Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 15.1 → 8.0

Time: 34.8s

Precision: binary64

Cost: 3464

Math

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

↓

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \left(\frac{y}{z - a} + \left(1 - \frac{z}{z - a}\right)\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (+
          (* (- y z) (- (/ t (- z a))))
          (* x (+ (/ y (- z a)) (- 1.0 (/ z (- z a)))))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -4e-188)
     t_1
     (if (<= t_2 0.0) (+ (* (+ -1.0 (/ y z)) (- t)) (* y (/ x 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 = ((y - z) * -(t / (z - a))) + (x * ((y / (z - a)) + (1.0 - (z / (z - a)))));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-188) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((-1.0 + (y / z)) * -t) + (y * (x / z));
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((y - z) * -(t / (z - a))) + (x * ((y / (z - a)) + (1.0d0 - (z / (z - a)))))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-188)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = (((-1.0d0) + (y / z)) * -t) + (y * (x / z))
    else
        tmp = t_1
    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 = ((y - z) * -(t / (z - a))) + (x * ((y / (z - a)) + (1.0 - (z / (z - a)))));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-188) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = ((-1.0 + (y / z)) * -t) + (y * (x / 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 = ((y - z) * -(t / (z - a))) + (x * ((y / (z - a)) + (1.0 - (z / (z - a)))))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-188:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = ((-1.0 + (y / z)) * -t) + (y * (x / 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(Float64(Float64(y - z) * Float64(-Float64(t / Float64(z - a)))) + Float64(x * Float64(Float64(y / Float64(z - a)) + Float64(1.0 - Float64(z / Float64(z - a))))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-188)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(-1.0 + Float64(y / z)) * Float64(-t)) + Float64(y * Float64(x / 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 = ((y - z) * -(t / (z - a))) + (x * ((y / (z - a)) + (1.0 - (z / (z - a)))));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-188)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = ((-1.0 + (y / z)) * -t) + (y * (x / 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[(N[(N[(y - z), $MachinePrecision] * (-N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision] + N[(x * N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(1.0 - N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-188], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision] + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999998e-188 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 6.9

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

   2. Simplified 6.9

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

      [Start] 6.9	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 6.9	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-12 [=>] 6.9	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{0 - \left(t - x\right)}}{z - a} \]
      rational.json-simplify-45 [=>] 6.9	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{x - \left(t - 0\right)}}{z - a} \]
      rational.json-simplify-5 [=>] 6.9	\[ x + \left(y - z\right) \cdot \frac{x - \color{blue}{t}}{z - a} \]

   3. Taylor expanded in x around 0 14.2

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

   4. Simplified 5.1

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

      [Start] 14.2	\[ -1 \cdot \frac{t \cdot \left(y - z\right)}{z - a} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-49 [=>] 5.9	\[ -1 \cdot \color{blue}{\left(\left(y - z\right) \cdot \frac{t}{z - a}\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-43 [=>] 5.9	\[ \color{blue}{\left(y - z\right) \cdot \left(\frac{t}{z - a} \cdot -1\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-9 [=>] 5.9	\[ \left(y - z\right) \cdot \color{blue}{\left(-\frac{t}{z - a}\right)} + \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right) \cdot x \]
      rational.json-simplify-2 [=>] 5.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + \color{blue}{x \cdot \left(\left(\frac{y}{z - a} + 1\right) - \frac{z}{z - a}\right)} \]
      rational.json-simplify-1 [=>] 5.9	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \left(\color{blue}{\left(1 + \frac{y}{z - a}\right)} - \frac{z}{z - a}\right) \]
      rational.json-simplify-48 [=>] 5.1	\[ \left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \color{blue}{\left(\frac{y}{z - a} + \left(1 - \frac{z}{z - a}\right)\right)} \]

   if -3.9999999999999998e-188 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 55.7

