Average Error: 23.8 → 23.8
Time: 821.0ms
Precision: binary64
\[\frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}\]
↓
\[\frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}\]
\frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}
↓
\frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}
double code(double x) {
	return ((double) (((double) (x * x)) / ((double) (((double) (3.14 * ((double) (((double) (((double) (0.1 * 0.1)) * ((double) (((double) (x * x)) - 1.0)))) + 1.0)))) * ((double) (((double) (((double) (0.1 * 0.1)) * ((double) (((double) (x * x)) - 1.0)))) + 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (x * x)) / ((double) (((double) (3.14 * ((double) (((double) (((double) (0.1 * 0.1)) * ((double) (((double) (x * x)) - 1.0)))) + 1.0)))) * ((double) (((double) (((double) (0.1 * 0.1)) * ((double) (((double) (x * x)) - 1.0)))) + 1.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.8

    \[\frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}\]

  2. Final simplification23.8

    \[\leadsto \frac{x \cdot x}{\left(3.14000000000000012 \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)\right) \cdot \left(\left(0.10000000000000001 \cdot 0.10000000000000001\right) \cdot \left(x \cdot x - 1\right) + 1\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (* x x) (* (* 3.14 (+ (* (* 0.1 0.1) (- (* x x) 1)) 1)) (+ (* (* 0.1 0.1) (- (* x x) 1)) 1)))"
  :precision binary64
  (/ (* x x) (* (* 3.14 (+ (* (* 0.1 0.1) (- (* x x) 1.0)) 1.0)) (+ (* (* 0.1 0.1) (- (* x x) 1.0)) 1.0))))