Average Error: 15.1 → 4.9
Time: 22.4s
Precision: binary64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.612935525843224 \cdot 10^{+41}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.610859612894739 \cdot 10^{-299}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(\frac{a \cdot \left(x \cdot y\right)}{z \cdot z} + \left(\frac{t \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{t \cdot a}{z} + \left(\frac{a \cdot \left(a \cdot \left(x \cdot y\right)\right)}{{z}^{3}} + \left(\left(t + \frac{x \cdot y}{z}\right) + \frac{t}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right) - \left(\frac{x \cdot a}{z} + \left(\frac{x \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{y \cdot t}{z} + \left(\frac{a \cdot \left(a \cdot \left(y \cdot t\right)\right)}{{z}^{3}} + \left(\frac{a \cdot \left(y \cdot t\right)}{z \cdot z} + \frac{x}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4.523655801934687 \cdot 10^{-23}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.9006975675827603 \cdot 10^{+208}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \frac{1}{\frac{1}{t - x}}\\ \end{array}\]
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 -6.612935525843224 \cdot 10^{+41}:\\
\;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.610859612894739 \cdot 10^{-299}:\\
\;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\
\;\;\;\;\left(\frac{a \cdot \left(x \cdot y\right)}{z \cdot z} + \left(\frac{t \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{t \cdot a}{z} + \left(\frac{a \cdot \left(a \cdot \left(x \cdot y\right)\right)}{{z}^{3}} + \left(\left(t + \frac{x \cdot y}{z}\right) + \frac{t}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right) - \left(\frac{x \cdot a}{z} + \left(\frac{x \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{y \cdot t}{z} + \left(\frac{a \cdot \left(a \cdot \left(y \cdot t\right)\right)}{{z}^{3}} + \left(\frac{a \cdot \left(y \cdot t\right)}{z \cdot z} + \frac{x}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4.523655801934687 \cdot 10^{-23}:\\
\;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\

\mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.9006975675827603 \cdot 10^{+208}:\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot \frac{1}{\frac{1}{t - x}}\\

\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)))) -6.612935525843224e+41)
   (+
    x
    (*
     (*
      (- y z)
      (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
     (/ (cbrt (- t x)) (cbrt (- a z)))))
   (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) -5.610859612894739e-299)
     (-
      (+ (/ (* y t) (- a z)) (+ x (/ (* x z) (- a z))))
      (+ (/ (* x y) (- a z)) (/ (* z t) (- a z))))
     (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 0.0)
       (-
        (+
         (/ (* a (* x y)) (* z z))
         (+
          (/ (* t (* a a)) (* z z))
          (+
           (/ (* t a) z)
           (+
            (/ (* a (* a (* x y))) (pow z 3.0))
            (+ (+ t (/ (* x y) z)) (/ t (pow (/ z a) 3.0)))))))
        (+
         (/ (* x a) z)
         (+
          (/ (* x (* a a)) (* z z))
          (+
           (/ (* y t) z)
           (+
            (/ (* a (* a (* y t))) (pow z 3.0))
            (+ (/ (* a (* y t)) (* z z)) (/ x (pow (/ z a) 3.0))))))))
       (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 4.523655801934687e-23)
         (-
          (+ (/ (* y t) (- a z)) (+ x (/ (* x z) (- a z))))
          (+ (/ (* x y) (- a z)) (/ (* z t) (- a z))))
         (if (<= (+ x (* (- y z) (/ (- t x) (- a z)))) 1.9006975675827603e+208)
           (+ x (* (- y z) (/ (- t x) (- a z))))
           (+ x (* (/ (- y z) (- a z)) (/ 1.0 (/ 1.0 (- t x)))))))))))
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)))) <= -6.612935525843224e+41) {
		tmp = x + (((y - z) * ((cbrt(t - x) * cbrt(t - x)) / (cbrt(a - z) * cbrt(a - z)))) * (cbrt(t - x) / cbrt(a - z)));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= -5.610859612894739e-299) {
		tmp = (((y * t) / (a - z)) + (x + ((x * z) / (a - z)))) - (((x * y) / (a - z)) + ((z * t) / (a - z)));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= 0.0) {
		tmp = (((a * (x * y)) / (z * z)) + (((t * (a * a)) / (z * z)) + (((t * a) / z) + (((a * (a * (x * y))) / pow(z, 3.0)) + ((t + ((x * y) / z)) + (t / pow((z / a), 3.0))))))) - (((x * a) / z) + (((x * (a * a)) / (z * z)) + (((y * t) / z) + (((a * (a * (y * t))) / pow(z, 3.0)) + (((a * (y * t)) / (z * z)) + (x / pow((z / a), 3.0)))))));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= 4.523655801934687e-23) {
		tmp = (((y * t) / (a - z)) + (x + ((x * z) / (a - z)))) - (((x * y) / (a - z)) + ((z * t) / (a - z)));
	} else if ((x + ((y - z) * ((t - x) / (a - z)))) <= 1.9006975675827603e+208) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = x + (((y - z) / (a - z)) * (1.0 / (1.0 / (t - x))));
	}
	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 5 regimes

