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

Percentage Accurate: 83.9% → 97.0%

Time: 12.0s

Alternatives: 12

Speedup: 0.6×

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: 83.9% 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, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{\frac{t - z}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.5e-27)
    (/ (* x_m (- y z)) (- t z))
    (/ (- y z) (/ (- t z) x_m)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.5e-27) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 (x_m <= 1.5d-27) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (y - z) / ((t - z) / x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.5e-27) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1.5e-27:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (y - z) / ((t - z) / x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1.5e-27)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(y - z) / Float64(Float64(t - z) / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1.5e-27)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (y - z) / ((t - z) / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1.5e-27], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.5000000000000001e-27

   1. Initial program 92.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   if 1.5000000000000001e-27 < x

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   6. Applied egg-rr 0

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

Alternative 2: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-121}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-38}:\\ \;\;\;\;\frac{x\_m}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -3e-23)
      t_1
      (if (<= z 3.8e-121)
        (/ (* x_m y) t)
        (if (<= z 4.8e-97) t_1 (if (<= z 3e-38) (/ x_m (/ t y)) t_1)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -3e-23) {
		tmp = t_1;
	} else if (z <= 3.8e-121) {
		tmp = (x_m * y) / t;
	} else if (z <= 4.8e-97) {
		tmp = t_1;
	} else if (z <= 3e-38) {
		tmp = x_m / (t / y);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 = x_m * (1.0d0 - (y / z))
    if (z <= (-3d-23)) then
        tmp = t_1
    else if (z <= 3.8d-121) then
        tmp = (x_m * y) / t
    else if (z <= 4.8d-97) then
        tmp = t_1
    else if (z <= 3d-38) then
        tmp = x_m / (t / y)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -3e-23) {
		tmp = t_1;
	} else if (z <= 3.8e-121) {
		tmp = (x_m * y) / t;
	} else if (z <= 4.8e-97) {
		tmp = t_1;
	} else if (z <= 3e-38) {
		tmp = x_m / (t / y);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -3e-23:
		tmp = t_1
	elif z <= 3.8e-121:
		tmp = (x_m * y) / t
	elif z <= 4.8e-97:
		tmp = t_1
	elif z <= 3e-38:
		tmp = x_m / (t / y)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3e-23)
		tmp = t_1;
	elseif (z <= 3.8e-121)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 4.8e-97)
		tmp = t_1;
	elseif (z <= 3e-38)
		tmp = Float64(x_m / Float64(t / y));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3e-23)
		tmp = t_1;
	elseif (z <= 3.8e-121)
		tmp = (x_m * y) / t;
	elseif (z <= 4.8e-97)
		tmp = t_1;
	elseif (z <= 3e-38)
		tmp = x_m / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3e-23], t$95$1, If[LessEqual[z, 3.8e-121], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.8e-97], t$95$1, If[LessEqual[z, 3e-38], N[(x$95$m / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000003e-23 or 3.8000000000000001e-121 < z < 4.8e-97 or 2.99999999999999989e-38 < z

   1. Initial program 81.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -3.00000000000000003e-23 < z < 3.8000000000000001e-121

   1. Initial program 95.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 4.8e-97 < z < 2.99999999999999989e-38

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 3: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -6000000.0)
      t_1
      (if (<= z 2.15e-36) (/ (* x_m (- y z)) t) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -6000000.0) {
		tmp = t_1;
	} else if (z <= 2.15e-36) {
		tmp = (x_m * (y - z)) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 = x_m * (1.0d0 - (y / z))
    if (z <= (-6000000.0d0)) then
        tmp = t_1
    else if (z <= 2.15d-36) then
        tmp = (x_m * (y - z)) / t
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -6000000.0) {
		tmp = t_1;
	} else if (z <= 2.15e-36) {
		tmp = (x_m * (y - z)) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -6000000.0:
		tmp = t_1
	elif z <= 2.15e-36:
		tmp = (x_m * (y - z)) / t
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6000000.0)
		tmp = t_1;
	elseif (z <= 2.15e-36)
		tmp = Float64(Float64(x_m * Float64(y - z)) / t);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6000000.0)
		tmp = t_1;
	elseif (z <= 2.15e-36)
		tmp = (x_m * (y - z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6000000.0], t$95$1, If[LessEqual[z, 2.15e-36], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6e6 or 2.1500000000000001e-36 < z

