Average Error: 0.2 → 0.1
Time: 7.8s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[x \cdot \left(9 \cdot x - 12\right) + 3\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
x \cdot \left(9 \cdot x - 12\right) + 3
double f(double x) {
        double r592994 = 3.0;
        double r592995 = x;
        double r592996 = r592995 * r592994;
        double r592997 = r592996 * r592995;
        double r592998 = 4.0;
        double r592999 = r592995 * r592998;
        double r593000 = r592997 - r592999;
        double r593001 = 1.0;
        double r593002 = r593000 + r593001;
        double r593003 = r592994 * r593002;
        return r593003;
}
↓
double f(double x) {
        double r593004 = x;
        double r593005 = 9.0;
        double r593006 = r593005 * r593004;
        double r593007 = 12.0;
        double r593008 = r593006 - r593007;
        double r593009 = r593004 * r593008;
        double r593010 = 3.0;
        double r593011 = r593009 + r593010;
        return r593011;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original0.2
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.2

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

  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. Taylor expanded around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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)))