Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Average Error: 2.2 → 1.3

Time: 6.7s

Precision: binary64

Math

\[\frac{x - y}{z - y} \cdot t \]

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y}\\ \mathbf{if}\;t_1 \leq -3.5609834547508955 \cdot 10^{-167}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \mathbf{elif}\;t_1 \leq 1.59977091405 \cdot 10^{-313}:\\ \;\;\;\;x \cdot t_2 - y \cdot t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ (- x y) (- z y)) t))

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ t (- z y))))
   (if (<= t_1 -3.5609834547508955e-167)
     (/ t (- (/ z (- x y)) (/ y (- x y))))
     (if (<= t_1 1.59977091405e-313) (- (* x t_2) (* y t_2)) (* t_1 t)))))

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t / (z - y);
	double tmp;
	if (t_1 <= -3.5609834547508955e-167) {
		tmp = t / ((z / (x - y)) - (y / (x - y)));
	} else if (t_1 <= 1.59977091405e-313) {
		tmp = (x * t_2) - (y * t_2);
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t / (z - y)
    if (t_1 <= (-3.5609834547508955d-167)) then
        tmp = t / ((z / (x - y)) - (y / (x - y)))
    else if (t_1 <= 1.59977091405d-313) then
        tmp = (x * t_2) - (y * t_2)
    else
        tmp = t_1 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * t;
}

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t / (z - y);
	double tmp;
	if (t_1 <= -3.5609834547508955e-167) {
		tmp = t / ((z / (x - y)) - (y / (x - y)));
	} else if (t_1 <= 1.59977091405e-313) {
		tmp = (x * t_2) - (y * t_2);
	} else {
		tmp = t_1 * t;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t / (z - y)
	tmp = 0
	if t_1 <= -3.5609834547508955e-167:
		tmp = t / ((z / (x - y)) - (y / (x - y)))
	elif t_1 <= 1.59977091405e-313:
		tmp = (x * t_2) - (y * t_2)
	else:
		tmp = t_1 * t
	return tmp

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x - y) / Float64(z - y)) * t)
end

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -3.5609834547508955e-167)
		tmp = Float64(t / Float64(Float64(z / Float64(x - y)) - Float64(y / Float64(x - y))));
	elseif (t_1 <= 1.59977091405e-313)
		tmp = Float64(Float64(x * t_2) - Float64(y * t_2));
	else
		tmp = Float64(t_1 * t);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t / (z - y);
	tmp = 0.0;
	if (t_1 <= -3.5609834547508955e-167)
		tmp = t / ((z / (x - y)) - (y / (x - y)));
	elseif (t_1 <= 1.59977091405e-313)
		tmp = (x * t_2) - (y * t_2);
	else
		tmp = t_1 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -3.5609834547508955e-167], N[(t / N[(N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1.59977091405e-313], N[(N[(x * t$95$2), $MachinePrecision] - N[(y * t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * t), $MachinePrecision]]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.2
Herbie	1.3

\[\frac{t}{\frac{z - y}{x - y}} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -3.56098345475089546e-167

   1. Initial program 2.5

      \[\frac{x - y}{z - y} \cdot t \]

   2. Applied egg-rr 2.2

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

   3. Taylor expanded in z around 0 2.2

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

   if -3.56098345475089546e-167 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.59977091405e-313

   1. Initial program 10.4

      \[\frac{x - y}{z - y} \cdot t \]

   2. Applied egg-rr 11.5

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

   3. Applied egg-rr 1.0

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

   if 1.59977091405e-313 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 1.0

      \[\frac{x - y}{z - y} \cdot t \]

   2. Applied egg-rr 0.9

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

   3. Applied egg-rr 1.0

      \[\leadsto \color{blue}{\frac{t}{1} \cdot \frac{x - y}{z - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -3.5609834547508955 \cdot 10^{-167}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y} - \frac{y}{x - y}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1.59977091405 \cdot 10^{-313}:\\ \;\;\;\;x \cdot \frac{t}{z - y} - y \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array} \]

Reproduce

herbie shell --seed 2022150 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))