Average Error: 0.1 → 0.1
Time: 9.8s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + x \cdot \left(9 \cdot x - 12\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + x \cdot \left(9 \cdot x - 12\right)
double f(double x) {
        double r1274993 = 3.0;
        double r1274994 = x;
        double r1274995 = r1274994 * r1274993;
        double r1274996 = r1274995 * r1274994;
        double r1274997 = 4.0;
        double r1274998 = r1274994 * r1274997;
        double r1274999 = r1274996 - r1274998;
        double r1275000 = 1.0;
        double r1275001 = r1274999 + r1275000;
        double r1275002 = r1274993 * r1275001;
        return r1275002;
}
↓
double f(double x) {
        double r1275003 = 3.0;
        double r1275004 = x;
        double r1275005 = 9.0;
        double r1275006 = r1275005 * r1275004;
        double r1275007 = 12.0;
        double r1275008 = r1275006 - r1275007;
        double r1275009 = r1275004 * r1275008;
        double r1275010 = r1275003 + r1275009;
        return r1275010;
}

Error

Bits error versus x

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.1

    \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(1 + x \cdot \left(x \cdot 3 - 4\right)\right)}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{3 + x \cdot \left(9 \cdot x - 12\right)}\]

  5. Final simplification0.1

    \[\leadsto 3 + x \cdot \left(9 \cdot x - 12\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3 (- (* (* 9 x) x) (* 12 x)))

  (* 3 (+ (- (* (* x 3) x) (* x 4)) 1)))