Average Error: 6.7 → 1.9
Time: 9.8s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot 2\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
\left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \cdot 2
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r777338 = 2.0;
        double r777339 = x;
        double r777340 = y;
        double r777341 = r777339 * r777340;
        double r777342 = z;
        double r777343 = t;
        double r777344 = r777342 * r777343;
        double r777345 = r777341 + r777344;
        double r777346 = a;
        double r777347 = b;
        double r777348 = c;
        double r777349 = r777347 * r777348;
        double r777350 = r777346 + r777349;
        double r777351 = r777350 * r777348;
        double r777352 = i;
        double r777353 = r777351 * r777352;
        double r777354 = r777345 - r777353;
        double r777355 = r777338 * r777354;
        return r777355;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r777356 = x;
        double r777357 = y;
        double r777358 = r777356 * r777357;
        double r777359 = z;
        double r777360 = t;
        double r777361 = r777359 * r777360;
        double r777362 = r777358 + r777361;
        double r777363 = a;
        double r777364 = b;
        double r777365 = c;
        double r777366 = r777364 * r777365;
        double r777367 = r777363 + r777366;
        double r777368 = i;
        double r777369 = r777365 * r777368;
        double r777370 = r777367 * r777369;
        double r777371 = r777362 - r777370;
        double r777372 = 2.0;
        double r777373 = r777371 * r777372;
        return r777373;
}

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

Original6.7
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 6.7

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

  5. Applied *-commutative1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019356 
(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))))