  2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -6.61293552584322434e41

    1. Initial program 5.9

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

    3. Applied add-cube-cbrt_binary64_31826.7

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

    4. Applied add-cube-cbrt_binary64_31826.9

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

    5. Applied times-frac_binary64_31536.9

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

    6. Applied associate-*r*_binary64_30873.9

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

    if -6.61293552584322434e41 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.6108596128947389e-299 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.523655801934687e-23

    1. Initial program 12.5

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

    2. Taylor expanded around 0 2.5

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

    if -5.6108596128947389e-299 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

    1. Initial program 61.6

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

    2. Taylor expanded around inf 18.3

      \[\leadsto \color{blue}{\left(\frac{a \cdot \left(x \cdot y\right)}{{z}^{2}} + \left(\frac{t \cdot {a}^{2}}{{z}^{2}} + \left(\frac{t \cdot a}{z} + \left(\frac{{a}^{2} \cdot \left(x \cdot y\right)}{{z}^{3}} + \left(\frac{t \cdot {a}^{3}}{{z}^{3}} + \left(t + \frac{x \cdot y}{z}\right)\right)\right)\right)\right)\right) - \left(\frac{a \cdot x}{z} + \left(\frac{{a}^{2} \cdot x}{{z}^{2}} + \left(\frac{t \cdot y}{z} + \left(\frac{t \cdot \left(y \cdot {a}^{2}\right)}{{z}^{3}} + \left(\frac{{a}^{3} \cdot x}{{z}^{3}} + \frac{t \cdot \left(y \cdot a\right)}{{z}^{2}}\right)\right)\right)\right)\right)}\]

    3. Simplified16.9

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

    if 4.523655801934687e-23 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.9006975675827603e208

    1. Initial program 2.0

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

    if 1.9006975675827603e208 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

    1. Initial program 10.9

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

    3. Applied add-cube-cbrt_binary64_318211.6

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

    4. Applied *-un-lft-identity_binary64_314711.6

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

    5. Applied times-frac_binary64_315311.6

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

    6. Applied associate-*r*_binary64_30877.0

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

    7. Simplified7.0

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

    9. Applied div-inv_binary64_31447.0

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

    10. Applied associate-*l*_binary64_308811.6

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

    11. Simplified11.0

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

    13. Applied div-inv_binary64_314411.0

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

    14. Applied *-un-lft-identity_binary64_314711.0

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

    15. Applied times-frac_binary64_315311.0

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

    16. Applied associate-*r*_binary64_30873.9

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

    17. Simplified3.8

      \[\leadsto x + \color{blue}{\frac{y - z}{a - z}} \cdot \frac{1}{\frac{1}{t - x}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -6.612935525843224 \cdot 10^{+41}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5.610859612894739 \cdot 10^{-299}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(\frac{a \cdot \left(x \cdot y\right)}{z \cdot z} + \left(\frac{t \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{t \cdot a}{z} + \left(\frac{a \cdot \left(a \cdot \left(x \cdot y\right)\right)}{{z}^{3}} + \left(\left(t + \frac{x \cdot y}{z}\right) + \frac{t}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right) - \left(\frac{x \cdot a}{z} + \left(\frac{x \cdot \left(a \cdot a\right)}{z \cdot z} + \left(\frac{y \cdot t}{z} + \left(\frac{a \cdot \left(a \cdot \left(y \cdot t\right)\right)}{{z}^{3}} + \left(\frac{a \cdot \left(y \cdot t\right)}{z \cdot z} + \frac{x}{{\left(\frac{z}{a}\right)}^{3}}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 4.523655801934687 \cdot 10^{-23}:\\ \;\;\;\;\left(\frac{y \cdot t}{a - z} + \left(x + \frac{x \cdot z}{a - z}\right)\right) - \left(\frac{x \cdot y}{a - z} + \frac{z \cdot t}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 1.9006975675827603 \cdot 10^{+208}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \frac{1}{\frac{1}{t - x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021098 
(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)))))