Average Error: 0.1 → 0.1
Time: 1.8s
Precision: binary64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + x \cdot \left(x \cdot 9 - 12\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + x \cdot \left(x \cdot 9 - 12\right)
(FPCore (x) :precision binary64 (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))
↓
(FPCore (x) :precision binary64 (+ 3.0 (* x (- (* x 9.0) 12.0))))
double code(double x) {
	return ((double) (3.0 * ((double) (((double) (((double) (((double) (x * 3.0)) * x)) - ((double) (x * 4.0)))) + 1.0))));
}
↓
double code(double x) {
	return ((double) (3.0 + ((double) (x * ((double) (((double) (x * 9.0)) - 12.0))))));
}

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 Error: 0.1 bits

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

  2. SimplifiedError: 0.1 bits

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

  3. Taylor expanded around 0 Error: 0.1 bits

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

  4. SimplifiedError: 0.1 bits

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

  5. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

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

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