Average Error: 0.2 → 0.5
Time: 37.3s
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 r11950257 = a;
        double r11950258 = r11950257 * r11950257;
        double r11950259 = b;
        double r11950260 = r11950259 * r11950259;
        double r11950261 = r11950258 + r11950260;
        double r11950262 = 2.0;
        double r11950263 = pow(r11950261, r11950262);
        double r11950264 = 4.0;
        double r11950265 = r11950264 * r11950260;
        double r11950266 = r11950263 + r11950265;
        double r11950267 = 1.0;
        double r11950268 = r11950266 - r11950267;
        return r11950268;
}
↓
double f(double a, double b) {
        double r11950269 = b;
        double r11950270 = r11950269 * r11950269;
        double r11950271 = a;
        double r11950272 = r11950271 * r11950271;
        double r11950273 = r11950270 + r11950272;
        double r11950274 = 2.0;
        double r11950275 = pow(r11950273, r11950274);
        double r11950276 = sqrt(r11950275);
        double r11950277 = cbrt(r11950276);
        double r11950278 = r11950277 * r11950277;
        double r11950279 = cbrt(r11950275);
        double r11950280 = r11950279 * r11950279;
        double r11950281 = r11950278 * r11950280;
        double r11950282 = 4.0;
        double r11950283 = r11950282 * r11950270;
        double r11950284 = r11950281 + r11950283;
        double r11950285 = 1.0;
        double r11950286 = r11950284 - r11950285;
        return r11950286;
}

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))