Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.5 → 7.6

Time: 54.5s

Precision: binary64

Cost: 3916

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(-\frac{t \cdot z}{a - z}\right) + x\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(t + \left(-\frac{\left(t - x\right) \cdot y}{z}\right)\right) - \left(-\frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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))))))
   (if (<= t_1 (- INFINITY))
     (+ (- (/ (* t z) (- a z))) x)
     (if (<= t_1 -5e-209)
       t_1
       (if (<= t_1 0.0)
         (- (+ t (- (/ (* (- t x) y) z))) (- (/ (* (- t x) a) z)))
         t_1)))))

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 tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -((t * z) / (a - z)) + x;
	} else if (t_1 <= -5e-209) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t + -(((t - x) * y) / z)) - -(((t - x) * a) / z);
	} else {
		tmp = t_1;
	}
	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 tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -((t * z) / (a - z)) + x;
	} else if (t_1 <= -5e-209) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t + -(((t - x) * y) / z)) - -(((t - x) * a) / z);
	} else {
		tmp = t_1;
	}
	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)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -((t * z) / (a - z)) + x
	elif t_1 <= -5e-209:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t + -(((t - x) * y) / z)) - -(((t - x) * a) / z)
	else:
		tmp = t_1
	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))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(-Float64(Float64(t * z) / Float64(a - z))) + x);
	elseif (t_1 <= -5e-209)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t + Float64(-Float64(Float64(Float64(t - x) * y) / z))) - Float64(-Float64(Float64(Float64(t - x) * a) / z)));
	else
		tmp = t_1;
	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)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -((t * z) / (a - z)) + x;
	elseif (t_1 <= -5e-209)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t + -(((t - x) * y) / z)) - -(((t - x) * a) / z);
	else
		tmp = t_1;
	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]}, If[LessEqual[t$95$1, (-Infinity)], N[((-N[(N[(t * z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[t$95$1, -5e-209], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision] - (-N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

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. Taylor expanded in t around inf 50.5

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

   3. Taylor expanded in y around 0 35.2

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a - z} + x} \]

   4. Simplified 35.2

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

      [Start] 35.2	\[ -1 \cdot \frac{t \cdot z}{a - z} + x \]
      rational.json-simplify-2 [=>] 35.2	\[ \color{blue}{\frac{t \cdot z}{a - z} \cdot -1} + x \]
      rational.json-simplify-9 [=>] 35.2	\[ \color{blue}{\left(-\frac{t \cdot z}{a - z}\right)} + x \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.0000000000000005e-209 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 5.6

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

   if -5.0000000000000005e-209 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 57.4

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

   2. Taylor expanded in z around inf 14.9

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

   3. Simplified 14.9

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

      [Start] 14.9	\[ \left(-1 \cdot \frac{y \cdot \left(t - x\right)}{z} + t\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-1 [=>] 14.9	\[ \color{blue}{\left(t + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}\right)} - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-2 [=>] 14.9	\[ \left(t + \color{blue}{\frac{y \cdot \left(t - x\right)}{z} \cdot -1}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-9 [=>] 14.9	\[ \left(t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)}\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-2 [=>] 14.9	\[ \left(t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot y}}{z}\right)\right) - -1 \cdot \frac{a \cdot \left(t - x\right)}{z} \]
      rational.json-simplify-2 [=>] 14.9	\[ \left(t + \left(-\frac{\left(t - x\right) \cdot y}{z}\right)\right) - \color{blue}{\frac{a \cdot \left(t - x\right)}{z} \cdot -1} \]
      rational.json-simplify-9 [=>] 14.9	\[ \left(t + \left(-\frac{\left(t - x\right) \cdot y}{z}\right)\right) - \color{blue}{\left(-\frac{a \cdot \left(t - x\right)}{z}\right)} \]
      rational.json-simplify-2 [=>] 14.9	\[ \left(t + \left(-\frac{\left(t - x\right) \cdot y}{z}\right)\right) - \left(-\frac{\color{blue}{\left(t - x\right) \cdot a}}{z}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 7.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;\left(-\frac{t \cdot z}{a - z}\right) + x\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-209}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t + \left(-\frac{\left(t - x\right) \cdot y}{z}\right)\right) - \left(-\frac{\left(t - x\right) \cdot a}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.6
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(-\frac{t \cdot z}{a - z}\right) + x\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	27.1
Cost	1632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-179}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a - z}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a} + x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 3
Error	27.2
Cost	1632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-178}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a - z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a} + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 4
Error	20.5
Cost	1496

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \left(1 + \left(-\frac{y - z}{a - z}\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-7}:\\ \;\;\;\;-\frac{z \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 380:\\ \;\;\;\;\left(-\frac{y}{z}\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	33.2
Cost	1436

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a - z}\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+236}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+51}:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a} + x\\ \end{array} \]

Alternative 6
Error	26.2
Cost	1368

\[\begin{array}{l} t_1 := \left(-\frac{t \cdot z}{a - z}\right) + x\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-77}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+164}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 7
Error	20.8
Cost	1368

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-178}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+164}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+223}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 8
Error	16.0
Cost	1296

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-17}:\\ \;\;\;\;x + \frac{\left(t - x\right) \cdot y}{a - z}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-8}:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	31.2
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6200000000000:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+66}:\\ \;\;\;\;\left(1 - \frac{y}{a}\right) \cdot x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	31.1
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -28000000000000:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+65}:\\ \;\;\;\;\left(1 - \frac{y}{a}\right) \cdot x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.1
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9000000000000:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.58 \cdot 10^{-24}:\\ \;\;\;\;-\frac{z \cdot t}{a - z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-294}:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+63}:\\ \;\;\;\;\left(1 - \frac{y}{a}\right) \cdot x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	27.0
Cost	1236

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-126}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a - z}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+65}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a} + x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 13
Error	19.9
Cost	1232

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a - z}\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	30.5
Cost	1172

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+165}:\\ \;\;\;\;\frac{a - y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	30.2
Cost	1104

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a - z}\right)\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a}{z}\\ \end{array} \]

Alternative 16
Error	29.2
Cost	1040

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10:\\ \;\;\;\;\frac{y \cdot t}{a} + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	34.2
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	34.2
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 4.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	31.3
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6200000000000:\\ \;\;\;\;x \cdot \left(1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+61}:\\ \;\;\;\;\left(1 - \frac{y}{a}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	33.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	62.1
Cost	64

\[0 \]

Alternative 23
Error	45.9
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023077 
(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)))))