Average Error: 6.3 → 1.8
Time: 37.0s
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 r452345 = 2.0;
        double r452346 = x;
        double r452347 = y;
        double r452348 = r452346 * r452347;
        double r452349 = z;
        double r452350 = t;
        double r452351 = r452349 * r452350;
        double r452352 = r452348 + r452351;
        double r452353 = a;
        double r452354 = b;
        double r452355 = c;
        double r452356 = r452354 * r452355;
        double r452357 = r452353 + r452356;
        double r452358 = r452357 * r452355;
        double r452359 = i;
        double r452360 = r452358 * r452359;
        double r452361 = r452352 - r452360;
        double r452362 = r452345 * r452361;
        return r452362;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r452363 = 2.0;
        double r452364 = x;
        double r452365 = y;
        double r452366 = r452364 * r452365;
        double r452367 = z;
        double r452368 = t;
        double r452369 = r452367 * r452368;
        double r452370 = r452366 + r452369;
        double r452371 = a;
        double r452372 = b;
        double r452373 = c;
        double r452374 = r452372 * r452373;
        double r452375 = r452371 + r452374;
        double r452376 = i;
        double r452377 = r452373 * r452376;
        double r452378 = r452375 * r452377;
        double r452379 = r452370 - r452378;
        double r452380 = r452363 * r452379;
        return r452380;
}

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

Original6.3
Target1.8
Herbie1.8
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.3

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

  3. Applied associate-*l*1.8

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

  4. Final simplification1.8

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

Reproduce

herbie shell --seed 2019325 
(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))))