Average Error: 0.4 → 0.4
Time: 20.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(\frac{1}{9 \cdot x} + y\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(\frac{1}{9 \cdot x} + y\right) - 1\right) \cdot \left(3 \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r362198 = 3.0;
        double r362199 = x;
        double r362200 = sqrt(r362199);
        double r362201 = r362198 * r362200;
        double r362202 = y;
        double r362203 = 1.0;
        double r362204 = 9.0;
        double r362205 = r362199 * r362204;
        double r362206 = r362203 / r362205;
        double r362207 = r362202 + r362206;
        double r362208 = r362207 - r362203;
        double r362209 = r362201 * r362208;
        return r362209;
}
↓
double f(double x, double y) {
        double r362210 = 1.0;
        double r362211 = 9.0;
        double r362212 = x;
        double r362213 = r362211 * r362212;
        double r362214 = r362210 / r362213;
        double r362215 = y;
        double r362216 = r362214 + r362215;
        double r362217 = r362216 - r362210;
        double r362218 = 3.0;
        double r362219 = sqrt(r362212);
        double r362220 = r362218 * r362219;
        double r362221 = r362217 * r362220;
        return r362221;
}

Error

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Bits error versus y

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Results

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Target

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

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 
(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)))