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

Average Error: 2.2 → 2.4

Time: 7.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t}{z - y}\\ t_2 := \frac{x - y}{z - y}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-260}:\\ \;\;\;\;\frac{t}{{t_2}^{-1}}\\ \mathbf{elif}\;y \leq 4.860029108699026 \cdot 10^{-62}:\\ \;\;\;\;x \cdot t_1 - y \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- z y))) (t_2 (/ (- x y) (- z y))))
   (if (<= y -1e-260)
     (/ t (pow t_2 -1.0))
     (if (<= y 4.860029108699026e-62) (- (* x t_1) (* y t_1)) (* t t_2)))))

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 = t / (z - y);
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (y <= -1e-260) {
		tmp = t / pow(t_2, -1.0);
	} else if (y <= 4.860029108699026e-62) {
		tmp = (x * t_1) - (y * t_1);
	} else {
		tmp = t * t_2;
	}
	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 = t / (z - y)
    t_2 = (x - y) / (z - y)
    if (y <= (-1d-260)) then
        tmp = t / (t_2 ** (-1.0d0))
    else if (y <= 4.860029108699026d-62) then
        tmp = (x * t_1) - (y * t_1)
    else
        tmp = t * t_2
    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 = t / (z - y);
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (y <= -1e-260) {
		tmp = t / Math.pow(t_2, -1.0);
	} else if (y <= 4.860029108699026e-62) {
		tmp = (x * t_1) - (y * t_1);
	} else {
		tmp = t * t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = t / (z - y)
	t_2 = (x - y) / (z - y)
	tmp = 0
	if y <= -1e-260:
		tmp = t / math.pow(t_2, -1.0)
	elif y <= 4.860029108699026e-62:
		tmp = (x * t_1) - (y * t_1)
	else:
		tmp = t * t_2
	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(t / Float64(z - y))
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (y <= -1e-260)
		tmp = Float64(t / (t_2 ^ -1.0));
	elseif (y <= 4.860029108699026e-62)
		tmp = Float64(Float64(x * t_1) - Float64(y * t_1));
	else
		tmp = Float64(t * t_2);
	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 = t / (z - y);
	t_2 = (x - y) / (z - y);
	tmp = 0.0;
	if (y <= -1e-260)
		tmp = t / (t_2 ^ -1.0);
	elseif (y <= 4.860029108699026e-62)
		tmp = (x * t_1) - (y * t_1);
	else
		tmp = t * t_2;
	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[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-260], N[(t / N[Power[t$95$2, -1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.860029108699026e-62], N[(N[(x * t$95$1), $MachinePrecision] - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision], N[(t * t$95$2), $MachinePrecision]]]]]

Target

Original	2.2
Target	2.2
Herbie	2.4

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

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999961e-261

   1. Initial program 1.9

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

   2. Applied egg-rr 1.9

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

   3. Applied egg-rr 2.1

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

   if -9.99999999999999961e-261 < y < 4.86002910869902591e-62

   1. Initial program 5.6

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

   2. Applied egg-rr 5.6

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

   3. Applied egg-rr 6.2

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

   if 4.86002910869902591e-62 < y

   1. Initial program 0.3

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

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-260}:\\ \;\;\;\;\frac{t}{{\left(\frac{x - y}{z - y}\right)}^{-1}}\\ \mathbf{elif}\;y \leq 4.860029108699026 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \frac{t}{z - y} - y \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z - y}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(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))