Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.0% → 97.0%

Time: 10.5s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{t - z} \end{array} \]

FPCore

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

C

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

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) / (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+28} \lor \neg \left(z \leq 7 \cdot 10^{+174}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.6e-32)
     t_2
     (if (<= z -3.8e-253)
       t_1
       (if (<= z 6e-111)
         (* (- y z) (/ x t))
         (if (<= z 1.05e-62)
           t_1
           (if (<= z 1.95e-41)
             (/ (* x (- y z)) t)
             (if (or (<= z 2.3e+28) (not (<= z 7e+174)))
               t_2
               (/ (* x (- z)) (- t z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.6e-32) {
		tmp = t_2;
	} else if (z <= -3.8e-253) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.05e-62) {
		tmp = t_1;
	} else if (z <= 1.95e-41) {
		tmp = (x * (y - z)) / t;
	} else if ((z <= 2.3e+28) || !(z <= 7e+174)) {
		tmp = t_2;
	} else {
		tmp = (x * -z) / (t - z);
	}
	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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-5.6d-32)) then
        tmp = t_2
    else if (z <= (-3.8d-253)) then
        tmp = t_1
    else if (z <= 6d-111) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.05d-62) then
        tmp = t_1
    else if (z <= 1.95d-41) then
        tmp = (x * (y - z)) / t
    else if ((z <= 2.3d+28) .or. (.not. (z <= 7d+174))) then
        tmp = t_2
    else
        tmp = (x * -z) / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.6e-32) {
		tmp = t_2;
	} else if (z <= -3.8e-253) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.05e-62) {
		tmp = t_1;
	} else if (z <= 1.95e-41) {
		tmp = (x * (y - z)) / t;
	} else if ((z <= 2.3e+28) || !(z <= 7e+174)) {
		tmp = t_2;
	} else {
		tmp = (x * -z) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -5.6e-32:
		tmp = t_2
	elif z <= -3.8e-253:
		tmp = t_1
	elif z <= 6e-111:
		tmp = (y - z) * (x / t)
	elif z <= 1.05e-62:
		tmp = t_1
	elif z <= 1.95e-41:
		tmp = (x * (y - z)) / t
	elif (z <= 2.3e+28) or not (z <= 7e+174):
		tmp = t_2
	else:
		tmp = (x * -z) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5.6e-32)
		tmp = t_2;
	elseif (z <= -3.8e-253)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.05e-62)
		tmp = t_1;
	elseif (z <= 1.95e-41)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif ((z <= 2.3e+28) || !(z <= 7e+174))
		tmp = t_2;
	else
		tmp = Float64(Float64(x * Float64(-z)) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -5.6e-32)
		tmp = t_2;
	elseif (z <= -3.8e-253)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.05e-62)
		tmp = t_1;
	elseif (z <= 1.95e-41)
		tmp = (x * (y - z)) / t;
	elseif ((z <= 2.3e+28) || ~((z <= 7e+174)))
		tmp = t_2;
	else
		tmp = (x * -z) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-32], t$95$2, If[LessEqual[z, -3.8e-253], t$95$1, If[LessEqual[z, 6e-111], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-62], t$95$1, If[LessEqual[z, 1.95e-41], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 2.3e+28], N[Not[LessEqual[z, 7e+174]], $MachinePrecision]], t$95$2, N[(N[(x * (-z)), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-114}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-62}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -3.5e-26)
     t_1
     (if (<= z -1.5e-250)
       (* x (/ y (- t z)))
       (if (<= z 9e-114)
         (* (- y z) (/ x t))
         (if (<= z 1.2e-62)
           (* y (/ x (- t z)))
           (if (<= z 2.6e-40) (* x (/ (- y z) t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.5e-26) {
		tmp = t_1;
	} else if (z <= -1.5e-250) {
		tmp = x * (y / (t - z));
	} else if (z <= 9e-114) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.2e-62) {
		tmp = y * (x / (t - z));
	} else if (z <= 2.6e-40) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = t_1;
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-3.5d-26)) then
        tmp = t_1
    else if (z <= (-1.5d-250)) then
        tmp = x * (y / (t - z))
    else if (z <= 9d-114) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.2d-62) then
        tmp = y * (x / (t - z))
    else if (z <= 2.6d-40) then
        tmp = x * ((y - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.5e-26) {
		tmp = t_1;
	} else if (z <= -1.5e-250) {
		tmp = x * (y / (t - z));
	} else if (z <= 9e-114) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.2e-62) {
		tmp = y * (x / (t - z));
	} else if (z <= 2.6e-40) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -3.5e-26:
		tmp = t_1
	elif z <= -1.5e-250:
		tmp = x * (y / (t - z))
	elif z <= 9e-114:
		tmp = (y - z) * (x / t)
	elif z <= 1.2e-62:
		tmp = y * (x / (t - z))
	elif z <= 2.6e-40:
		tmp = x * ((y - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.5e-26)
