Average Error: 0.0 → 0.0
Time: 21.3s
Precision: 64
\[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]
↓
\[d1 \cdot \left(\left(d2 + d4\right) - \left(d1 + d3\right)\right)\]
double f(double d1, double d2, double d3, double d4) {
        double r74890533 = d1;
        double r74890534 = d2;
        double r74890535 = r74890533 * r74890534;
        double r74890536 = d3;
        double r74890537 = r74890533 * r74890536;
        double r74890538 = r74890535 - r74890537;
        double r74890539 = d4;
        double r74890540 = r74890539 * r74890533;
        double r74890541 = r74890538 + r74890540;
        double r74890542 = r74890533 * r74890533;
        double r74890543 = r74890541 - r74890542;
        return r74890543;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r74890544 = d1;
        double r74890545 = d2;
        double r74890546 = d4;
        double r74890547 = r74890545 + r74890546;
        double r74890548 = d3;
        double r74890549 = r74890544 + r74890548;
        double r74890550 = r74890547 - r74890549;
        double r74890551 = r74890544 * r74890550;
        return r74890551;
}


\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1
↓
d1 \cdot \left(\left(d2 + d4\right) - \left(d1 + d3\right)\right)

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Bits error versus d4

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right)\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019102 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"

  :herbie-target
  (* d1 (- (+ (- d2 d3) d4) d1))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))