Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.5 → 6.7

Time: 27.6s

Precision: binary64

Cost: 3533

Math

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

↓

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 10^{-165}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

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 (- INFINITY))
     (+ x (/ 1.0 (/ (- a z) (* (- y z) (- t x)))))
     (if (or (<= t_1 -5e-294) (not (<= t_1 1e-165)))
       t_1
       (+ t (/ (- x t) (/ z (- y a))))))))

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 <= -((double) INFINITY)) {
		tmp = x + (1.0 / ((a - z) / ((y - z) * (t - x))));
	} else if ((t_1 <= -5e-294) || !(t_1 <= 1e-165)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (1.0 / ((a - z) / ((y - z) * (t - x))));
	} else if ((t_1 <= -5e-294) || !(t_1 <= 1e-165)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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 <= -math.inf:
		tmp = x + (1.0 / ((a - z) / ((y - z) * (t - x))))
	elif (t_1 <= -5e-294) or not (t_1 <= 1e-165):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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 <= Float64(-Inf))
		tmp = Float64(x + Float64(1.0 / Float64(Float64(a - z) / Float64(Float64(y - z) * Float64(t - x)))));
	elseif ((t_1 <= -5e-294) || !(t_1 <= 1e-165))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	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 <= -Inf)
		tmp = x + (1.0 / ((a - z) / ((y - z) * (t - x))));
	elseif ((t_1 <= -5e-294) || ~((t_1 <= 1e-165)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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, (-Infinity)], N[(x + N[(1.0 / N[(N[(a - z), $MachinePrecision] / N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-294], N[Not[LessEqual[t$95$1, 1e-165]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $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)))) < -inf.0

   1. Initial program 64.0

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

   2. Applied egg-rr 12.8

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000003e-294 or 1e-165 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 5.4

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

   if -5.0000000000000003e-294 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-165

   1. Initial program 52.4

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

   2. Applied egg-rr 47.8

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

   3. Taylor expanded in z around inf 18.8

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

   4. Simplified 12.1

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

      [Start] 18.8	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      +-commutative [=>] 18.8	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      associate--l+ [=>] 18.8	\[ \color{blue}{t + \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right)} \]
      associate-*r/ [=>] 18.8	\[ t + \left(\color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z}} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z}\right) \]
      associate-*r/ [=>] 18.8	\[ t + \left(\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right)}{z} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}}\right) \]
      div-sub [<=] 18.8	\[ t + \color{blue}{\frac{-1 \cdot \left(y \cdot \left(t - x\right)\right) - -1 \cdot \left(a \cdot \left(t - x\right)\right)}{z}} \]
      distribute-lft-out-- [=>] 18.8	\[ t + \frac{\color{blue}{-1 \cdot \left(y \cdot \left(t - x\right) - a \cdot \left(t - x\right)\right)}}{z} \]
      associate-*r/ [<=] 18.8	\[ t + \color{blue}{-1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 18.8	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 18.8	\[ \color{blue}{t - \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      distribute-rgt-out-- [=>] 18.8	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z} \]
      associate-/l* [=>] 12.1	\[ t - \color{blue}{\frac{t - x}{\frac{z}{y - a}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 6.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot \left(t - x\right)}}\\ \mathbf{elif}\;x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-294} \lor \neg \left(x - \left(y - z\right) \cdot \frac{x - t}{a - z} \leq 10^{-165}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.9
Cost	3533

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -5 \cdot 10^{-294}\right) \land t_1 \leq 10^{-165}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	6.7
Cost	3533

\[\begin{array}{l} t_1 := x - \left(y - z\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-294} \lor \neg \left(t_1 \leq 10^{-165}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3
Error	29.2
Cost	1896

\[\begin{array}{l} t_1 := \frac{t - x}{\frac{z}{a - y}}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := x - \frac{t}{\frac{a - z}{z}}\\ t_4 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-30}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+144}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a - z}\right)\\ \end{array} \]

Alternative 4
Error	29.2
Cost	1896

\[\begin{array}{l} t_1 := \frac{t - x}{\frac{z}{a - y}}\\ t_2 := x - \frac{t}{\frac{a - z}{z}}\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -1.38 \cdot 10^{+125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-30}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+143}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+163}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+259}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a - z}\right)\\ \end{array} \]

Alternative 5
Error	28.0
Cost	1500

\[\begin{array}{l} t_1 := x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-134}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-48}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{+23}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+259}:\\ \;\;\;\;\frac{t - x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{a - z}\right)\\ \end{array} \]

Alternative 6
Error	27.8
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -78000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-131}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-306}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	37.5
Cost	1240

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ t_2 := t + \frac{a}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{-a}{z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.34 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	24.7
Cost	1236

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-201}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	37.5
Cost	1108

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-a}{z}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+87}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	35.3
Cost	1108

\[\begin{array}{l} t_1 := \frac{y}{z} \cdot \left(x - t\right)\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.46:\\ \;\;\;\;t + \frac{t \cdot a}{z}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+103}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	22.1
Cost	1105

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.09:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-18} \lor \neg \left(z \leq 3.5 \cdot 10^{-24}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12
Error	26.8
Cost	1104

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	22.7
Cost	1104

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-41}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-201}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	16.6
Cost	1100

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-18}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;z \leq 0.84:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	16.7
Cost	1100

\[\begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-24}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-6}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	34.0
Cost	844

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+95}:\\ \;\;\;\;t - \frac{x \cdot a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	34.2
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+129} \lor \neg \left(z \leq 2.05 \cdot 10^{+86}\right):\\ \;\;\;\;t + \frac{a}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 18
Error	36.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	62.1
Cost	64

\[0 \]

Alternative 20
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023060 
(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)))))