Average Error: 24.7 → 7.7
Time: 10.3s
Precision: binary64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -9.167360412588197 \cdot 10^{-295}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\left(\left(y \cdot \frac{a}{t} + \left(y + \frac{x \cdot z}{t}\right)\right) + \frac{a}{t} \cdot \frac{x \cdot z}{t}\right) - \left(\left(y \cdot \frac{z}{t} + x \cdot \frac{a}{t}\right) + \frac{a}{t} \cdot \left(y \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2.283615310228694 \cdot 10^{+305}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -9.167360412588197 \cdot 10^{-295}:\\
\;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\
\;\;\;\;\left(\left(y \cdot \frac{a}{t} + \left(y + \frac{x \cdot z}{t}\right)\right) + \frac{a}{t} \cdot \frac{x \cdot z}{t}\right) - \left(\left(y \cdot \frac{z}{t} + x \cdot \frac{a}{t}\right) + \frac{a}{t} \cdot \left(y \cdot \frac{z}{t}\right)\right)\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2.283615310228694 \cdot 10^{+305}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\mathbf{else}:\\
\;\;\;\;y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* (- y x) (- z t)) (- a t))) -9.167360412588197e-295)
   (+ x (/ (- y x) (/ (- a t) (- z t))))
   (if (<= (+ x (/ (* (- y x) (- z t)) (- a t))) 0.0)
     (-
      (+ (+ (* y (/ a t)) (+ y (/ (* x z) t))) (* (/ a t) (/ (* x z) t)))
      (+ (+ (* y (/ z t)) (* x (/ a t))) (* (/ a t) (* y (/ z t)))))
     (if (<= (+ x (/ (* (- y x) (- z t)) (- a t))) 2.283615310228694e+305)
       (+ x (* (* (- y x) (- z t)) (/ 1.0 (- a t))))
       (* y (- (/ z (- a t)) (/ t (- a t))))))))
double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + (((y - x) * (z - t)) / (a - t))) <= -9.167360412588197e-295) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if ((x + (((y - x) * (z - t)) / (a - t))) <= 0.0) {
		tmp = (((y * (a / t)) + (y + ((x * z) / t))) + ((a / t) * ((x * z) / t))) - (((y * (z / t)) + (x * (a / t))) + ((a / t) * (y * (z / t))));
	} else if ((x + (((y - x) * (z - t)) / (a - t))) <= 2.283615310228694e+305) {
		tmp = x + (((y - x) * (z - t)) * (1.0 / (a - t)));
	} else {
		tmp = y * ((z / (a - t)) - (t / (a - t)));
	}
	return tmp;
}

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

Original24.7
Target9.4
Herbie7.7
\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.1673604125881965e-295

    1. Initial program 21.9

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

    3. Applied associate-/l*_binary647.4

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

    if -9.1673604125881965e-295 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

    1. Initial program 60.6

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

    3. Applied *-un-lft-identity_binary6460.6

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

    4. Applied times-frac_binary6460.4

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

    5. Simplified60.4

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

    7. Applied add-cbrt-cube_binary6460.4

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

    8. Simplified60.4

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

    9. Taylor expanded around 0 2.8

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

    10. Simplified1.2

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

    if 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.2836153102286941e305

    1. Initial program 1.9

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

    3. Applied *-un-lft-identity_binary641.9

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

    4. Applied times-frac_binary642.8

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

    5. Simplified2.8

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

    7. Applied div-inv_binary642.9

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

    8. Applied associate-*r*_binary642.0

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

    9. Simplified2.0

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

    if 2.2836153102286941e305 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

    1. Initial program 63.7

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

    3. Applied *-un-lft-identity_binary6463.7

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

    4. Applied times-frac_binary6417.7

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

    5. Simplified17.7

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

    7. Applied add-cbrt-cube_binary6421.5

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

    8. Simplified21.5

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

    9. Taylor expanded around -inf 25.4

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(\frac{t}{a - t} - \frac{z}{a - t}\right)\right)}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification7.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -9.167360412588197 \cdot 10^{-295}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;\left(\left(y \cdot \frac{a}{t} + \left(y + \frac{x \cdot z}{t}\right)\right) + \frac{a}{t} \cdot \frac{x \cdot z}{t}\right) - \left(\left(y \cdot \frac{z}{t} + x \cdot \frac{a}{t}\right) + \frac{a}{t} \cdot \left(y \cdot \frac{z}{t}\right)\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 2.283615310228694 \cdot 10^{+305}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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