Average Error: 2.0 → 2.8
Time: 7.5s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r478316 = x;
        double r478317 = y;
        double r478318 = z;
        double r478319 = r478317 * r478318;
        double r478320 = r478316 + r478319;
        double r478321 = t;
        double r478322 = a;
        double r478323 = r478321 * r478322;
        double r478324 = r478320 + r478323;
        double r478325 = r478322 * r478318;
        double r478326 = b;
        double r478327 = r478325 * r478326;
        double r478328 = r478324 + r478327;
        return r478328;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r478329 = y;
        double r478330 = z;
        double r478331 = r478329 * r478330;
        double r478332 = x;
        double r478333 = a;
        double r478334 = t;
        double r478335 = b;
        double r478336 = r478330 * r478335;
        double r478337 = r478334 + r478336;
        double r478338 = r478333 * r478337;
        double r478339 = r478332 + r478338;
        double r478340 = r478331 + r478339;
        return r478340;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target0.3
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -2.7469216095314014e+134 or 5.016277967361233 < b

    1. Initial program 0.6

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

    if -2.7469216095314014e+134 < b < 5.016277967361233

    1. Initial program 2.7

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

    2. Simplified0.5

      \[\leadsto \color{blue}{y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.8

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.75897431883642871e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))