Average Error: 0.3 → 0.3
Time: 9.1s
Precision: 64
\[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]
↓
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}
↓
\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32
double f(double d1, double d2, double d3) {
        double r3318485 = d1;
        double r3318486 = d2;
        double r3318487 = r3318485 * r3318486;
        double r3318488 = d3;
        double r3318489 = 5.0;
        double r3318490 = /* ERROR: no posit support in C */;
        double r3318491 = r3318488 + r3318490;
        double r3318492 = r3318491 * r3318485;
        double r3318493 = r3318487 + r3318492;
        double r3318494 = 32.0;
        double r3318495 = /* ERROR: no posit support in C */;
        double r3318496 = r3318485 * r3318495;
        double r3318497 = r3318493 + r3318496;
        return r3318497;
}
↓
double f(double d1, double d2, double d3) {
        double r3318498 = d1;
        double r3318499 = d2;
        double r3318500 = r3318498 * r3318499;
        double r3318501 = d3;
        double r3318502 = 5.0;
        double r3318503 = r3318501 + r3318502;
        double r3318504 = r3318503 * r3318498;
        double r3318505 = r3318500 + r3318504;
        double r3318506 = 32.0;
        double r3318507 = r3318498 * r3318506;
        double r3318508 = r3318505 + r3318507;
        return r3318508;
}

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Derivation

  1. Initial program 0.3

    \[\frac{\left(\frac{\left(d1 \cdot d2\right)}{\left(\left(\frac{d3}{\left(5\right)}\right) \cdot d1\right)}\right)}{\left(d1 \cdot \left(32\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]

Reproduce

herbie shell --seed 2019120 
(FPCore (d1 d2 d3)
  :name "FastMath dist3"
  (+.p16 (+.p16 (*.p16 d1 d2) (*.p16 (+.p16 d3 (real->posit16 5)) d1)) (*.p16 d1 (real->posit16 32))))