Average Error: 0.1 → 0.1
Time: 10.4s
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 r651234 = 3.0;
        double r651235 = x;
        double r651236 = r651235 * r651234;
        double r651237 = r651236 * r651235;
        double r651238 = 4.0;
        double r651239 = r651235 * r651238;
        double r651240 = r651237 - r651239;
        double r651241 = 1.0;
        double r651242 = r651240 + r651241;
        double r651243 = r651234 * r651242;
        return r651243;
}
↓
double f(double x) {
        double r651244 = x;
        double r651245 = 9.0;
        double r651246 = r651245 * r651244;
        double r651247 = 12.0;
        double r651248 = r651246 - r651247;
        double r651249 = r651244 * r651248;
        double r651250 = 3.0;
        double r651251 = r651249 + r651250;
        return r651251;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))