Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Percentage Accurate: 67.3% → 97.3%

Time: 12.9s

Alternatives: 8

Speedup: 1.1×

• 48.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 * x) / (y * y)) + ((z * z) / (t * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * x) / (y * y)) + ((z * z) / (t * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} t_1 := \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{if}\;x\_m \leq 4.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{x\_m}{\frac{y}{\frac{x\_m}{y}}} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{\frac{y}{x\_m}}}{y} + t\_1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ z t) (/ t z))))
   (if (<= x_m 4.2e-271)
     (+ (/ x_m (/ y (/ x_m y))) t_1)
     (+ (/ (/ x_m (/ y x_m)) y) t_1))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double t_1 = (z / t) / (t / z);
	double tmp;
	if (x_m <= 4.2e-271) {
		tmp = (x_m / (y / (x_m / y))) + t_1;
	} else {
		tmp = ((x_m / (y / x_m)) / y) + t_1;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / t) / (t / z)
    if (x_m <= 4.2d-271) then
        tmp = (x_m / (y / (x_m / y))) + t_1
    else
        tmp = ((x_m / (y / x_m)) / y) + t_1
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double t_1 = (z / t) / (t / z);
	double tmp;
	if (x_m <= 4.2e-271) {
		tmp = (x_m / (y / (x_m / y))) + t_1;
	} else {
		tmp = ((x_m / (y / x_m)) / y) + t_1;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	t_1 = (z / t) / (t / z)
	tmp = 0
	if x_m <= 4.2e-271:
		tmp = (x_m / (y / (x_m / y))) + t_1
	else:
		tmp = ((x_m / (y / x_m)) / y) + t_1
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	t_1 = Float64(Float64(z / t) / Float64(t / z))
	tmp = 0.0
	if (x_m <= 4.2e-271)
		tmp = Float64(Float64(x_m / Float64(y / Float64(x_m / y))) + t_1);
	else
		tmp = Float64(Float64(Float64(x_m / Float64(y / x_m)) / y) + t_1);
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	t_1 = (z / t) / (t / z);
	tmp = 0.0;
	if (x_m <= 4.2e-271)
		tmp = (x_m / (y / (x_m / y))) + t_1;
	else
		tmp = ((x_m / (y / x_m)) / y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$95$m, 4.2e-271], N[(N[(x$95$m / N[(y / N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(x$95$m / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4.2000000000000001e-271

   1. Initial program 66.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.2000000000000001e-271 < x

   1. Initial program 80.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   8. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \frac{x\_m}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+157}:\\ \;\;\;\;x\_m \cdot \frac{\frac{x\_m}{y}}{y} + \frac{z \cdot z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{-\frac{t}{z} \cdot \left(0 - t\right)}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= z 1.6e-132)
   (* (/ x_m y) (/ x_m y))
   (if (<= z 7.5e+157)
     (+ (* x_m (/ (/ x_m y) y)) (/ (* z z) (* t t)))
     (/ z (- (* (/ t z) (- 0.0 t)))))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 1.6e-132) {
		tmp = (x_m / y) * (x_m / y);
	} else if (z <= 7.5e+157) {
		tmp = (x_m * ((x_m / y) / y)) + ((z * z) / (t * t));
	} else {
		tmp = z / -((t / z) * (0.0 - t));
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.6d-132) then
        tmp = (x_m / y) * (x_m / y)
    else if (z <= 7.5d+157) then
        tmp = (x_m * ((x_m / y) / y)) + ((z * z) / (t * t))
    else
        tmp = z / -((t / z) * (0.0d0 - t))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 1.6e-132) {
		tmp = (x_m / y) * (x_m / y);
	} else if (z <= 7.5e+157) {
		tmp = (x_m * ((x_m / y) / y)) + ((z * z) / (t * t));
	} else {
		tmp = z / -((t / z) * (0.0 - t));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if z <= 1.6e-132:
		tmp = (x_m / y) * (x_m / y)
	elif z <= 7.5e+157:
		tmp = (x_m * ((x_m / y) / y)) + ((z * z) / (t * t))
	else:
		tmp = z / -((t / z) * (0.0 - t))
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (z <= 1.6e-132)
		tmp = Float64(Float64(x_m / y) * Float64(x_m / y));
	elseif (z <= 7.5e+157)
		tmp = Float64(Float64(x_m * Float64(Float64(x_m / y) / y)) + Float64(Float64(z * z) / Float64(t * t)));
	else
		tmp = Float64(z / Float64(-Float64(Float64(t / z) * Float64(0.0 - t))));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if (z <= 1.6e-132)
		tmp = (x_m / y) * (x_m / y);
	elseif (z <= 7.5e+157)
		tmp = (x_m * ((x_m / y) / y)) + ((z * z) / (t * t));
	else
		tmp = z / -((t / z) * (0.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[z, 1.6e-132], N[(N[(x$95$m / y), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+157], N[(N[(x$95$m * N[(N[(x$95$m / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / (-N[(N[(t / z), $MachinePrecision] * N[(0.0 - t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 1.6000000000000001e-132

