Average Error: 6.2 → 1.9
Time: 7.6s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]
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) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r714072 = 2.0;
        double r714073 = x;
        double r714074 = y;
        double r714075 = r714073 * r714074;
        double r714076 = z;
        double r714077 = t;
        double r714078 = r714076 * r714077;
        double r714079 = r714075 + r714078;
        double r714080 = a;
        double r714081 = b;
        double r714082 = c;
        double r714083 = r714081 * r714082;
        double r714084 = r714080 + r714083;
        double r714085 = r714084 * r714082;
        double r714086 = i;
        double r714087 = r714085 * r714086;
        double r714088 = r714079 - r714087;
        double r714089 = r714072 * r714088;
        return r714089;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r714090 = 2.0;
        double r714091 = x;
        double r714092 = y;
        double r714093 = r714091 * r714092;
        double r714094 = z;
        double r714095 = t;
        double r714096 = r714094 * r714095;
        double r714097 = r714093 + r714096;
        double r714098 = a;
        double r714099 = b;
        double r714100 = c;
        double r714101 = r714099 * r714100;
        double r714102 = r714098 + r714101;
        double r714103 = i;
        double r714104 = r714100 * r714103;
        double r714105 = r714102 * r714104;
        double r714106 = r714097 - r714105;
        double r714107 = r714090 * r714106;
        return r714107;
}

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

Original6.2
Target1.9
Herbie1.9
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.2

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

  3. Applied associate-*l*1.9

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

  4. Final simplification1.9

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

Reproduce

herbie shell --seed 2020060 
(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))))