Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.4 → 4.2

Time: 53.2s

Precision: binary64

Cost: 3916

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(\left(t_2 + 1\right) - \frac{y}{a - z}\right) \cdot x + -1 \cdot \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;\left(-y \cdot \frac{x - t}{a - z}\right) + \left(x + \left(x - t\right) \cdot t_2\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \left(-a\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{z - a}}{\frac{1}{x - t}}\\ \end{array} \]

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) (/ (- t x) (- a z))))) (t_2 (/ z (- a z))))
   (if (<= t_1 (- INFINITY))
     (+ (* (- (+ t_2 1.0) (/ y (- a z))) x) (* -1.0 (/ (* t (- z y)) (- a z))))
     (if (<= t_1 -2e-302)
       (+ (- (* y (/ (- x t) (- a z)))) (+ x (* (- x t) t_2)))
       (if (<= t_1 0.0)
         (+ (* (- y z) (- (/ t (- z a)))) (* (+ y (- a)) (/ x z)))
         (+ x (/ (/ (- y z) (- z a)) (/ 1.0 (- x t)))))))))

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) * ((t - x) / (a - z)));
	double t_2 = z / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((t_2 + 1.0) - (y / (a - z))) * x) + (-1.0 * ((t * (z - y)) / (a - z)));
	} else if (t_1 <= -2e-302) {
		tmp = -(y * ((x - t) / (a - z))) + (x + ((x - t) * t_2));
	} else if (t_1 <= 0.0) {
		tmp = ((y - z) * -(t / (z - a))) + ((y + -a) * (x / z));
	} else {
		tmp = x + (((y - z) / (z - a)) / (1.0 / (x - t)));
	}
	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) * ((t - x) / (a - z)));
	double t_2 = z / (a - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((t_2 + 1.0) - (y / (a - z))) * x) + (-1.0 * ((t * (z - y)) / (a - z)));
	} else if (t_1 <= -2e-302) {
		tmp = -(y * ((x - t) / (a - z))) + (x + ((x - t) * t_2));
	} else if (t_1 <= 0.0) {
		tmp = ((y - z) * -(t / (z - a))) + ((y + -a) * (x / z));
	} else {
		tmp = x + (((y - z) / (z - a)) / (1.0 / (x - t)));
	}
	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) * ((t - x) / (a - z)))
	t_2 = z / (a - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((t_2 + 1.0) - (y / (a - z))) * x) + (-1.0 * ((t * (z - y)) / (a - z)))
	elif t_1 <= -2e-302:
		tmp = -(y * ((x - t) / (a - z))) + (x + ((x - t) * t_2))
	elif t_1 <= 0.0:
		tmp = ((y - z) * -(t / (z - a))) + ((y + -a) * (x / z))
	else:
		tmp = x + (((y - z) / (z - a)) / (1.0 / (x - t)))
	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(t - x) / Float64(a - z))))
	t_2 = Float64(z / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(t_2 + 1.0) - Float64(y / Float64(a - z))) * x) + Float64(-1.0 * Float64(Float64(t * Float64(z - y)) / Float64(a - z))));
	elseif (t_1 <= -2e-302)
		tmp = Float64(Float64(-Float64(y * Float64(Float64(x - t) / Float64(a - z)))) + Float64(x + Float64(Float64(x - t) * t_2)));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(y - z) * Float64(-Float64(t / Float64(z - a)))) + Float64(Float64(y + Float64(-a)) * Float64(x / z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - z) / Float64(z - a)) / Float64(1.0 / Float64(x - t))));
	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) * ((t - x) / (a - z)));
	t_2 = z / (a - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((t_2 + 1.0) - (y / (a - z))) * x) + (-1.0 * ((t * (z - y)) / (a - z)));
	elseif (t_1 <= -2e-302)
		tmp = -(y * ((x - t) / (a - z))) + (x + ((x - t) * t_2));
	elseif (t_1 <= 0.0)
		tmp = ((y - z) * -(t / (z - a))) + ((y + -a) * (x / z));
	else
		tmp = x + (((y - z) / (z - a)) / (1.0 / (x - t)));
	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[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(t$95$2 + 1.0), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(-1.0 * N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-302], N[((-N[(y * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(x + N[(N[(x - t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(y - z), $MachinePrecision] * (-N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] + N[(N[(y + (-a)), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] / N[(1.0 / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 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. Simplified 58.6

