Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 23.23% → 9.32%

Time: 24.1s

Precision: binary64

Cost: 3789

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-211} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

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) (/ (- t x) (- a z))))))
   (if (<= t_1 -1e+306)
     (+ x (* (/ 1.0 (- a z)) (* (- y z) (- t x))))
     (if (or (<= t_1 -2e-211) (not (<= t_1 0.0)))
       t_1
       (+ (+ t (* (- t x) (/ a z))) (* (/ y z) (- 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 tmp;
	if (t_1 <= -1e+306) {
		tmp = x + ((1.0 / (a - z)) * ((y - z) * (t - x)));
	} else if ((t_1 <= -2e-211) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (t + ((t - x) * (a / z))) + ((y / z) * (x - t));
	}
	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) * ((t - x) / (a - z)))
    if (t_1 <= (-1d+306)) then
        tmp = x + ((1.0d0 / (a - z)) * ((y - z) * (t - x)))
    else if ((t_1 <= (-2d-211)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = t_1
    else
        tmp = (t + ((t - x) * (a / z))) + ((y / z) * (x - t))
    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) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x + ((1.0 / (a - z)) * ((y - z) * (t - x)));
	} else if ((t_1 <= -2e-211) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = (t + ((t - x) * (a / z))) + ((y / z) * (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)))
	tmp = 0
	if t_1 <= -1e+306:
		tmp = x + ((1.0 / (a - z)) * ((y - z) * (t - x)))
	elif (t_1 <= -2e-211) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = (t + ((t - x) * (a / z))) + ((y / z) * (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))))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(a - z)) * Float64(Float64(y - z) * Float64(t - x))));
	elseif ((t_1 <= -2e-211) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(t + Float64(Float64(t - x) * Float64(a / z))) + Float64(Float64(y / z) * 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)));
	tmp = 0.0;
	if (t_1 <= -1e+306)
		tmp = x + ((1.0 / (a - z)) * ((y - z) * (t - x)));
	elseif ((t_1 <= -2e-211) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = (t + ((t - x) * (a / z))) + ((y / z) * (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]}, If[LessEqual[t$95$1, -1e+306], N[(x + N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e-211], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(N[(t + N[(N[(t - x), $MachinePrecision] * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(x - t), $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)))) < -1.00000000000000002e306

   1. Initial program 89.45

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

   2. Simplified 23.21

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

      [Start] 89.45	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      associate-*r/ [=>] 23.21	\[ x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

   3. Applied egg-rr 23.3

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

   if -1.00000000000000002e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000017e-211 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 8.9

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

   if -2.00000000000000017e-211 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 89.06

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

   2. Simplified 88.58

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

      [Start] 89.06	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 89.06	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 88.58	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around inf 23.5

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

   4. Simplified 9.91

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

      [Start] 23.5	\[ -1 \cdot \frac{y \cdot \left(t - x\right)}{z} + \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) \]
      +-commutative [=>] 23.5	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + -1 \cdot \frac{y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 23.5	\[ \left(t + \frac{a \cdot \left(t - x\right)}{z}\right) + \color{blue}{\left(-\frac{y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 23.5	\[ \color{blue}{\left(t + \frac{a \cdot \left(t - x\right)}{z}\right) - \frac{y \cdot \left(t - x\right)}{z}} \]
      associate-*l/ [<=] 17.79	\[ \left(t + \color{blue}{\frac{a}{z} \cdot \left(t - x\right)}\right) - \frac{y \cdot \left(t - x\right)}{z} \]
      associate-*l/ [<=] 9.91	\[ \left(t + \frac{a}{z} \cdot \left(t - x\right)\right) - \color{blue}{\frac{y}{z} \cdot \left(t - x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 9.32

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-211} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\left(t + \left(t - x\right) \cdot \frac{a}{z}\right) + \frac{y}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.34%
Cost	3533

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-211} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2
Error	10.52%
Cost	2633

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-211} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3
Error	45.56%
Cost	1897

\[\begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t \leq -112000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-131}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-112}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-37}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+142} \lor \neg \left(t \leq 1.8 \cdot 10^{+166}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{z}{-a}\\ \end{array} \]

Alternative 4
Error	37.83%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.66 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+54}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	37.8%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	37.41%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+142}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.00125:\\ \;\;\;\;x + \frac{t}{1 - \frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	37.46%
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.0014:\\ \;\;\;\;x + \frac{t}{1 + \frac{y - a}{z}}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	30.36%
Cost	1232

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.66 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+132}:\\ \;\;\;\;x + \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 9
Error	22.6%
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-146}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	39.51%
Cost	1105

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-93} \lor \neg \left(z \leq 5.3 \cdot 10^{-37}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11
Error	35.79%
Cost	1105

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-92} \lor \neg \left(z \leq 1.7 \cdot 10^{-33}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12
Error	52.91%
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	45.28%
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	44.59%
Cost	908

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-64}:\\ \;\;\;\;x + t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \end{array} \]

Alternative 15
Error	44.26%
Cost	844

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -48000000000000:\\ \;\;\;\;z \cdot \left(-\frac{t}{a - z}\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	44.59%
Cost	844

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-65}:\\ \;\;\;\;x + t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	55.88%
Cost	716

\[\begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	44.11%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+64} \lor \neg \left(z \leq 2.9 \cdot 10^{-11}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 19
Error	55.5%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20
Error	71.08%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(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)))))