Average Error: 0.0 → 0.0
Time: 1.6m
Precision: 64
\[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1\]
↓
\[(\left(d2 - d3\right) \cdot d1 + \left(d1 \cdot \left(d4 - d1\right)\right))_*\]
\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1
↓
(\left(d2 - d3\right) \cdot d1 + \left(d1 \cdot \left(d4 - d1\right)\right))_*
double f(double d1, double d2, double d3, double d4) {
        double r52294561 = d1;
        double r52294562 = d2;
        double r52294563 = r52294561 * r52294562;
        double r52294564 = d3;
        double r52294565 = r52294561 * r52294564;
        double r52294566 = r52294563 - r52294565;
        double r52294567 = d4;
        double r52294568 = r52294567 * r52294561;
        double r52294569 = r52294566 + r52294568;
        double r52294570 = r52294561 * r52294561;
        double r52294571 = r52294569 - r52294570;
        return r52294571;
}
↓
double f(double d1, double d2, double d3, double d4) {
        double r52294572 = d2;
        double r52294573 = d3;
        double r52294574 = r52294572 - r52294573;
        double r52294575 = d1;
        double r52294576 = d4;
        double r52294577 = r52294576 - r52294575;
        double r52294578 = r52294575 * r52294577;
        double r52294579 = fma(r52294574, r52294575, r52294578);
        return r52294579;
}

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

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

  4. Applied distribute-rgt-in0.0

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

  6. Applied fma-def0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"

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

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