Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.7 → 4.2

Time: 29.3s

Precision: binary64

Cost: 2761

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-290} \lor \neg \left(t_1 \leq 5 \cdot 10^{-296}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \left(\left(y - z\right) \cdot \frac{-1}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

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 (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -1e-290) (not (<= t_1 5e-296)))
     (+ x (* (- x t) (* (- y z) (/ -1.0 (- a z)))))
     (+ 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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 5e-296)) {
		tmp = x + ((x - t) * ((y - z) * (-1.0 / (a - z))));
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	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 + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-1d-290)) .or. (.not. (t_1 <= 5d-296))) then
        tmp = x + ((x - t) * ((y - z) * ((-1.0d0) / (a - z))))
    else
        tmp = t + ((x - t) / (z / (y - a)))
    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 + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-290) || !(t_1 <= 5e-296)) {
		tmp = x + ((x - t) * ((y - z) * (-1.0 / (a - z))));
	} 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 + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-290) or not (t_1 <= 5e-296):
		tmp = x + ((x - t) * ((y - z) * (-1.0 / (a - z))))
	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(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -1e-290) || !(t_1 <= 5e-296))
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(y - z) * Float64(-1.0 / Float64(a - z)))));
	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 + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-290) || ~((t_1 <= 5e-296)))
		tmp = x + ((x - t) * ((y - z) * (-1.0 / (a - z))));
	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[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-290], N[Not[LessEqual[t$95$1, 5e-296]], $MachinePrecision]], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(-1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.0000000000000001e-290 or 5.0000000000000003e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 7.3

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

   2. Simplified 19.0

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

      [Start] 7.3	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      associate-*r/ [=>] 19.0	\[ x + \color{blue}{\frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}} \]

   3. Applied egg-rr 4.3

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

   if -1.0000000000000001e-290 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000003e-296

   1. Initial program 60.7

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

   2. Simplified 60.2

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

      [Start] 60.7	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      +-commutative [=>] 60.7	\[ \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x} \]
      fma-def [=>] 60.2	\[ \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]

   3. Taylor expanded in z around -inf 13.0

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

   4. Simplified 3.6

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

      [Start] 13.0	\[ -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z} + t \]
      +-commutative [=>] 13.0	\[ \color{blue}{t + -1 \cdot \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      mul-1-neg [=>] 13.0	\[ t + \color{blue}{\left(-\frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}\right)} \]
      unsub-neg [=>] 13.0	\[ \color{blue}{t - \frac{-1 \cdot \left(a \cdot \left(t - x\right)\right) + y \cdot \left(t - x\right)}{z}} \]
      associate-*r* [=>] 13.0	\[ t - \frac{\color{blue}{\left(-1 \cdot a\right) \cdot \left(t - x\right)} + y \cdot \left(t - x\right)}{z} \]
      distribute-rgt-out [=>] 13.0	\[ t - \frac{\color{blue}{\left(t - x\right) \cdot \left(-1 \cdot a + y\right)}}{z} \]
      associate-/l* [=>] 3.6	\[ t - \color{blue}{\frac{t - x}{\frac{z}{-1 \cdot a + y}}} \]
      +-commutative [=>] 3.6	\[ t - \frac{t - x}{\frac{z}{\color{blue}{y + -1 \cdot a}}} \]
      mul-1-neg [=>] 3.6	\[ t - \frac{t - x}{\frac{z}{y + \color{blue}{\left(-a\right)}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 4.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -1 \cdot 10^{-290} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 5 \cdot 10^{-296}\right):\\ \;\;\;\;x + \left(x - t\right) \cdot \left(\left(y - z\right) \cdot \frac{-1}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.6
Cost	4432

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-296}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	6.4
Cost	3533

\[\begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x - \frac{t \cdot \left(z - y\right)}{a}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-290} \lor \neg \left(t_1 \leq 5 \cdot 10^{-296}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 3
Error	26.7
Cost	2556

\[\begin{array}{l} t_1 := t - \frac{y}{\frac{z}{t - x}}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ t_3 := x - \frac{t}{\frac{a - z}{z}}\\ t_4 := x - \frac{y}{a} \cdot \left(x - t\right)\\ t_5 := \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{+170}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a - z}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-51}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-46}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+65}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+179}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Error	26.5
Cost	2160

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t - \frac{y}{\frac{z}{t - x}}\\ t_3 := x - \frac{t}{\frac{a - z}{z}}\\ t_4 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+65}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+177}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	32.1
Cost	1832

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1800000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-204}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-245}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	32.6
Cost	1636

\[\begin{array}{l} t_1 := \frac{y - a}{\frac{z}{x}}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+123}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1550000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-204}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-252}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	28.1
Cost	1632

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq -1.28 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x + \frac{y}{-\frac{a}{x}}\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-247}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+85}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]

Alternative 8
Error	22.6
Cost	1501

\[\begin{array}{l} t_1 := x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+87} \lor \neg \left(a \leq 1.95 \cdot 10^{+122}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 9
Error	16.7
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	14.7
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	14.2
Cost	1496

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+67}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-63}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(z - y\right) \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	25.1
Cost	1369

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.75 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-249}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-13} \lor \neg \left(a \leq 3.3 \cdot 10^{+87}\right) \land a \leq 1.7 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	25.4
Cost	1369

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-247}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-13} \lor \neg \left(a \leq 7 \cdot 10^{+87}\right) \land a \leq 8 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 14
Error	22.7
Cost	1368

\[\begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+75}:\\ \;\;\;\;x - \frac{t}{\frac{a - z}{z}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-93}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-105}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{t - x}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 15
Error	32.4
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1400000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Error	32.6
Cost	1244

\[\begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+66}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1750000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-246}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Error	32.6
Cost	1244

\[\begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1450000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-204}:\\ \;\;\;\;x - y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-251}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	20.7
Cost	1236

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2000000000:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -1.96 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-14}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	16.6
Cost	1232

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a - z}{y - z}}\\ t_2 := t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	32.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21
Error	35.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 22
Error	45.3
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023018 
(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)))))