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

      [Start] 64.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 64.0	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-8 [=>] 64.0	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{\left(t - x\right) \cdot -1}}{z - a} \]
      rational.json-simplify-49 [=>] 64.0	\[ x + \left(y - z\right) \cdot \color{blue}{\left(-1 \cdot \frac{t - x}{z - a}\right)} \]
      rational.json-simplify-43 [<=] 64.0	\[ x + \color{blue}{\frac{t - x}{z - a} \cdot \left(\left(y - z\right) \cdot -1\right)} \]
      rational.json-simplify-5 [<=] 64.0	\[ x + \frac{t - x}{\color{blue}{\left(z - a\right) - 0}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-50 [=>] 64.0	\[ x + \color{blue}{\frac{-\left(t - x\right)}{0 - \left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-12 [<=] 64.0	\[ x + \frac{-\left(t - x\right)}{\color{blue}{-\left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-10 [=>] 64.0	\[ x + \frac{-\left(t - x\right)}{\color{blue}{\frac{z - a}{-1}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-61 [=>] 64.0	\[ x + \color{blue}{\frac{-1}{\frac{z - a}{-\left(t - x\right)}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-9 [=>] 64.0	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\left(-\left(y - z\right)\right)} \]
      rational.json-simplify-10 [=>] 64.0	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\frac{y - z}{-1}} \]
      rational.json-simplify-55 [=>] 58.6	\[ x + \color{blue}{\frac{\frac{y - z}{-1}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}}} \]
      rational.json-simplify-10 [<=] 58.6	\[ x + \frac{\color{blue}{-\left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-12 [=>] 58.6	\[ x + \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-45 [=>] 58.6	\[ x + \frac{\color{blue}{z - \left(y - 0\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-5 [=>] 58.6	\[ x + \frac{z - \color{blue}{y}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-46 [<=] 58.6	\[ x + \frac{z - y}{\color{blue}{\frac{z - a}{\left(-\left(t - x\right)\right) \cdot -1}}} \]
      rational.json-simplify-2 [=>] 58.6	\[ x + \frac{z - y}{\frac{z - a}{\color{blue}{-1 \cdot \left(-\left(t - x\right)\right)}}} \]
      rational.json-simplify-46 [=>] 58.6	\[ x + \frac{z - y}{\color{blue}{\frac{\frac{z - a}{-1}}{-\left(t - x\right)}}} \]
      rational.json-simplify-10 [<=] 58.6	\[ x + \frac{z - y}{\frac{\color{blue}{-\left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 58.6	\[ x + \frac{z - y}{\frac{\color{blue}{0 - \left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-45 [=>] 58.6	\[ x + \frac{z - y}{\frac{\color{blue}{a - \left(z - 0\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-5 [=>] 58.6	\[ x + \frac{z - y}{\frac{a - \color{blue}{z}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 58.6	\[ x + \frac{z - y}{\frac{a - z}{\color{blue}{0 - \left(t - x\right)}}} \]

   3. Taylor expanded in x around 0 4.2

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.9999999999999999e-302

   1. Initial program 5.6

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

   2. Simplified 5.8

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

      [Start] 5.6	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 5.6	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-8 [=>] 5.6	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{\left(t - x\right) \cdot -1}}{z - a} \]
      rational.json-simplify-49 [=>] 5.6	\[ x + \left(y - z\right) \cdot \color{blue}{\left(-1 \cdot \frac{t - x}{z - a}\right)} \]
      rational.json-simplify-43 [<=] 5.6	\[ x + \color{blue}{\frac{t - x}{z - a} \cdot \left(\left(y - z\right) \cdot -1\right)} \]
      rational.json-simplify-5 [<=] 5.6	\[ x + \frac{t - x}{\color{blue}{\left(z - a\right) - 0}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-50 [=>] 5.6	\[ x + \color{blue}{\frac{-\left(t - x\right)}{0 - \left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-12 [<=] 5.6	\[ x + \frac{-\left(t - x\right)}{\color{blue}{-\left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-10 [=>] 5.6	\[ x + \frac{-\left(t - x\right)}{\color{blue}{\frac{z - a}{-1}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-61 [=>] 5.8	\[ x + \color{blue}{\frac{-1}{\frac{z - a}{-\left(t - x\right)}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-9 [=>] 5.8	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\left(-\left(y - z\right)\right)} \]
      rational.json-simplify-10 [=>] 5.8	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\frac{y - z}{-1}} \]
      rational.json-simplify-55 [=>] 5.8	\[ x + \color{blue}{\frac{\frac{y - z}{-1}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}}} \]
      rational.json-simplify-10 [<=] 5.8	\[ x + \frac{\color{blue}{-\left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-12 [=>] 5.8	\[ x + \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-45 [=>] 5.8	\[ x + \frac{\color{blue}{z - \left(y - 0\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-5 [=>] 5.8	\[ x + \frac{z - \color{blue}{y}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-46 [<=] 5.8	\[ x + \frac{z - y}{\color{blue}{\frac{z - a}{\left(-\left(t - x\right)\right) \cdot -1}}} \]
      rational.json-simplify-2 [=>] 5.8	\[ x + \frac{z - y}{\frac{z - a}{\color{blue}{-1 \cdot \left(-\left(t - x\right)\right)}}} \]
      rational.json-simplify-46 [=>] 5.8	\[ x + \frac{z - y}{\color{blue}{\frac{\frac{z - a}{-1}}{-\left(t - x\right)}}} \]
      rational.json-simplify-10 [<=] 5.8	\[ x + \frac{z - y}{\frac{\color{blue}{-\left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 5.8	\[ x + \frac{z - y}{\frac{\color{blue}{0 - \left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-45 [=>] 5.8	\[ x + \frac{z - y}{\frac{\color{blue}{a - \left(z - 0\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-5 [=>] 5.8	\[ x + \frac{z - y}{\frac{a - \color{blue}{z}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 5.8	\[ x + \frac{z - y}{\frac{a - z}{\color{blue}{0 - \left(t - x\right)}}} \]

