Average Error: 0.2 → 0.5
Time: 38.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}} \cdot \sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(\sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}} \cdot \sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r11950581 = a;
        double r11950582 = r11950581 * r11950581;
        double r11950583 = b;
        double r11950584 = r11950583 * r11950583;
        double r11950585 = r11950582 + r11950584;
        double r11950586 = 2.0;
        double r11950587 = pow(r11950585, r11950586);
        double r11950588 = 4.0;
        double r11950589 = r11950588 * r11950584;
        double r11950590 = r11950587 + r11950589;
        double r11950591 = 1.0;
        double r11950592 = r11950590 - r11950591;
        return r11950592;
}
↓
double f(double a, double b) {
        double r11950593 = b;
        double r11950594 = r11950593 * r11950593;
        double r11950595 = a;
        double r11950596 = r11950595 * r11950595;
        double r11950597 = r11950594 + r11950596;
        double r11950598 = 2.0;
        double r11950599 = pow(r11950597, r11950598);
        double r11950600 = sqrt(r11950599);
        double r11950601 = cbrt(r11950600);
        double r11950602 = r11950601 * r11950601;
        double r11950603 = cbrt(r11950599);
        double r11950604 = r11950603 * r11950603;
        double r11950605 = r11950602 * r11950604;
        double r11950606 = 4.0;
        double r11950607 = r11950606 * r11950594;
        double r11950608 = r11950605 + r11950607;
        double r11950609 = 1.0;
        double r11950610 = r11950608 - r11950609;
        return r11950610;
}

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 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.5

    \[\leadsto \left(\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \sqrt[3]{\color{blue}{\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt{{\left(a \cdot a + b \cdot b\right)}^{2}}}} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  6. Applied cbrt-prod0.5

    \[\leadsto \left(\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \color{blue}{\left(\sqrt[3]{\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2}}} \cdot \sqrt[3]{\sqrt{{\left(a \cdot a + b \cdot b\right)}^{2}}}\right)} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  7. Final simplification0.5

    \[\leadsto \left(\left(\sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}} \cdot \sqrt[3]{\sqrt{{\left(b \cdot b + a \cdot a\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(b \cdot b\right)\right) - 1\]

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))