   1. Initial program 79.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -6e6 < z < 2.1500000000000001e-36

   1. Initial program 96.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 4: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-33}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -3e-22) t_1 (if (<= z 1.85e-33) (/ (* x_m y) (- t z)) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -3e-22) {
		tmp = t_1;
	} else if (z <= 1.85e-33) {
		tmp = (x_m * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 = x_m * (1.0d0 - (y / z))
    if (z <= (-3d-22)) then
        tmp = t_1
    else if (z <= 1.85d-33) then
        tmp = (x_m * y) / (t - z)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -3e-22) {
		tmp = t_1;
	} else if (z <= 1.85e-33) {
		tmp = (x_m * y) / (t - z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -3e-22:
		tmp = t_1
	elif z <= 1.85e-33:
		tmp = (x_m * y) / (t - z)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3e-22)
		tmp = t_1;
	elseif (z <= 1.85e-33)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3e-22)
		tmp = t_1;
	elseif (z <= 1.85e-33)
		tmp = (x_m * y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3e-22], t$95$1, If[LessEqual[z, 1.85e-33], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e-22 or 1.85000000000000007e-33 < z

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.9999999999999999e-22 < z < 1.85000000000000007e-33

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(1 - \frac{y}{z}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -130000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-34}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x\_m}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -130000000.0)
      t_1
      (if (<= z 9.6e-34) (* (- y z) (/ x_m t)) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -130000000.0) {
		tmp = t_1;
	} else if (z <= 9.6e-34) {
		tmp = (y - z) * (x_m / t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 = x_m * (1.0d0 - (y / z))
    if (z <= (-130000000.0d0)) then
        tmp = t_1
    else if (z <= 9.6d-34) then
        tmp = (y - z) * (x_m / t)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -130000000.0) {
		tmp = t_1;
	} else if (z <= 9.6e-34) {
		tmp = (y - z) * (x_m / t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -130000000.0:
		tmp = t_1
	elif z <= 9.6e-34:
		tmp = (y - z) * (x_m / t)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -130000000.0)
		tmp = t_1;
	elseif (z <= 9.6e-34)
		tmp = Float64(Float64(y - z) * Float64(x_m / t));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -130000000.0)
		tmp = t_1;
	elseif (z <= 9.6e-34)
		tmp = (y - z) * (x_m / t);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -130000000.0], t$95$1, If[LessEqual[z, 9.6e-34], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e8 or 9.59999999999999965e-34 < z

   1. Initial program 79.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -1.3e8 < z < 9.59999999999999965e-34

   1. Initial program 96.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

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

Alternative 6: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-23}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -7.8e-23) x_m (if (<= z 1.7e-33) (/ (* x_m y) t) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-23) {
		tmp = x_m;
	} else if (z <= 1.7e-33) {
		tmp = (x_m * y) / t;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 <= (-7.8d-23)) then
        tmp = x_m
    else if (z <= 1.7d-33) then
        tmp = (x_m * y) / t
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-23) {
		tmp = x_m;
	} else if (z <= 1.7e-33) {
		tmp = (x_m * y) / t;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -7.8e-23:
		tmp = x_m
	elif z <= 1.7e-33:
		tmp = (x_m * y) / t
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -7.8e-23)
		tmp = x_m;
	elseif (z <= 1.7e-33)
		tmp = Float64(Float64(x_m * y) / t);
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e-23)
		tmp = x_m;
	elseif (z <= 1.7e-33)
		tmp = (x_m * y) / t;
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -7.8e-23], x$95$m, If[LessEqual[z, 1.7e-33], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e-23 or 1.7e-33 < z

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -7.8e-23 < z < 1.7e-33

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-23}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{\frac{t}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -9e-23) x_m (if (<= z 3.5e-34) (/ y (/ t x_m)) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -9e-23) {
		tmp = x_m;
	} else if (z <= 3.5e-34) {
		tmp = y / (t / x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 <= (-9d-23)) then
        tmp = x_m
    else if (z <= 3.5d-34) then
        tmp = y / (t / x_m)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -9e-23) {
		tmp = x_m;
	} else if (z <= 3.5e-34) {
		tmp = y / (t / x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -9e-23:
		tmp = x_m
	elif z <= 3.5e-34:
		tmp = y / (t / x_m)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -9e-23)
		tmp = x_m;
	elseif (z <= 3.5e-34)
		tmp = Float64(y / Float64(t / x_m));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -9e-23)
		tmp = x_m;
	elseif (z <= 3.5e-34)
		tmp = y / (t / x_m);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -9e-23], x$95$m, If[LessEqual[z, 3.5e-34], N[(y / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999995e-23 or 3.5e-34 < z