   3. Taylor expanded in y around 0 19.7

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

   4. Simplified 3.7

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

      [Start] 19.7	\[ -1 \cdot \frac{y \cdot \left(x - t\right)}{a - z} + \left(\frac{z \cdot \left(x - t\right)}{a - z} + x\right) \]
      rational.json-simplify-2 [=>] 19.7	\[ \color{blue}{\frac{y \cdot \left(x - t\right)}{a - z} \cdot -1} + \left(\frac{z \cdot \left(x - t\right)}{a - z} + x\right) \]
      rational.json-simplify-9 [=>] 19.7	\[ \color{blue}{\left(-\frac{y \cdot \left(x - t\right)}{a - z}\right)} + \left(\frac{z \cdot \left(x - t\right)}{a - z} + x\right) \]
      rational.json-simplify-2 [=>] 19.7	\[ \left(-\frac{\color{blue}{\left(x - t\right) \cdot y}}{a - z}\right) + \left(\frac{z \cdot \left(x - t\right)}{a - z} + x\right) \]
      rational.json-simplify-49 [=>] 15.3	\[ \left(-\color{blue}{y \cdot \frac{x - t}{a - z}}\right) + \left(\frac{z \cdot \left(x - t\right)}{a - z} + x\right) \]
      rational.json-simplify-1 [=>] 15.3	\[ \left(-y \cdot \frac{x - t}{a - z}\right) + \color{blue}{\left(x + \frac{z \cdot \left(x - t\right)}{a - z}\right)} \]
      rational.json-simplify-49 [=>] 3.7	\[ \left(-y \cdot \frac{x - t}{a - z}\right) + \left(x + \color{blue}{\left(x - t\right) \cdot \frac{z}{a - z}}\right) \]

   if -1.9999999999999999e-302 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 61.7

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

   2. Simplified 61.7

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

      [Start] 61.7	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 61.7	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-12 [=>] 61.7	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{0 - \left(t - x\right)}}{z - a} \]
      rational.json-simplify-45 [=>] 61.7	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{x - \left(t - 0\right)}}{z - a} \]
      rational.json-simplify-5 [=>] 61.7	\[ x + \left(y - z\right) \cdot \frac{x - \color{blue}{t}}{z - a} \]

   3. Taylor expanded in x around 0 46.1

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

   4. Simplified 28.1

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

      [Start] 46.1	\[ -1 \cdot \frac{t \cdot \left(y - z\right)}{z - a} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-49 [=>] 46.9	\[ -1 \cdot \color{blue}{\left(\left(y - z\right) \cdot \frac{t}{z - a}\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-43 [=>] 46.9	\[ \color{blue}{\left(y - z\right) \cdot \left(\frac{t}{z - a} \cdot -1\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-9 [=>] 46.9	\[ \left(y - z\right) \cdot \color{blue}{\left(-\frac{t}{z - a}\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-2 [=>] 46.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \color{blue}{x \cdot \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right)} \]
      rational.json-simplify-1 [=>] 46.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \left(\color{blue}{\left(1 + \frac{y}{z - a}\right)} - \frac{z}{z - a}\right) \]
      rational.json-simplify-48 [=>] 28.1	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \color{blue}{\left(\frac{y}{z - a} + \left(1 - \frac{z}{z - a}\right)\right)} \]

   5. Taylor expanded in z around inf 17.9

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

   6. Simplified 6.0

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

      [Start] 17.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \frac{\left(y + -1 \cdot a\right) \cdot x}{z} \]
      rational.json-simplify-2 [=>] 17.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \frac{\color{blue}{x \cdot \left(y + -1 \cdot a\right)}}{z} \]
      rational.json-simplify-49 [=>] 6.0	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \color{blue}{\left(y + -1 \cdot a\right) \cdot \frac{x}{z}} \]
      rational.json-simplify-2 [=>] 6.0	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \color{blue}{a \cdot -1}\right) \cdot \frac{x}{z} \]
      rational.json-simplify-9 [=>] 6.0	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \color{blue}{\left(-a\right)}\right) \cdot \frac{x}{z} \]