		tmp = t_1;
	elseif (z <= -1.5e-250)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 9e-114)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.2e-62)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 2.6e-40)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.5e-26)
		tmp = t_1;
	elseif (z <= -1.5e-250)
		tmp = x * (y / (t - z));
	elseif (z <= 9e-114)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.2e-62)
		tmp = y * (x / (t - z));
	elseif (z <= 2.6e-40)
		tmp = x * ((y - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-26], t$95$1, If[LessEqual[z, -1.5e-250], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-114], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-62], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-40], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -3.7e-23)
     t_2
     (if (<= z -2.9e-249)
       t_1
       (if (<= z 6e-111)
         (* (- y z) (/ x t))
         (if (<= z 1.9e-62)
           t_1
           (if (<= z 3.6e-41) (* x (/ (- y z) t)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.7e-23) {
		tmp = t_2;
	} else if (z <= -2.9e-249) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.9e-62) {
		tmp = t_1;
	} else if (z <= 3.6e-41) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = 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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-3.7d-23)) then
        tmp = t_2
    else if (z <= (-2.9d-249)) then
        tmp = t_1
    else if (z <= 6d-111) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.9d-62) then
        tmp = t_1
    else if (z <= 3.6d-41) then
        tmp = x * ((y - z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -3.7e-23) {
		tmp = t_2;
	} else if (z <= -2.9e-249) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.9e-62) {
		tmp = t_1;
	} else if (z <= 3.6e-41) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -3.7e-23:
		tmp = t_2
	elif z <= -2.9e-249:
		tmp = t_1
	elif z <= 6e-111:
		tmp = (y - z) * (x / t)
	elif z <= 1.9e-62:
		tmp = t_1
	elif z <= 3.6e-41:
		tmp = x * ((y - z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.7e-23)
		tmp = t_2;
	elseif (z <= -2.9e-249)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.9e-62)
		tmp = t_1;
	elseif (z <= 3.6e-41)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.7e-23)
		tmp = t_2;
	elseif (z <= -2.9e-249)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.9e-62)
		tmp = t_1;
	elseif (z <= 3.6e-41)
		tmp = x * ((y - z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e-23], t$95$2, If[LessEqual[z, -2.9e-249], t$95$1, If[LessEqual[z, 6e-111], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-62], t$95$1, If[LessEqual[z, 3.6e-41], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t - z}{y}}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t z) y))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.5e-23)
     t_2
     (if (<= z -1.95e-253)
       t_1
       (if (<= z 6e-111)
         (* (- y z) (/ x t))
         (if (<= z 1.85e-62)
           t_1
           (if (<= z 4.8e-40) (/ (* x (- y z)) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.5e-23) {
		tmp = t_2;
	} else if (z <= -1.95e-253) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.85e-62) {
		tmp = t_1;
	} else if (z <= 4.8e-40) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = 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
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - z) / y)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-1.5d-23)) then
        tmp = t_2
    else if (z <= (-1.95d-253)) then
        tmp = t_1
    else if (z <= 6d-111) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.85d-62) then
        tmp = t_1
    else if (z <= 4.8d-40) then
        tmp = (x * (y - z)) / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - z) / y);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.5e-23) {
		tmp = t_2;
	} else if (z <= -1.95e-253) {
		tmp = t_1;
	} else if (z <= 6e-111) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.85e-62) {
		tmp = t_1;
	} else if (z <= 4.8e-40) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - z) / y)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.5e-23:
		tmp = t_2
	elif z <= -1.95e-253:
		tmp = t_1
	elif z <= 6e-111:
		tmp = (y - z) * (x / t)
	elif z <= 1.85e-62:
		tmp = t_1
	elif z <= 4.8e-40:
		tmp = (x * (y - z)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - z) / y))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.5e-23)
		tmp = t_2;
	elseif (z <= -1.95e-253)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.85e-62)
		tmp = t_1;
	elseif (z <= 4.8e-40)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - z) / y);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.5e-23)
		tmp = t_2;
	elseif (z <= -1.95e-253)
		tmp = t_1;
	elseif (z <= 6e-111)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.85e-62)
		tmp = t_1;
