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

↓

\[\mathsf{fma}\left(\frac{x}{8}, 1, \mathsf{fma}\left(-\frac{y}{2}, z, t\right)\right)\]

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

↓

\mathsf{fma}\left(\frac{x}{8}, 1, \mathsf{fma}\left(-\frac{y}{2}, z, t\right)\right)

double f(double x, double y, double z, double t) {
        double r3062 = 1.0;
        double r3063 = 8.0;
        double r3064 = r3062 / r3063;
        double r3065 = x;
        double r3066 = r3064 * r3065;
        double r3067 = y;
        double r3068 = z;
        double r3069 = r3067 * r3068;
        double r3070 = 2.0;
        double r3071 = r3069 / r3070;
        double r3072 = r3066 - r3071;
        double r3073 = t;
        double r3074 = r3072 + r3073;
        return r3074;
}

↓

double f(double x, double y, double z, double t) {
        double r3075 = x;
        double r3076 = 8.0;
        double r3077 = r3075 / r3076;
        double r3078 = 1.0;
        double r3079 = y;
        double r3080 = 2.0;
        double r3081 = r3079 / r3080;
        double r3082 = -r3081;
        double r3083 = z;
        double r3084 = t;
        double r3085 = fma(r3082, r3083, r3084);
        double r3086 = fma(r3077, r3078, r3085);
        return r3086;
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Original	0.0
Target	0.0
Herbie	0.0

Derivation

Initial program 0.0
\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]
Simplified0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{8}, 1, \mathsf{fma}\left(-\frac{y}{2}, z, t\right)\right)}\]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(\frac{x}{8}, 1, \mathsf{fma}\left(-\frac{y}{2}, z, t\right)\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8) t) (* (/ z 2) y))

  (+ (- (* (/ 1 8) x) (/ (* y z) 2)) t))

Error

Target

Derivation

Reproduce