Average Error: 0.4 → 0.5
Time: 19.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(\sqrt{\sqrt[3]{3}} \cdot \left(\left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(\sqrt{\sqrt[3]{3}} \cdot \left(\left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)
double f(double x, double y) {
        double r22994104 = 3.0;
        double r22994105 = x;
        double r22994106 = sqrt(r22994105);
        double r22994107 = r22994104 * r22994106;
        double r22994108 = y;
        double r22994109 = 1.0;
        double r22994110 = 9.0;
        double r22994111 = r22994105 * r22994110;
        double r22994112 = r22994109 / r22994111;
        double r22994113 = r22994108 + r22994112;
        double r22994114 = r22994113 - r22994109;
        double r22994115 = r22994107 * r22994114;
        return r22994115;
}
↓
double f(double x, double y) {
        double r22994116 = 3.0;
        double r22994117 = cbrt(r22994116);
        double r22994118 = sqrt(r22994117);
        double r22994119 = 1.0;
        double r22994120 = x;
        double r22994121 = 9.0;
        double r22994122 = r22994120 * r22994121;
        double r22994123 = r22994119 / r22994122;
        double r22994124 = y;
        double r22994125 = r22994123 + r22994124;
        double r22994126 = r22994125 - r22994119;
        double r22994127 = sqrt(r22994120);
        double r22994128 = r22994126 * r22994127;
        double r22994129 = r22994118 * r22994128;
        double r22994130 = r22994129 * r22994118;
        double r22994131 = r22994117 * r22994117;
        double r22994132 = r22994130 * r22994131;
        return r22994132;
}

Error

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Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]

  6. Applied associate-*l*0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.6

    \[\leadsto \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\color{blue}{\left(\sqrt{\sqrt[3]{3}} \cdot \sqrt{\sqrt[3]{3}}\right)} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)\]

  9. Applied associate-*l*0.5

    \[\leadsto \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{3}} \cdot \left(\sqrt{\sqrt[3]{3}} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)\right)}\]

  10. Final simplification0.5

    \[\leadsto \left(\left(\sqrt{\sqrt[3]{3}} \cdot \left(\left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right) \cdot \sqrt{x}\right)\right) \cdot \sqrt{\sqrt[3]{3}}\right) \cdot \left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))