Average Error: 11.1 → 1.4
Time: 3.0s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{y - z}{a - z} \cdot t\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{y - z}{a - z} \cdot t
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (((double) (y - z)) * t)) / ((double) (a - z)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) ((((double) (y - z)) / ((double) (a - z))) * t))));
}

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
Target0.6
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 11.1

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

  2. Simplified3.2

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

  4. Applied add-cube-cbrt3.7

    \[\leadsto x + \left(y - z\right) \cdot \frac{t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

  5. Applied *-un-lft-identity3.7

    \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot t}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

  6. Applied times-frac3.7

    \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}\right)}\]

  7. Applied associate-*r*1.9

    \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t}{\sqrt[3]{a - z}}}\]

  8. Simplified1.9

    \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t}{\sqrt[3]{a - z}}\]
  9. Using strategy rm

  10. Applied pow11.9

    \[\leadsto x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \color{blue}{{\left(\frac{t}{\sqrt[3]{a - z}}\right)}^{1}}\]

  11. Applied pow11.9

    \[\leadsto x + \color{blue}{{\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right)}^{1}} \cdot {\left(\frac{t}{\sqrt[3]{a - z}}\right)}^{1}\]

  12. Applied pow-prod-down1.9

    \[\leadsto x + \color{blue}{{\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}\right)}^{1}}\]

  13. Simplified1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2020182 
(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))))