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

   2. Simplified 55.8

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

      [Start] 55.7	\[ x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
      rational.json-simplify-50 [=>] 55.7	\[ x + \left(y - z\right) \cdot \color{blue}{\frac{-\left(t - x\right)}{z - a}} \]
      rational.json-simplify-8 [=>] 55.7	\[ x + \left(y - z\right) \cdot \frac{\color{blue}{\left(t - x\right) \cdot -1}}{z - a} \]
      rational.json-simplify-49 [=>] 55.7	\[ x + \left(y - z\right) \cdot \color{blue}{\left(-1 \cdot \frac{t - x}{z - a}\right)} \]
      rational.json-simplify-43 [<=] 55.7	\[ x + \color{blue}{\frac{t - x}{z - a} \cdot \left(\left(y - z\right) \cdot -1\right)} \]
      rational.json-simplify-5 [<=] 55.7	\[ x + \frac{t - x}{\color{blue}{\left(z - a\right) - 0}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-50 [=>] 55.7	\[ x + \color{blue}{\frac{-\left(t - x\right)}{0 - \left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-12 [<=] 55.7	\[ x + \frac{-\left(t - x\right)}{\color{blue}{-\left(z - a\right)}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-10 [=>] 55.7	\[ x + \frac{-\left(t - x\right)}{\color{blue}{\frac{z - a}{-1}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-61 [=>] 55.7	\[ x + \color{blue}{\frac{-1}{\frac{z - a}{-\left(t - x\right)}}} \cdot \left(\left(y - z\right) \cdot -1\right) \]
      rational.json-simplify-9 [=>] 55.7	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\left(-\left(y - z\right)\right)} \]
      rational.json-simplify-10 [=>] 55.7	\[ x + \frac{-1}{\frac{z - a}{-\left(t - x\right)}} \cdot \color{blue}{\frac{y - z}{-1}} \]
      rational.json-simplify-55 [=>] 55.8	\[ x + \color{blue}{\frac{\frac{y - z}{-1}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}}} \]
      rational.json-simplify-10 [<=] 55.8	\[ x + \frac{\color{blue}{-\left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-12 [=>] 55.8	\[ x + \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-45 [=>] 55.8	\[ x + \frac{\color{blue}{z - \left(y - 0\right)}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-5 [=>] 55.8	\[ x + \frac{z - \color{blue}{y}}{\frac{\frac{z - a}{-\left(t - x\right)}}{-1}} \]
      rational.json-simplify-46 [<=] 55.8	\[ x + \frac{z - y}{\color{blue}{\frac{z - a}{\left(-\left(t - x\right)\right) \cdot -1}}} \]
      rational.json-simplify-2 [=>] 55.8	\[ x + \frac{z - y}{\frac{z - a}{\color{blue}{-1 \cdot \left(-\left(t - x\right)\right)}}} \]
      rational.json-simplify-46 [=>] 55.8	\[ x + \frac{z - y}{\color{blue}{\frac{\frac{z - a}{-1}}{-\left(t - x\right)}}} \]
      rational.json-simplify-10 [<=] 55.8	\[ x + \frac{z - y}{\frac{\color{blue}{-\left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 55.8	\[ x + \frac{z - y}{\frac{\color{blue}{0 - \left(z - a\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-45 [=>] 55.8	\[ x + \frac{z - y}{\frac{\color{blue}{a - \left(z - 0\right)}}{-\left(t - x\right)}} \]
      rational.json-simplify-5 [=>] 55.8	\[ x + \frac{z - y}{\frac{a - \color{blue}{z}}{-\left(t - x\right)}} \]
      rational.json-simplify-12 [=>] 55.8	\[ x + \frac{z - y}{\frac{a - z}{\color{blue}{0 - \left(t - x\right)}}} \]

   3. Taylor expanded in z around inf 45.5

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

   4. Simplified 42.4

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

      [Start] 45.5	\[ \left(-1 \cdot \left(x - t\right) + \left(\frac{y \cdot \left(x - t\right)}{z} + x\right)\right) - \frac{a \cdot \left(x - t\right)}{z} \]
      rational.json-simplify-1 [=>] 45.5	\[ \left(-1 \cdot \left(x - t\right) + \color{blue}{\left(x + \frac{y \cdot \left(x - t\right)}{z}\right)}\right) - \frac{a \cdot \left(x - t\right)}{z} \]
      rational.json-simplify-41 [=>] 45.5	\[ \color{blue}{\left(x + \left(\frac{y \cdot \left(x - t\right)}{z} + -1 \cdot \left(x - t\right)\right)\right)} - \frac{a \cdot \left(x - t\right)}{z} \]
      rational.json-simplify-49 [=>] 45.3	\[ \left(x + \left(\color{blue}{\left(x - t\right) \cdot \frac{y}{z}} + -1 \cdot \left(x - t\right)\right)\right) - \frac{a \cdot \left(x - t\right)}{z} \]
      rational.json-simplify-51 [=>] 45.4	\[ \left(x + \color{blue}{\left(x - t\right) \cdot \left(-1 + \frac{y}{z}\right)}\right) - \frac{a \cdot \left(x - t\right)}{z} \]
      rational.json-simplify-49 [=>] 42.4	\[ \left(x + \left(x - t\right) \cdot \left(-1 + \frac{y}{z}\right)\right) - \color{blue}{\left(x - t\right) \cdot \frac{a}{z}} \]

