Average Error: 14.6 → 0.3
Time: 23.2s
Precision: 64
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
↓
\[\frac{\frac{\pi}{a + b}}{\frac{2 \cdot \left(b - a\right)}{\frac{1}{a} - \frac{1}{b}}}\]
\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)
↓
\frac{\frac{\pi}{a + b}}{\frac{2 \cdot \left(b - a\right)}{\frac{1}{a} - \frac{1}{b}}}
double f(double a, double b) {
        double r1070064 = atan2(1.0, 0.0);
        double r1070065 = 2.0;
        double r1070066 = r1070064 / r1070065;
        double r1070067 = 1.0;
        double r1070068 = b;
        double r1070069 = r1070068 * r1070068;
        double r1070070 = a;
        double r1070071 = r1070070 * r1070070;
        double r1070072 = r1070069 - r1070071;
        double r1070073 = r1070067 / r1070072;
        double r1070074 = r1070066 * r1070073;
        double r1070075 = r1070067 / r1070070;
        double r1070076 = r1070067 / r1070068;
        double r1070077 = r1070075 - r1070076;
        double r1070078 = r1070074 * r1070077;
        return r1070078;
}
↓
double f(double a, double b) {
        double r1070079 = atan2(1.0, 0.0);
        double r1070080 = a;
        double r1070081 = b;
        double r1070082 = r1070080 + r1070081;
        double r1070083 = r1070079 / r1070082;
        double r1070084 = 2.0;
        double r1070085 = r1070081 - r1070080;
        double r1070086 = r1070084 * r1070085;
        double r1070087 = 1.0;
        double r1070088 = r1070087 / r1070080;
        double r1070089 = r1070087 / r1070081;
        double r1070090 = r1070088 - r1070089;
        double r1070091 = r1070086 / r1070090;
        double r1070092 = r1070083 / r1070091;
        return r1070092;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

    \[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]

  2. Simplified9.2

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{2 \cdot \left(b - a\right)} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}\]
  3. Using strategy rm

  4. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b} \cdot \left(\frac{1}{a} - \frac{1}{b}\right)}{2 \cdot \left(b - a\right)}}\]
  5. Using strategy rm

  6. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{\frac{2 \cdot \left(b - a\right)}{\frac{1}{a} - \frac{1}{b}}}}\]

  7. Final simplification0.3

    \[\leadsto \frac{\frac{\pi}{a + b}}{\frac{2 \cdot \left(b - a\right)}{\frac{1}{a} - \frac{1}{b}}}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))