Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.9 → 8.0

Time: 21.7s

Precision: binary64

Cost: 3144

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \left(-\frac{\left(t - x\right) \cdot \left(y - a\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t_1 - \left(z \cdot t_1 - x\right)\\ \end{array} \]

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 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -2e-211)
     t_2
     (if (<= t_2 0.0)
       (+ t (- (/ (* (- t x) (- y a)) z)))
       (- (* y t_1) (- (* z t_1) x))))))

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 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-211) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else {
		tmp = (y * t_1) - ((z * t_1) - x);
	}
	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 = (t - x) / (a - z)
    t_2 = x + ((y - z) * t_1)
    if (t_2 <= (-2d-211)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = t + -(((t - x) * (y - a)) / z)
    else
        tmp = (y * t_1) - ((z * t_1) - x)
    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 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-211) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + -(((t - x) * (y - a)) / z);
	} else {
		tmp = (y * t_1) - ((z * t_1) - x);
	}
	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 = (t - x) / (a - z)
	t_2 = x + ((y - z) * t_1)
	tmp = 0
	if t_2 <= -2e-211:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + -(((t - x) * (y - a)) / z)
	else:
		tmp = (y * t_1) - ((z * t_1) - x)
	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(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-211)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-Float64(Float64(Float64(t - x) * Float64(y - a)) / z)));
	else
		tmp = Float64(Float64(y * t_1) - Float64(Float64(z * t_1) - x));
	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 = (t - x) / (a - z);
	t_2 = x + ((y - z) * t_1);
	tmp = 0.0;
	if (t_2 <= -2e-211)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + -(((t - x) * (y - a)) / z);
	else
		tmp = (y * t_1) - ((z * t_1) - x);
	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[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-211], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + (-N[(N[(N[(t - x), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision], N[(N[(y * t$95$1), $MachinePrecision] - N[(N[(z * t$95$1), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.0

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

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

   1. Initial program 57.0

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

   2. Taylor expanded in z around -inf 15.0

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

   3. Simplified 15.0

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

      [Start] 15.0	\[ -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} + t \]
      rational_best_oopsla_all_46_json_45_simplify-35 [=>] 15.0	\[ \color{blue}{t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 15.0	\[ t + \color{blue}{\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z} \cdot -1} \]
      rational_best_oopsla_all_46_json_45_simplify-92 [=>] 15.0	\[ t + \color{blue}{\left(-\frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 15.0	\[ t + \left(-\frac{y \cdot \left(t - x\right) - \color{blue}{\left(t - x\right) \cdot a}}{z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 15.0	\[ t + \left(-\frac{\color{blue}{\left(t - x\right) \cdot \left(y - a\right)}}{z}\right) \]

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

   1. Initial program 7.5

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

   2. Applied egg-rr 7.3

      \[\leadsto \color{blue}{y \cdot \frac{t - x}{a - z} - \left(z \cdot \frac{t - x}{a - z} - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 8.0

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

Alternatives

Alternative 1
Error	8.1
Cost	2952

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

Alternative 2
Error	8.1
Cost	2632

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

Alternative 3
Error	35.3
Cost	1636

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := \left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -16:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-118}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	35.4
Cost	1636

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ t_2 := \left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -16:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	21.0
Cost	1496

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t + \left(-\frac{y \cdot \left(t - x\right)}{z}\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-134}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \end{array} \]

Alternative 6
Error	27.4
Cost	1368

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5200000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	26.8
Cost	1368

\[\begin{array}{l} t_1 := \frac{y \cdot t}{a - z} + t\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -0.0016:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-10}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a} + x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	31.9
Cost	1304

\[\begin{array}{l} t_1 := x + x \cdot \left(-\frac{y}{a}\right)\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-285}:\\ \;\;\;\;\left(\frac{t}{a} - \frac{x}{a}\right) \cdot y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \end{array} \]

Alternative 9
Error	34.3
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -55000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \end{array} \]

Alternative 10
Error	18.2
Cost	1232

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z} + t\\ \mathbf{if}\;z \leq -1 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-213}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-133}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	36.2
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+110}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -16.5:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-300}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	26.8
Cost	1104

\[\begin{array}{l} t_1 := \frac{y \cdot t}{a - z} + t\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -0.0027:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	27.0
Cost	1104

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-268}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	22.6
Cost	1104

\[\begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-92}:\\ \;\;\;\;t + \left(-\frac{t_1}{z}\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{t_1}{a} + x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	31.7
Cost	1040

\[\begin{array}{l} t_1 := x + x \cdot \left(-\frac{y}{a}\right)\\ t_2 := t \cdot \left(-\frac{z}{a - z}\right)\\ \mathbf{if}\;z \leq -6400000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \end{array} \]

Alternative 16
Error	17.0
Cost	968

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-93}:\\ \;\;\;\;t + \left(-\frac{y \cdot \left(t - x\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	35.7
Cost	844

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-284}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Error	35.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+40}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19
Error	45.5
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)))))