Average Error: 0.5 → 0.4
Time: 9.2s
Precision: 64
\[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]
↓
\[d1 \cdot \left(d2 + \left(\left(\left(-d3\right) + d4\right) - d1\right)\right)\]
\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)
↓
d1 \cdot \left(d2 + \left(\left(\left(-d3\right) + d4\right) - d1\right)\right)
double f(double d1, double d2, double d3, double d4) {
        double r3024238 = d1;
        double r3024239 = d2;
        double r3024240 = r3024238 * r3024239;
        double r3024241 = d3;
        double r3024242 = r3024238 * r3024241;
        double r3024243 = r3024240 - r3024242;
        double r3024244 = d4;
        double r3024245 = r3024244 * r3024238;
        double r3024246 = r3024243 + r3024245;
        double r3024247 = r3024238 * r3024238;
        double r3024248 = r3024246 - r3024247;
        return r3024248;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r3024249 = d1;
        double r3024250 = d2;
        double r3024251 = d3;
        double r3024252 = -r3024251;
        double r3024253 = d4;
        double r3024254 = r3024252 + r3024253;
        double r3024255 = r3024254 - r3024249;
        double r3024256 = r3024250 + r3024255;
        double r3024257 = r3024249 * r3024256;
        return r3024257;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Bits error versus d4

Derivation

  1. Initial program 0.5

    \[\left(\frac{\left(\left(d1 \cdot d2\right) - \left(d1 \cdot d3\right)\right)}{\left(d4 \cdot d1\right)}\right) - \left(d1 \cdot d1\right)\]

  2. Simplified0.4

    \[\leadsto \color{blue}{d1 \cdot \left(\frac{\left(d2 - d3\right)}{\left(d4 - d1\right)}\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.4

    \[\leadsto d1 \cdot \left(\frac{\color{blue}{\left(\frac{d2}{\left(-d3\right)}\right)}}{\left(d4 - d1\right)}\right)\]

  5. Applied associate-+l+0.4

    \[\leadsto d1 \cdot \color{blue}{\left(\frac{d2}{\left(\frac{\left(-d3\right)}{\left(d4 - d1\right)}\right)}\right)}\]
  6. Using strategy rm

  7. Applied associate-+r-0.4

    \[\leadsto d1 \cdot \left(\frac{d2}{\color{blue}{\left(\left(\frac{\left(-d3\right)}{d4}\right) - d1\right)}}\right)\]

  8. Final simplification0.4

    \[\leadsto d1 \cdot \left(d2 + \left(\left(\left(-d3\right) + d4\right) - d1\right)\right)\]

Reproduce

herbie shell --seed 2019107 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  (-.p16 (+.p16 (-.p16 (*.p16 d1 d2) (*.p16 d1 d3)) (*.p16 d4 d1)) (*.p16 d1 d1)))