Average Error: 11.1 → 11.1
Time: 13.5s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{\left(y - z\right) \cdot t}{a - z}
double f(double x, double y, double z, double t, double a) {
        double r403953 = x;
        double r403954 = y;
        double r403955 = z;
        double r403956 = r403954 - r403955;
        double r403957 = t;
        double r403958 = r403956 * r403957;
        double r403959 = a;
        double r403960 = r403959 - r403955;
        double r403961 = r403958 / r403960;
        double r403962 = r403953 + r403961;
        return r403962;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r403963 = x;
        double r403964 = y;
        double r403965 = z;
        double r403966 = r403964 - r403965;
        double r403967 = t;
        double r403968 = r403966 * r403967;
        double r403969 = a;
        double r403970 = r403969 - r403965;
        double r403971 = r403968 / r403970;
        double r403972 = r403963 + r403971;
        return r403972;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.1
Target0.5
Herbie11.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0

    1. Initial program 64.0

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.2

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 3.652589666400001e+275

    1. Initial program 0.2

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]

    if 3.652589666400001e+275 < (/ (* (- y z) t) (- a z))

    1. Initial program 59.0

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity59.0

      \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{1 \cdot \left(a - z\right)}}\]

    4. Applied times-frac1.5

      \[\leadsto x + \color{blue}{\frac{y - z}{1} \cdot \frac{t}{a - z}}\]

    5. Simplified1.5

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

  4. Final simplification11.1

    \[\leadsto x + \frac{\left(y - z\right) \cdot t}{a - z}\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))