Average Error: 6.4 → 2.0
Time: 7.4s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r658119 = 2.0;
        double r658120 = x;
        double r658121 = y;
        double r658122 = r658120 * r658121;
        double r658123 = z;
        double r658124 = t;
        double r658125 = r658123 * r658124;
        double r658126 = r658122 + r658125;
        double r658127 = a;
        double r658128 = b;
        double r658129 = c;
        double r658130 = r658128 * r658129;
        double r658131 = r658127 + r658130;
        double r658132 = r658131 * r658129;
        double r658133 = i;
        double r658134 = r658132 * r658133;
        double r658135 = r658126 - r658134;
        double r658136 = r658119 * r658135;
        return r658136;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r658137 = 2.0;
        double r658138 = x;
        double r658139 = y;
        double r658140 = r658138 * r658139;
        double r658141 = z;
        double r658142 = t;
        double r658143 = r658141 * r658142;
        double r658144 = r658140 + r658143;
        double r658145 = a;
        double r658146 = b;
        double r658147 = c;
        double r658148 = r658146 * r658147;
        double r658149 = r658145 + r658148;
        double r658150 = cbrt(r658149);
        double r658151 = i;
        double r658152 = r658147 * r658151;
        double r658153 = r658150 * r658152;
        double r658154 = r658150 * r658153;
        double r658155 = r658150 * r658154;
        double r658156 = r658144 - r658155;
        double r658157 = r658137 * r658156;
        return r658157;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.4
Target1.7
Herbie2.0
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.4

    \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  2. Using strategy rm

  3. Applied associate-*l*1.7

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(c \cdot i\right)\right)\]

  6. Applied associate-*l*2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)}\right)\]
  7. Using strategy rm

  8. Applied associate-*l*2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)}\right)\]

  9. Final simplification2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(c \cdot i\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))