Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)\]
↓
\[3.0 + \left(9.0 \cdot x - 12.0\right) \cdot x\]
3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)
↓
3.0 + \left(9.0 \cdot x - 12.0\right) \cdot x
double f(double x) {
        double r39943555 = 3.0;
        double r39943556 = x;
        double r39943557 = r39943556 * r39943555;
        double r39943558 = r39943557 * r39943556;
        double r39943559 = 4.0;
        double r39943560 = r39943556 * r39943559;
        double r39943561 = r39943558 - r39943560;
        double r39943562 = 1.0;
        double r39943563 = r39943561 + r39943562;
        double r39943564 = r39943555 * r39943563;
        return r39943564;
}
↓
double f(double x) {
        double r39943565 = 3.0;
        double r39943566 = 9.0;
        double r39943567 = x;
        double r39943568 = r39943566 * r39943567;
        double r39943569 = 12.0;
        double r39943570 = r39943568 - r39943569;
        double r39943571 = r39943570 * r39943567;
        double r39943572 = r39943565 + r39943571;
        return r39943572;
}

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
\[3.0 + \left(\left(9.0 \cdot x\right) \cdot x - 12.0 \cdot x\right)\]

Derivation

  1. Initial program 0.1

    \[3.0 \cdot \left(\left(\left(x \cdot 3.0\right) \cdot x - x \cdot 4.0\right) + 1.0\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(9.0 \cdot {x}^{2} + 3.0\right) - 12.0 \cdot x}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{3.0 + x \cdot \left(9.0 \cdot x - 12.0\right)}\]

  4. Final simplification0.1

    \[\leadsto 3.0 + \left(9.0 \cdot x - 12.0\right) \cdot x\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))