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

Average Error: 2.1 → 1.2

Time: 5.0s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(\frac{x}{z - y} - \frac{y}{z - y}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-272}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

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))))
   (if (<= t_1 -1e-121)
     (* t (- (/ x (- z y)) (/ y (- z y))))
     (if (<= t_1 2e-272)
       (* (- x y) (/ t (- z y)))
       (/ t (/ (- z y) (- x y)))))))

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 tmp;
	if (t_1 <= -1e-121) {
		tmp = t * ((x / (z - y)) - (y / (z - y)));
	} else if (t_1 <= 2e-272) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((z - y) / (x - y));
	}
	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) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-1d-121)) then
        tmp = t * ((x / (z - y)) - (y / (z - y)))
    else if (t_1 <= 2d-272) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / ((z - y) / (x - y))
    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 tmp;
	if (t_1 <= -1e-121) {
		tmp = t * ((x / (z - y)) - (y / (z - y)));
	} else if (t_1 <= 2e-272) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((z - y) / (x - y));
	}
	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)
	tmp = 0
	if t_1 <= -1e-121:
		tmp = t * ((x / (z - y)) - (y / (z - y)))
	elif t_1 <= 2e-272:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / ((z - y) / (x - y))
	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))
	tmp = 0.0
	if (t_1 <= -1e-121)
		tmp = Float64(t * Float64(Float64(x / Float64(z - y)) - Float64(y / Float64(z - y))));
	elseif (t_1 <= 2e-272)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(z - y) / Float64(x - y)));
	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);
	tmp = 0.0;
	if (t_1 <= -1e-121)
		tmp = t * ((x / (z - y)) - (y / (z - y)));
	elseif (t_1 <= 2e-272)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / ((z - y) / (x - y));
	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]}, If[LessEqual[t$95$1, -1e-121], N[(t * N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-272], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.1
Herbie	1.2

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.9999999999999998e-122

   1. Initial program 2.6

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

   2. Taylor expanded in x around 0 10.7

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

   3. Taylor expanded in t around 0 2.6

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

   4. Simplified 2.6

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

   if -9.9999999999999998e-122 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999986e-272

   1. Initial program 8.4

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

   2. Applied egg-rr 9.3

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

   3. Applied egg-rr 1.4

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

   if 1.99999999999999986e-272 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 0.8

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

   2. Applied egg-rr 0.7

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

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t \cdot \left(\frac{x}{z - y} - \frac{y}{z - y}\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-272}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022170 
(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))