Average Error: 14.8 → 5.5
Time: 1.1min
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -7.780159800658845 \cdot 10^{-264}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 8.861297595452242 \cdot 10^{-41} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 6.505858290759375 \cdot 10^{+291}\right):\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{z \cdot t}{a - z} + \frac{x \cdot y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -7.780159800658845 \cdot 10^{-264}:\\
\;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\\

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

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 8.861297595452242 \cdot 10^{-41} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 6.505858290759375 \cdot 10^{+291}\right):\\
\;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{z \cdot t}{a - z} + \frac{x \cdot y}{a - z}\right)\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) -7.780159800658845e-264)
   (+
    x
    (*
     (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z)))
     (* (/ (- t x) (cbrt (- a z))) (/ (cbrt (- y z)) (cbrt (- a z))))))
   (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 0.0)
     (- (+ t (+ (/ (* x y) z) (/ (* t a) z))) (+ (/ (* x a) z) (/ (* y t) z)))
     (if (or (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 8.861297595452242e-41)
             (not
              (<=
               (+ x (* (- y z) (/ (- t x) (- a z))))
               6.505858290759375e+291)))
       (-
        (+ (/ (* y t) (- a z)) (+ x (/ (* x z) (- a z))))
        (+ (/ (* z t) (- a z)) (/ (* x y) (- a z))))
       (+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y - z) * ((t - x) / (a - z)))) <= -7.780159800658845e-264) {
		tmp = x + (((cbrt(y - z) * cbrt(y - z)) / cbrt(a - z)) * (((t - x) / cbrt(a - z)) * (cbrt(y - z) / cbrt(a - z))));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= 0.0) {
		tmp = (t + (((x * y) / z) + ((t * a) / z))) - (((x * a) / z) + ((y * t) / z));
	} else if (((x + ((y - z) * ((t - x) / (a - z)))) <= 8.861297595452242e-41) || !((x + ((y - z) * ((t - x) / (a - z)))) <= 6.505858290759375e+291)) {
		tmp = (((y * t) / (a - z)) + (x + ((x * z) / (a - z)))) - (((z * t) / (a - z)) + ((x * y) / (a - z)));
	} else {
		tmp = x + ((y - z) * ((t / (a - z)) - (x / (a - z))));
	}
	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

Derivation

  1. Split input into 4 regimes

  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -7.7801598006588446e-264

    1. Initial program 7.0

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

    3. Applied add-cube-cbrt_binary64_11367.7

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

    4. Applied *-un-lft-identity_binary64_11017.7

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

    5. Applied times-frac_binary64_11077.7

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

    6. Applied associate-*r*_binary64_10415.0

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

    7. Simplified5.0

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

    9. Applied add-cube-cbrt_binary64_11364.9

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

    10. Applied times-frac_binary64_11074.9

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

    11. Applied associate-*l*_binary64_10424.6

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

    12. Simplified4.6

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

    if -7.7801598006588446e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 59.9

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

    2. Taylor expanded around inf 13.2

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

    3. Simplified13.2

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

    if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 8.8612975954522422e-41 or 6.5058582907593745e291 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 19.2

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

    3. Applied clear-num_binary64_110019.8

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

    5. Applied div-inv_binary64_109819.9

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

    6. Applied add-cube-cbrt_binary64_113619.9

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

    7. Applied times-frac_binary64_110719.2

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

    8. Applied associate-*r*_binary64_10416.3

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

    9. Taylor expanded around 0 7.3

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

    10. Simplified7.3

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

    if 8.8612975954522422e-41 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 6.5058582907593745e291

    1. Initial program 2.4

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

    3. Applied div-sub_binary64_11062.4

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

  4. Final simplification5.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -7.780159800658845 \cdot 10^{-264}:\\ \;\;\;\;x + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{t - x}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t + \left(\frac{x \cdot y}{z} + \frac{t \cdot a}{z}\right)\right) - \left(\frac{x \cdot a}{z} + \frac{y \cdot t}{z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 8.861297595452242 \cdot 10^{-41} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 6.505858290759375 \cdot 10^{+291}\right):\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{z \cdot t}{a - z} + \frac{x \cdot y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021076 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))