   5. Taylor expanded in a around 0 57.0

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

   6. Taylor expanded in x around 0 26.2

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

   7. Simplified 22.6

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

      [Start] 26.2	\[ \frac{y \cdot x}{z} + -1 \cdot \left(\left(\frac{y}{z} - 1\right) \cdot t\right) \]
      rational.json-simplify-1 [=>] 26.2	\[ \color{blue}{-1 \cdot \left(\left(\frac{y}{z} - 1\right) \cdot t\right) + \frac{y \cdot x}{z}} \]
      rational.json-simplify-15 [<=] 26.2	\[ -1 \cdot \left(\color{blue}{\left(\frac{y}{z} + -1\right)} \cdot t\right) + \frac{y \cdot x}{z} \]
      rational.json-simplify-43 [=>] 26.2	\[ \color{blue}{\left(\frac{y}{z} + -1\right) \cdot \left(t \cdot -1\right)} + \frac{y \cdot x}{z} \]
      rational.json-simplify-1 [=>] 26.2	\[ \color{blue}{\left(-1 + \frac{y}{z}\right)} \cdot \left(t \cdot -1\right) + \frac{y \cdot x}{z} \]
      rational.json-simplify-9 [=>] 26.2	\[ \left(-1 + \frac{y}{z}\right) \cdot \color{blue}{\left(-t\right)} + \frac{y \cdot x}{z} \]
      rational.json-simplify-2 [=>] 26.2	\[ \left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + \frac{\color{blue}{x \cdot y}}{z} \]
      rational.json-simplify-49 [=>] 22.6	\[ \left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + \color{blue}{y \cdot \frac{x}{z}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 8.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -4 \cdot 10^{-188}:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \left(\frac{y}{z - a} + \left(1 - \frac{z}{z - a}\right)\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \left(-\frac{t}{z - a}\right) + x \cdot \left(\frac{y}{z - a} + \left(1 - \frac{z}{z - a}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	9.0
Cost	4172

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a} + \left(-1 \cdot \frac{z \cdot \left(x - t\right)}{z - a} + x\right)\\ \end{array} \]

Alternative 2
Error	9.9
Cost	3660

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{z}{a - z} + 1\right) - \frac{y}{a - z}\right) \cdot x\\ \end{array} \]

Alternative 3
Error	10.7
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-268}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4
Error	10.0
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right) + x \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5
Error	10.0
Cost	3532

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(-1 + \frac{y}{z}\right) \cdot \left(-t\right) + y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6
Error	19.3
Cost	1364

\[\begin{array}{l} t_1 := t - \frac{a}{z} \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-305}:\\ \;\;\;\;x + \frac{z - y}{\frac{z - a}{t}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-244}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-192}:\\ \;\;\;\;x + \frac{z - y}{\frac{a - z}{x}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+194}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	25.8
Cost	1300

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -22500000000000:\\ \;\;\;\;x + \left(-\frac{z - y}{a}\right) \cdot t\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{-\frac{a}{t}}\\ \end{array} \]

Alternative 8
Error	36.4
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	30.8
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+130}:\\ \;\;\;\;x + \left(-t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	30.8
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+131}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+112}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	30.7
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+133}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+111}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	29.5
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{+21}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	29.2
Cost	1240

\[\begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+139}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;x + t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -1.88 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-175}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	25.9
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{t}{a} \cdot \left(y - z\right)\\ t_2 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -2000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-69}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	25.9
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{t}{a} \cdot \left(y - z\right)\\ t_2 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -7600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-70}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	25.8
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -11000000000000:\\ \;\;\;\;x + \left(-\frac{z - y}{a}\right) \cdot t\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-67}:\\ \;\;\;\;t - \frac{a \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{a} \cdot \left(y - z\right)\\ \end{array} \]

Alternative 17
Error	18.5
Cost	1100

\[\begin{array}{l} t_1 := x + t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-192}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \frac{a}{z} \cdot \left(x - t\right)\\ \end{array} \]

Alternative 18
Error	26.5
Cost	972

\[\begin{array}{l} t_1 := x + \frac{t}{a} \cdot \left(y - z\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+148}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	26.8
Cost	840

\[\begin{array}{l} t_1 := x + \frac{t}{a} \cdot \left(y - z\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	33.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -9.7 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	28.7
Cost	712

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	28.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-89}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 23
Error	36.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.7 \cdot 10^{-66}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	45.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023074 
(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)))))