   1. Initial program 69.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.6000000000000001e-132 < z < 7.5e157

   1. Initial program 81.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   if 7.5e157 < z

   1. Initial program 66.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{+224}:\\ \;\;\;\;x\_m \cdot \frac{\frac{x\_m}{y}}{y} + \frac{\frac{z}{t} \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{-\frac{t}{z} \cdot \left(0 - t\right)}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= z 5.6e+224)
   (+ (* x_m (/ (/ x_m y) y)) (/ (* (/ z t) z) t))
   (/ z (- (* (/ t z) (- 0.0 t))))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 5.6e+224) {
		tmp = (x_m * ((x_m / y) / y)) + (((z / t) * z) / t);
	} else {
		tmp = z / -((t / z) * (0.0 - t));
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 5.6d+224) then
        tmp = (x_m * ((x_m / y) / y)) + (((z / t) * z) / t)
    else
        tmp = z / -((t / z) * (0.0d0 - t))
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 5.6e+224) {
		tmp = (x_m * ((x_m / y) / y)) + (((z / t) * z) / t);
	} else {
		tmp = z / -((t / z) * (0.0 - t));
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if z <= 5.6e+224:
		tmp = (x_m * ((x_m / y) / y)) + (((z / t) * z) / t)
	else:
		tmp = z / -((t / z) * (0.0 - t))
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (z <= 5.6e+224)
		tmp = Float64(Float64(x_m * Float64(Float64(x_m / y) / y)) + Float64(Float64(Float64(z / t) * z) / t));
	else
		tmp = Float64(z / Float64(-Float64(Float64(t / z) * Float64(0.0 - t))));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if (z <= 5.6e+224)
		tmp = (x_m * ((x_m / y) / y)) + (((z / t) * z) / t);
	else
		tmp = z / -((t / z) * (0.0 - t));
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[z, 5.6e+224], N[(N[(x$95$m * N[(N[(x$95$m / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(z / t), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(z / (-N[(N[(t / z), $MachinePrecision] * N[(0.0 - t), $MachinePrecision]), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.60000000000000016e224

   1. Initial program 72.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   6. Applied egg-rr 0

      \[\leadsto expr\]

   if 5.60000000000000016e224 < z

   1. Initial program 71.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 20000:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{\frac{y}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 20000.0)
   (/ (/ x_m y) (/ y x_m))
   (* (/ (/ z t) t) z)))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 20000.0) {
		tmp = (x_m / y) / (y / x_m);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 20000.0d0) then
        tmp = (x_m / y) / (y / x_m)
    else
        tmp = ((z / t) / t) * z
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 20000.0) {
		tmp = (x_m / y) / (y / x_m);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 20000.0:
		tmp = (x_m / y) / (y / x_m)
	else:
		tmp = ((z / t) / t) * z
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 20000.0)
		tmp = Float64(Float64(x_m / y) / Float64(y / x_m));
	else
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 20000.0)
		tmp = (x_m / y) / (y / x_m);
	else
		tmp = ((z / t) / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 20000.0], N[(N[(x$95$m / y), $MachinePrecision] / N[(y / x$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e4

   1. Initial program 74.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2e4 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot z}{t \cdot t} \leq 20000:\\ \;\;\;\;\frac{x\_m}{y} \cdot \frac{x\_m}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= (/ (* z z) (* t t)) 20000.0)
   (* (/ x_m y) (/ x_m y))
   (* (/ (/ z t) t) z)))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 20000.0) {
		tmp = (x_m / y) * (x_m / y);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * z) / (t * t)) <= 20000.0d0) then
        tmp = (x_m / y) * (x_m / y)
    else
        tmp = ((z / t) / t) * z
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if (((z * z) / (t * t)) <= 20000.0) {
		tmp = (x_m / y) * (x_m / y);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if ((z * z) / (t * t)) <= 20000.0:
		tmp = (x_m / y) * (x_m / y)
	else:
		tmp = ((z / t) / t) * z
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (Float64(Float64(z * z) / Float64(t * t)) <= 20000.0)
		tmp = Float64(Float64(x_m / y) * Float64(x_m / y));
	else
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if (((z * z) / (t * t)) <= 20000.0)
		tmp = (x_m / y) * (x_m / y);
	else
		tmp = ((z / t) / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[N[(N[(z * z), $MachinePrecision] / N[(t * t), $MachinePrecision]), $MachinePrecision], 20000.0], N[(N[(x$95$m / y), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z z) (*.f64 t t)) < 2e4