	elseif (z <= 4.8e-40)
		tmp = (x * (y - z)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-23], t$95$2, If[LessEqual[z, -1.95e-253], t$95$1, If[LessEqual[z, 6e-111], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-62], t$95$1, If[LessEqual[z, 4.8e-40], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-59} \lor \neg \left(z \leq 2.3 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e-59) (not (<= z 2.3e-52)))
   (* x (- 1.0 (/ y z)))
   (* y (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-59) || !(z <= 2.3e-52)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y * (x / 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
    real(8) :: tmp
    if ((z <= (-2.1d-59)) .or. (.not. (z <= 2.3d-52))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = y * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-59) || !(z <= 2.3e-52)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e-59) or not (z <= 2.3e-52):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = y * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e-59) || !(z <= 2.3e-52))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.1e-59) || ~((z <= 2.3e-52)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = y * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e-59], N[Not[LessEqual[z, 2.3e-52]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-32} \lor \neg \left(z \leq 3.8 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-32) (not (<= z 3.8e-40)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-32) || !(z <= 3.8e-40)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	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
    real(8) :: tmp
    if ((z <= (-8.8d-32)) .or. (.not. (z <= 3.8d-40))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-32) || !(z <= 3.8e-40)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-32) or not (z <= 3.8e-40):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-32) || !(z <= 3.8e-40))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-32) || ~((z <= 3.8e-40)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-32], N[Not[LessEqual[z, 3.8e-40]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-24} \lor \neg \left(z \leq 3.4 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-24) (not (<= z 3.4e-52)))
   (* x (- 1.0 (/ y z)))
   (* y (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-24) || !(z <= 3.4e-52)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y * (x / (t - z));
	}
	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
    real(8) :: tmp
    if ((z <= (-2d-24)) .or. (.not. (z <= 3.4d-52))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = y * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-24) || !(z <= 3.4e-52)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = y * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-24) or not (z <= 3.4e-52):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = y * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-24) || !(z <= 3.4e-52))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-24) || ~((z <= 3.4e-52)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = y * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-24], N[Not[LessEqual[z, 3.4e-52]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.38e-40) x (if (<= z 1.5e+17) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.38e-40) {
		tmp = x;
	} else if (z <= 1.5e+17) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if (z <= (-1.38d-40)) then
        tmp = x
    else if (z <= 1.5d+17) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.38e-40) {
		tmp = x;
	} else if (z <= 1.5e+17) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.38e-40:
		tmp = x
	elif z <= 1.5e+17:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.38e-40)
		tmp = x;
	elseif (z <= 1.5e+17)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.38e-40)
		tmp = x;
	elseif (z <= 1.5e+17)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.38e-40], x, If[LessEqual[z, 1.5e+17], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e-40) x (if (<= z 1.4e+18) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e-40) {
		tmp = x;
	} else if (z <= 1.4e+18) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if (z <= (-5.9d-40)) then
        tmp = x
    else if (z <= 1.4d+18) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e-40) {
		tmp = x;
	} else if (z <= 1.4e+18) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e-40:
		tmp = x
	elif z <= 1.4e+18:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e-40)
		tmp = x;
	elseif (z <= 1.4e+18)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e-40)
		tmp = x;
	elseif (z <= 1.4e+18)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e-40], x, If[LessEqual[z, 1.4e+18], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 35.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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