Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 22.4% → 9.8%

Time: 28.6s

Precision: binary64

Cost: 3272

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t - \frac{a - y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(z - a\right) \cdot \frac{-1}{t - x}} + \left(x - \frac{z}{\frac{a - z}{t - x}}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- y z) (/ (- t x) (- a z)))))

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (- y z) (/ (- x t) (- a z))))))
   (if (<= t_1 -5e-281)
     t_1
     (if (<= t_1 0.0)
       (- t (/ (- a y) (/ z x)))
       (+
        (/ y (* (- z a) (/ -1.0 (- t x))))
        (- x (/ z (/ (- a z) (- t x)))))))))

C

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 t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-281) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t - ((a - y) / (z / x));
	} else {
		tmp = (y / ((z - a) * (-1.0 / (t - x)))) + (x - (z / ((a - z) / (t - x))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y - z) * ((t - x) / (a - z)))
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y - z) * ((x - t) / (a - z)))
    if (t_1 <= (-5d-281)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = t - ((a - y) / (z / x))
    else
        tmp = (y / ((z - a) * ((-1.0d0) / (t - x)))) + (x - (z / ((a - z) / (t - x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y - z) * ((t - x) / (a - z)));
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y - z) * ((x - t) / (a - z)));
	double tmp;
	if (t_1 <= -5e-281) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = t - ((a - y) / (z / x));
	} else {
		tmp = (y / ((z - a) * (-1.0 / (t - x)))) + (x - (z / ((a - z) / (t - x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

↓

def code(x, y, z, t, a):
	t_1 = x - ((y - z) * ((x - t) / (a - z)))
	tmp = 0
	if t_1 <= -5e-281:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = t - ((a - y) / (z / x))
	else:
		tmp = (y / ((z - a) * (-1.0 / (t - x)))) + (x - (z / ((a - z) / (t - x))))
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -5e-281)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(t - Float64(Float64(a - y) / Float64(z / x)));
	else
		tmp = Float64(Float64(y / Float64(Float64(z - a) * Float64(-1.0 / Float64(t - x)))) + Float64(x - Float64(z / Float64(Float64(a - z) / Float64(t - x)))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y - z) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -5e-281)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = t - ((a - y) / (z / x));
	else
		tmp = (y / ((z - a) * (-1.0 / (t - x)))) + (x - (z / ((a - z) / (t - x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-281], t$95$1, If[LessEqual[t$95$1, 0.0], N[(t - N[(N[(a - y), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(N[(z - a), $MachinePrecision] * N[(-1.0 / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(z / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-281

   1. Initial program 10.82

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

   if -4.9999999999999998e-281 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 94.79

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

   2. Simplified 94.11

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
      Proof

      [Start] 94.79	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 94.79	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 94.11	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 21.05

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

   4. Simplified 5.91

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

      [Start] 21.05	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 21.05	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 21.05	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 21.05	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 21.05	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 21.05	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 5.91	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 5.91	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 5.91	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

   5. Taylor expanded in t around 0 21.02

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

   6. Simplified 3.22

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

      [Start] 21.02	\[ t - -1 \cdot \frac{\left(y - a\right) \cdot x}{z} \]
      mul-1-neg [=>] 21.02	\[ t - \color{blue}{\left(-\frac{\left(y - a\right) \cdot x}{z}\right)} \]
      associate-/l* [=>] 3.22	\[ t - \left(-\color{blue}{\frac{y - a}{\frac{z}{x}}}\right) \]
      distribute-neg-frac [=>] 3.22	\[ t - \color{blue}{\frac{-\left(y - a\right)}{\frac{z}{x}}} \]

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

   1. Initial program 11.54

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

   2. Applied egg-rr 29.72

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

   3. Simplified 15.85

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

      [Start] 29.72	\[ x + \frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{{\left(\sqrt[3]{a - z}\right)}^{2}}}{\sqrt[3]{a - z}} \]
      associate-/l* [=>] 15.85	\[ x + \frac{\color{blue}{\frac{y - z}{\frac{{\left(\sqrt[3]{a - z}\right)}^{2}}{t - x}}}}{\sqrt[3]{a - z}} \]

   4. Applied egg-rr 10.77

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

   5. Applied egg-rr 10.82

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

4. Final simplification 9.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-281}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;t - \frac{a - y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(z - a\right) \cdot \frac{-1}{t - x}} + \left(x - \frac{z}{\frac{a - z}{t - x}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.78%
Cost	3144

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{a - z}{t - x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t - \frac{a - y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t_2} - \left(\frac{z}{t_2} - x\right)\\ \end{array} \]

Alternative 2
Error	10.11%
Cost	2633

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-281} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a - y}{\frac{z}{x}}\\ \end{array} \]

Alternative 3
Error	49.65%
Cost	1636

\[\begin{array}{l} t_1 := t - x \cdot \frac{a}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-232}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-141}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+190}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	49.96%
Cost	1636

\[\begin{array}{l} t_1 := t - x \cdot \frac{a}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a - z}\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+187}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	49.15%
Cost	1372

\[\begin{array}{l} t_1 := t - x \cdot \frac{a}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+191}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	49.05%
Cost	1372

\[\begin{array}{l} t_1 := t - x \cdot \frac{a}{z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-301}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+179}:\\ \;\;\;\;x - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	40.51%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	41.42%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-251}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	38.92%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-253}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	37.77%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-252}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	30.33%
Cost	1236

\[\begin{array}{l} t_1 := \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 - t_1\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-47}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 190000000:\\ \;\;\;\;x + \frac{t}{1 + \frac{y - a}{z}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+134}:\\ \;\;\;\;t \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	39.29%
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	24.18%
Cost	1100

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-115}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	22.64%
Cost	1100

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-114}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	44.15%
Cost	1040

\[\begin{array}{l} t_1 := \frac{-t}{\frac{z}{y - z}}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-301}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	48.7%
Cost	976

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-254}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(1 + \frac{a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	30.75%
Cost	972

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	56.15%
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	30.38%
Cost	841

\[\begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{+19} \lor \neg \left(a \leq 4.8 \cdot 10^{-45}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]

Alternative 20
Error	42.86%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+14} \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;t - x \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 21
Error	56.02%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Error	71.47%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023088 
(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)))))