   1. Initial program 74.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2e4 < (/.f64 (*.f64 z z) (*.f64 t t))

   1. Initial program 70.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x\_m \cdot \frac{\frac{x\_m}{y}}{y} + \frac{\frac{z}{t}}{\frac{t}{z}} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (+ (* x_m (/ (/ x_m y) y)) (/ (/ z t) (/ t z))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	return (x_m * ((x_m / y) / y)) + ((z / t) / (t / z));
}

Fortran

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

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	return (x_m * ((x_m / y) / y)) + ((z / t) / (t / z));
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	return (x_m * ((x_m / y) / y)) + ((z / t) / (t / z))

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	return Float64(Float64(x_m * Float64(Float64(x_m / y) / y)) + Float64(Float64(z / t) / Float64(t / z)))
end

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := N[(N[(x$95$m * N[(N[(x$95$m / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.1%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 7: 72.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \begin{array}{l} \mathbf{if}\;t \cdot t \leq 2.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{z}{t \cdot t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \frac{x\_m}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t)
 :precision binary64
 (if (<= (* t t) 2.5e+134) (* (/ z (* t t)) z) (* (/ x_m y) (/ x_m y))))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 2.5e+134) {
		tmp = (z / (t * t)) * z;
	} else {
		tmp = (x_m / y) * (x_m / y);
	}
	return tmp;
}

Fortran

x_m = abs(x)
real(8) function code(x_m, y, z, t)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t * t) <= 2.5d+134) then
        tmp = (z / (t * t)) * z
    else
        tmp = (x_m / y) * (x_m / y)
    end if
    code = tmp
end function

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	double tmp;
	if ((t * t) <= 2.5e+134) {
		tmp = (z / (t * t)) * z;
	} else {
		tmp = (x_m / y) * (x_m / y);
	}
	return tmp;
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	tmp = 0
	if (t * t) <= 2.5e+134:
		tmp = (z / (t * t)) * z
	else:
		tmp = (x_m / y) * (x_m / y)
	return tmp

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	tmp = 0.0
	if (Float64(t * t) <= 2.5e+134)
		tmp = Float64(Float64(z / Float64(t * t)) * z);
	else
		tmp = Float64(Float64(x_m / y) * Float64(x_m / y));
	end
	return tmp
end

MATLAB

x_m = abs(x);
function tmp_2 = code(x_m, y, z, t)
	tmp = 0.0;
	if ((t * t) <= 2.5e+134)
		tmp = (z / (t * t)) * z;
	else
		tmp = (x_m / y) * (x_m / y);
	end
	tmp_2 = tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := If[LessEqual[N[(t * t), $MachinePrecision], 2.5e+134], N[(N[(z / N[(t * t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 t t) < 2.4999999999999999e134

   1. Initial program 79.3%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2.4999999999999999e134 < (*.f64 t t)

   1. Initial program 62.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 59.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ \frac{x\_m}{y} \cdot \frac{x\_m}{y} \end{array} \]

FPCore

x_m = (fabs.f64 x)
(FPCore (x_m y z t) :precision binary64 (* (/ x_m y) (/ x_m y)))

C

x_m = fabs(x);
double code(double x_m, double y, double z, double t) {
	return (x_m / y) * (x_m / y);
}

Fortran

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

Java

x_m = Math.abs(x);
public static double code(double x_m, double y, double z, double t) {
	return (x_m / y) * (x_m / y);
}

Python

x_m = math.fabs(x)
def code(x_m, y, z, t):
	return (x_m / y) * (x_m / y)

Julia

x_m = abs(x)
function code(x_m, y, z, t)
	return Float64(Float64(x_m / y) * Float64(x_m / y))
end

MATLAB

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

Wolfram

x_m = N[Abs[x], $MachinePrecision]
code[x$95$m_, y_, z_, t_] := N[(N[(x$95$m / y), $MachinePrecision] * N[(x$95$m / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.1%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around inf 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

9. Applied egg-rr 0

   \[\leadsto expr\]
10. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0)))

C

double code(double x, double y, double z, double t) {
	return pow((x / y), 2.0) + pow((z / t), 2.0);
}

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) ** 2.0d0) + ((z / t) ** 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.pow((x / y), 2.0) + Math.pow((z / t), 2.0);
}

Python

def code(x, y, z, t):
	return math.pow((x / y), 2.0) + math.pow((z / t), 2.0)

Julia

function code(x, y, z, t)
	return Float64((Float64(x / y) ^ 2.0) + (Float64(z / t) ^ 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x / y) ^ 2.0) + ((z / t) ^ 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(z / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (pow (/ x y) 2) (pow (/ z t) 2)))

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