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -8.9999999999999995e-23 < z < 3.5e-34

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   10. Simplified 0

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

Alternative 8: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-22}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 10^{-33}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -2e-22) x_m (if (<= z 1e-33) (* x_m (/ y t)) x_m))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -2e-22) {
		tmp = x_m;
	} else if (z <= 1e-33) {
		tmp = x_m * (y / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 <= (-2d-22)) then
        tmp = x_m
    else if (z <= 1d-33) then
        tmp = x_m * (y / t)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -2e-22) {
		tmp = x_m;
	} else if (z <= 1e-33) {
		tmp = x_m * (y / t);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -2e-22:
		tmp = x_m
	elif z <= 1e-33:
		tmp = x_m * (y / t)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -2e-22)
		tmp = x_m;
	elseif (z <= 1e-33)
		tmp = Float64(x_m * Float64(y / t));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -2e-22)
		tmp = x_m;
	elseif (z <= 1e-33)
		tmp = x_m * (y / t);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -2e-22], x$95$m, If[LessEqual[z, 1e-33], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-22 or 1.0000000000000001e-33 < z

   1. Initial program 80.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.0000000000000001e-22 < z < 1.0000000000000001e-33

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 9: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.65 \cdot 10^{+41}:\\ \;\;\;\;\frac{x\_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1.65e+41)
    (/ (* x_m (- y z)) (- t z))
    (* (/ x_m (- t z)) (- y z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.65e+41) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 (x_m <= 1.65d+41) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (x_m / (t - z)) * (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1.65e+41) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1.65e+41:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (x_m / (t - z)) * (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1.65e+41)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1.65e+41)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (x_m / (t - z)) * (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1.65e+41], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.65e41

   1. Initial program 92.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   if 1.65e41 < x

   1. Initial program 69.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

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

Alternative 10: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 10^{-10}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 1e-10) (* (/ (- y z) (- t z)) x_m) (* (/ x_m (- t z)) (- y z)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e-10) {
		tmp = ((y - z) / (t - z)) * x_m;
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 (x_m <= 1d-10) then
        tmp = ((y - z) / (t - z)) * x_m
    else
        tmp = (x_m / (t - z)) * (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (x_m <= 1e-10) {
		tmp = ((y - z) / (t - z)) * x_m;
	} else {
		tmp = (x_m / (t - z)) * (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if x_m <= 1e-10:
		tmp = ((y - z) / (t - z)) * x_m
	else:
		tmp = (x_m / (t - z)) * (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (x_m <= 1e-10)
		tmp = Float64(Float64(Float64(y - z) / Float64(t - z)) * x_m);
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (x_m <= 1e-10)
		tmp = ((y - z) / (t - z)) * x_m;
	else
		tmp = (x_m / (t - z)) * (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[x$95$m, 1e-10], N[(N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000004e-10

   1. Initial program 92.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.00000000000000004e-10 < x

   1. Initial program 74.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

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

Alternative 11: 88.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 9.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z 9.4e+157) (* (/ x_m (- t z)) (- y z)) (* x_m (- 1.0 (/ y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 9.4e+157) {
		tmp = (x_m / (t - z)) * (y - z);
	} else {
		tmp = x_m * (1.0 - (y / z));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    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 <= 9.4d+157) then
        tmp = (x_m / (t - z)) * (y - z)
    else
        tmp = x_m * (1.0d0 - (y / z))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= 9.4e+157) {
		tmp = (x_m / (t - z)) * (y - z);
	} else {
		tmp = x_m * (1.0 - (y / z));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= 9.4e+157:
		tmp = (x_m / (t - z)) * (y - z)
	else:
		tmp = x_m * (1.0 - (y / z))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= 9.4e+157)
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(y - z));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= 9.4e+157)
		tmp = (x_m / (t - z)) * (y - z);
	else
		tmp = x_m * (1.0 - (y / z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, 9.4e+157], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 9.40000000000000061e157

   1. Initial program 88.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 9.40000000000000061e157 < z

   1. Initial program 81.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 12: 35.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot x\_m \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * x_m
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * x_m;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 87.9%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Add Preprocessing

3. Taylor expanded in z around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 96.5% 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 2024110 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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