Rosa's Benchmark

Average Error: 0.1 → 0.1

Time: 22.1s

Precision: 64

Math

\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]

↓

\[\mathsf{fma}\left(0.954929658551372, x, \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(-0.12900613773279798\right)\right)\right)\]

C

double f(double x) {
        double r839416 = 0.954929658551372;
        double r839417 = x;
        double r839418 = r839416 * r839417;
        double r839419 = 0.12900613773279798;
        double r839420 = r839417 * r839417;
        double r839421 = r839420 * r839417;
        double r839422 = r839419 * r839421;
        double r839423 = r839418 - r839422;
        return r839423;
}

↓

double f(double x) {
        double r839424 = 0.954929658551372;
        double r839425 = x;
        double r839426 = r839425 * r839425;
        double r839427 = r839426 * r839425;
        double r839428 = 0.12900613773279798;
        double r839429 = -r839428;
        double r839430 = r839427 * r839429;
        double r839431 = fma(r839424, r839425, r839430);
        return r839431;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
2. Using strategy rm

3. Applied fma-neg 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.954929658551372, x, \left(-0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\right)\right)}\]

4. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(0.954929658551372, x, \left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(-0.12900613773279798\right)\right)\right)\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x)
  :name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))