Average Error: 10.8 → 1.2
Time: 2.8s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{t}{\frac{a - z}{y - z}}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{t}{\frac{a - z}{y - z}}
double code(double x, double y, double z, double t, double a) {
	return (x + (((y - z) * t) / (a - z)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return (x + (t / ((a - z) / (y - z))));
}

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

Original10.8
Target0.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied *-commutative10.8

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

  4. Applied associate-/l*1.2

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

  5. Final simplification1.2

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

Reproduce

herbie shell --seed 2020078 
(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))))