Average Error: 0.1 → 0.1
Time: 2.5s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x
double f(double x) {
        double r611021 = 3.0;
        double r611022 = x;
        double r611023 = r611022 * r611021;
        double r611024 = r611023 * r611022;
        double r611025 = 4.0;
        double r611026 = r611022 * r611025;
        double r611027 = r611024 - r611026;
        double r611028 = 1.0;
        double r611029 = r611027 + r611028;
        double r611030 = r611021 * r611029;
        return r611030;
}
↓
double f(double x) {
        double r611031 = 9.0;
        double r611032 = x;
        double r611033 = 2.0;
        double r611034 = pow(r611032, r611033);
        double r611035 = r611031 * r611034;
        double r611036 = 3.0;
        double r611037 = r611035 + r611036;
        double r611038 = 12.0;
        double r611039 = r611038 * r611032;
        double r611040 = r611037 - r611039;
        return r611040;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 
(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)))