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

   1. Initial program 7.0

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

   2. Simplified 7.0

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

      [Start] 7.0	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 7.0	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-12 [=>] 7.0	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{0 - \left(t - x\right)}}{z - a} \]
      rational.json-simplify-45 [=>] 7.0	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{x - \left(t - 0\right)}}{z - a} \]
      rational.json-simplify-5 [=>] 7.0	\[ x + \left(y - z\right) \cdot \frac{x - \color{blue}{t}}{z - a} \]

   3. Applied egg-rr 4.1

      \[\leadsto x + \color{blue}{\frac{\frac{y - z}{z - a}}{\frac{1}{x - t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 4.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;\left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right) \cdot x + -1 \cdot \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-302}:\\ \;\;\;\;\left(-y \cdot \frac{x - t}{a - z}\right) + \left(x + \left(x - t\right) \cdot \frac{z}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \left(-a\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{z - a}}{\frac{1}{x - t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	4.3
Cost	3916

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{1}{x - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{1}{z - a}}{\frac{t_2}{y - z}}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;\left(-y \cdot \frac{x - t}{a - z}\right) + \left(x + \left(x - t\right) \cdot \frac{z}{a - z}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \left(-a\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - z}{z - a}}{t_2}\\ \end{array} \]

Alternative 2
Error	8.8
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-214}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	4.6
Cost	3016

\[\begin{array}{l} t_1 := x + \frac{\frac{y - z}{z - a}}{\frac{1}{x - t}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \left(y + \left(-a\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	9.5
Cost	2760

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x - t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-214}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{\frac{1}{x - t} \cdot \left(a - z\right)}\\ \end{array} \]

Alternative 5
Error	7.0
Cost	2760

\[\begin{array}{l} t_1 := x + \frac{\frac{y - z}{z - a}}{\frac{1}{x - t}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-275}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	9.5
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{z - y}{\frac{a - z}{x - t}}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-214}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	33.8
Cost	1632

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-302}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+80}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	24.9
Cost	1632

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-26}:\\ \;\;\;\;-1 \cdot \frac{t \cdot \left(z - y\right)}{a - z}\\ \mathbf{elif}\;z \leq 0.0265:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;-\frac{y \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+41}:\\ \;\;\;\;\left(x + \left(\left(t - x\right) + 1\right)\right) - 1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+94}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	30.4
Cost	1500

\[\begin{array}{l} t_1 := \left(z - y\right) \cdot \frac{t}{z - a}\\ t_2 := x + \frac{y \cdot t}{a}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t \leq -27000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-279}:\\ \;\;\;\;x - \frac{y \cdot x}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	30.6
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := \left(z - y\right) \cdot \frac{t}{z - a}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-110}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-279}:\\ \;\;\;\;x - \frac{y \cdot x}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	30.6
Cost	1500

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ t_3 := \left(z - y\right) \cdot \frac{t}{z - a}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-111}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-279}:\\ \;\;\;\;x - \frac{y \cdot x}{a}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	24.2
Cost	1500

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-29}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 0.0265:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+21}:\\ \;\;\;\;-\frac{y \cdot \left(x - t\right)}{a - z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+73}:\\ \;\;\;\;x + z \cdot \left(-\frac{t}{a - z}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	33.5
Cost	1240

\[\begin{array}{l} t_1 := \left(1 - \frac{y}{a}\right) \cdot x\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-250}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 40000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	25.5
Cost	1236

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-28}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	24.9
Cost	1236

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-29}:\\ \;\;\;\;\left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	22.0
Cost	1232

\[\begin{array}{l} t_1 := x + t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -41000000000000:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+163}:\\ \;\;\;\;t + a \cdot \frac{t - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \frac{z - y}{a - z}\\ \end{array} \]

Alternative 17
Error	18.2
Cost	1232

\[\begin{array}{l} t_1 := x + t \cdot \frac{z - y}{z - a}\\ t_2 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-97}:\\ \;\;\;\;x + \frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	30.6
Cost	1040

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := \left(\frac{y}{z} - 1\right) \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	32.6
Cost	976

\[\begin{array}{l} t_1 := \left(1 - \frac{y}{a}\right) \cdot x\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-292}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	32.0
Cost	976

\[\begin{array}{l} t_1 := t \cdot \frac{z}{z - a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-249}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	32.6
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+114}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

Alternative 22
Error	18.5
Cost	968

\[\begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a}{z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+153}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	36.0
Cost	844

\[\begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 0.00039:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	37.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25
Error	36.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023064 
(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)))))