Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.7 → 3.8

Time: 37.9s

Precision: binary64

Cost: 2892

Math

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

↓

\[\begin{array}{l} t_1 := x + \begin{array}{l} \mathbf{if}\;y - z \ne 0:\\ \;\;\;\;\frac{x - t}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - y\right) \cdot \left(t - x\right)}{z - a}\\ \end{array}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
          (if (!= (- y z) 0.0)
            (/ (- x t) (/ (- z a) (- y z)))
            (/ (* (- z y) (- t x)) (- z a)))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -2e-301)
     t_1
     (if (<= t_2 0.0) (+ (- (* (/ (- t x) z) (- y a))) t) 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 tmp;
	if ((y - z) != 0.0) {
		tmp = (x - t) / ((z - a) / (y - z));
	} else {
		tmp = ((z - y) * (t - x)) / (z - a);
	}
	double t_1 = x + tmp;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp_1;
	if (t_2 <= -2e-301) {
		tmp_1 = t_1;
	} else if (t_2 <= 0.0) {
		tmp_1 = -(((t - x) / z) * (y - a)) + t;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

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
    real(8) :: tmp_1
    if ((y - z) /= 0.0d0) then
        tmp = (x - t) / ((z - a) / (y - z))
    else
        tmp = ((z - y) * (t - x)) / (z - a)
    end if
    t_1 = x + tmp
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-2d-301)) then
        tmp_1 = t_1
    else if (t_2 <= 0.0d0) then
        tmp_1 = -(((t - x) / z) * (y - a)) + t
    else
        tmp_1 = t_1
    end if
    code = tmp_1
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 tmp;
	if ((y - z) != 0.0) {
		tmp = (x - t) / ((z - a) / (y - z));
	} else {
		tmp = ((z - y) * (t - x)) / (z - a);
	}
	double t_1 = x + tmp;
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp_1;
	if (t_2 <= -2e-301) {
		tmp_1 = t_1;
	} else if (t_2 <= 0.0) {
		tmp_1 = -(((t - x) / z) * (y - a)) + t;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

Python

def code(x, y, z, t, a):
	return x + ((y - z) * ((t - x) / (a - z)))

↓

def code(x, y, z, t, a):
	tmp = 0
	if (y - z) != 0.0:
		tmp = (x - t) / ((z - a) / (y - z))
	else:
		tmp = ((z - y) * (t - x)) / (z - a)
	t_1 = x + tmp
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp_1 = 0
	if t_2 <= -2e-301:
		tmp_1 = t_1
	elif t_2 <= 0.0:
		tmp_1 = -(((t - x) / z) * (y - a)) + t
	else:
		tmp_1 = t_1
	return tmp_1

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)
	tmp = 0.0
	if (Float64(y - z) != 0.0)
		tmp = Float64(Float64(x - t) / Float64(Float64(z - a) / Float64(y - z)));
	else
		tmp = Float64(Float64(Float64(z - y) * Float64(t - x)) / Float64(z - a));
	end
	t_1 = Float64(x + tmp)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp_1 = 0.0
	if (t_2 <= -2e-301)
		tmp_1 = t_1;
	elseif (t_2 <= 0.0)
		tmp_1 = Float64(Float64(-Float64(Float64(Float64(t - x) / z) * Float64(y - a))) + t);
	else
		tmp_1 = t_1;
	end
	return tmp_1
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y - z) * ((t - x) / (a - z)));
end

↓

function tmp_3 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y - z) ~= 0.0)
		tmp = (x - t) / ((z - a) / (y - z));
	else
		tmp = ((z - y) * (t - x)) / (z - a);
	end
	t_1 = x + tmp;
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp_2 = 0.0;
	if (t_2 <= -2e-301)
		tmp_2 = t_1;
	elseif (t_2 <= 0.0)
		tmp_2 = -(((t - x) / z) * (y - a)) + t;
	else
		tmp_2 = t_1;
	end
	tmp_3 = tmp_2;
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 + If[Unequal[N[(y - z), $MachinePrecision], 0.0], N[(N[(x - t), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(z - a), $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, -2e-301], t$95$1, If[LessEqual[t$95$2, 0.0], N[((-N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]) + t), $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)))) < -2.00000000000000013e-301 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 7.6

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

   2. Applied egg-rr 4.3

      \[\leadsto x + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;y - z \ne 0:\\ \;\;\;\;\frac{x - t}{\frac{z - a}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - y\right) \cdot \left(t - x\right)}{z - a}\\ } \end{array}} \]

   if -2.00000000000000013e-301 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 61.4

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

   2. Taylor expanded in z around -inf 12.6

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

   3. Simplified 12.6

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

   4. Applied egg-rr 0.7

      \[\leadsto \left(-\color{blue}{\frac{t - x}{z} \cdot \left(y - a\right)}\right) + t \]
3. Recombined 2 regimes into one program.

Alternatives

Alternative 1
Error	6.7
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	3.9
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	5.2
Cost	2632

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;x + \begin{array}{l} \mathbf{if}\;x - t \ne 0:\\ \;\;\;\;\frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - y\right) \cdot \left(t - x\right)}{z - a}\\ \end{array}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4
Error	37.5
Cost	1504

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-281}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-219}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+100}:\\ \;\;\;\;\left(1 + \frac{z}{a}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	18.2
Cost	1296

\[\begin{array}{l} t_1 := \left(-\frac{t - x}{z} \cdot \left(y - a\right)\right) + t\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 62000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	17.4
Cost	1296

\[\begin{array}{l} t_1 := \left(-\frac{y - a}{z} \cdot \left(t - x\right)\right) + t\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	37.4
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 68000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+98}:\\ \;\;\;\;\left(1 + \frac{z}{a}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	18.2
Cost	1232

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{x \cdot \left(a - y\right)}{z}\right) + t\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.62:\\ \;\;\;\;\left(-\frac{y}{z} \cdot \left(t - x\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.8
Cost	1168

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;\left(-\frac{x \cdot \left(a - y\right)}{z}\right) + t\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1160:\\ \;\;\;\;\left(-\frac{y}{z} \cdot \left(t - x\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	37.5
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \frac{y - z}{a}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Error	20.1
Cost	904

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 90:\\ \;\;\;\;\left(-\frac{y}{z} \cdot \left(t - x\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	35.2
Cost	844

\[\begin{array}{l} t_1 := \left(1 + \frac{z}{a}\right) \cdot x\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4200:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+172}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	31.4
Cost	840

\[\begin{array}{l} t_1 := \left(-\frac{t \cdot z}{a}\right) + x\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 112000:\\ \;\;\;\;\left(1 - \frac{y - a}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	26.4
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{a} \cdot \left(t - x\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 95:\\ \;\;\;\;\left(1 - \frac{y - a}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	32.6
Cost	776

\[\begin{array}{l} t_1 := \left(-\frac{t \cdot z}{a}\right) + x\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1750:\\ \;\;\;\;t - \frac{y \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	36.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	46.0
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(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)))))