x, t\right)\right)} \]

  3. Taylor expanded in y around 0 0.0

    \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(y \cdot z\right)} \]

  4. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y \cdot z, -0.5, t\right)\right)} \]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(0.125, x, \mathsf{fma}\left(y \cdot z, -0.5, t\right)\right) \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))