Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.5% → 96.3%

Time: 13.2s

Alternatives: 15

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

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

Initial Program: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

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

Alternative 1: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x\_m}{-1} \cdot \frac{\frac{-2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x\_m}}\\ \end{array} \end{array} \]

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 2.0) 2e-78)
    (* (/ x_m -1.0) (/ (/ -2.0 z) (- y t)))
    (/ (/ 2.0 z) (/ (- 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 ((x_m * 2.0) <= 2e-78) {
		tmp = (x_m / -1.0) * ((-2.0 / z) / (y - t));
	} else {
		tmp = (2.0 / z) / ((y - t) / 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 * 2.0d0) <= 2d-78) then
        tmp = (x_m / (-1.0d0)) * (((-2.0d0) / z) / (y - t))
    else
        tmp = (2.0d0 / z) / ((y - t) / 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 * 2.0) <= 2e-78) {
		tmp = (x_m / -1.0) * ((-2.0 / z) / (y - t));
	} else {
		tmp = (2.0 / z) / ((y - t) / 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 * 2.0) <= 2e-78:
		tmp = (x_m / -1.0) * ((-2.0 / z) / (y - t))
	else:
		tmp = (2.0 / z) / ((y - t) / 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 (Float64(x_m * 2.0) <= 2e-78)
		tmp = Float64(Float64(x_m / -1.0) * Float64(Float64(-2.0 / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 / z) / Float64(Float64(y - t) / 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 * 2.0) <= 2e-78)
		tmp = (x_m / -1.0) * ((-2.0 / z) / (y - t));
	else
		tmp = (2.0 / z) / ((y - t) / 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[N[(x$95$m * 2.0), $MachinePrecision], 2e-78], N[(N[(x$95$m / -1.0), $MachinePrecision] * N[(N[(-2.0 / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 2e-78

   1. Initial program 92.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 2e-78 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.0%

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

   4. Applied egg-rr 0

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

Alternative 2: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{-2}{t} \cdot x\_m}{z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{x\_m \cdot 2}{z}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{\frac{x\_m}{t}}{-0.5}}{z}\\ \mathbf{elif}\;t \leq 13500000:\\ \;\;\;\;\frac{x\_m \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{z}}{\frac{t}{x\_m}}\\ \end{array} \end{array} \]

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 (<= t -1.08e+20)
    (/ (* (/ -2.0 t) x_m) z)
    (if (<= t 4e-185)
      (/ (/ (* x_m 2.0) z) y)
      (if (<= t 8.5e-168)
        (/ (/ (/ x_m t) -0.5) z)
        (if (<= t 13500000.0)
          (/ (* x_m 2.0) (* y z))
          (/ (/ -2.0 z) (/ 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 (t <= -1.08e+20) {
		tmp = ((-2.0 / t) * x_m) / z;
	} else if (t <= 4e-185) {
		tmp = ((x_m * 2.0) / z) / y;
	} else if (t <= 8.5e-168) {
		tmp = ((x_m / t) / -0.5) / z;
	} else if (t <= 13500000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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 (t <= (-1.08d+20)) then
        tmp = (((-2.0d0) / t) * x_m) / z
    else if (t <= 4d-185) then
        tmp = ((x_m * 2.0d0) / z) / y
    else if (t <= 8.5d-168) then
        tmp = ((x_m / t) / (-0.5d0)) / z
    else if (t <= 13500000.0d0) then
        tmp = (x_m * 2.0d0) / (y * z)
    else
        tmp = ((-2.0d0) / z) / (t / 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 (t <= -1.08e+20) {
		tmp = ((-2.0 / t) * x_m) / z;
	} else if (t <= 4e-185) {
		tmp = ((x_m * 2.0) / z) / y;
	} else if (t <= 8.5e-168) {
		tmp = ((x_m / t) / -0.5) / z;
	} else if (t <= 13500000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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 t <= -1.08e+20:
		tmp = ((-2.0 / t) * x_m) / z
	elif t <= 4e-185:
		tmp = ((x_m * 2.0) / z) / y
	elif t <= 8.5e-168:
		tmp = ((x_m / t) / -0.5) / z
	elif t <= 13500000.0:
		tmp = (x_m * 2.0) / (y * z)
	else:
		tmp = (-2.0 / z) / (t / 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 (t <= -1.08e+20)
		tmp = Float64(Float64(Float64(-2.0 / t) * x_m) / z);
	elseif (t <= 4e-185)
		tmp = Float64(Float64(Float64(x_m * 2.0) / z) / y);
	elseif (t <= 8.5e-168)
		tmp = Float64(Float64(Float64(x_m / t) / -0.5) / z);
	elseif (t <= 13500000.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(y * z));
	else
		tmp = Float64(Float64(-2.0 / z) / Float64(t / 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 (t <= -1.08e+20)
		tmp = ((-2.0 / t) * x_m) / z;
	elseif (t <= 4e-185)
		tmp = ((x_m * 2.0) / z) / y;
	elseif (t <= 8.5e-168)
		tmp = ((x_m / t) / -0.5) / z;
	elseif (t <= 13500000.0)
		tmp = (x_m * 2.0) / (y * z);
	else
		tmp = (-2.0 / z) / (t / 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[t, -1.08e+20], N[(N[(N[(-2.0 / t), $MachinePrecision] * x$95$m), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 4e-185], N[(N[(N[(x$95$m * 2.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8.5e-168], N[(N[(N[(x$95$m / t), $MachinePrecision] / -0.5), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 13500000.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 / z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if t < -1.08e20

   1. Initial program 90.6%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -1.08e20 < t < 4e-185

   1. Initial program 93.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 4e-185 < t < 8.4999999999999994e-168

   1. Initial program 84.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 8.4999999999999994e-168 < t < 1.35e7

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.35e7 < t

   1. Initial program 83.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{-2}{t} \cdot x\_m}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{x\_m \cdot 2}{z}}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 66000000:\\ \;\;\;\;\frac{x\_m \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{z}}{\frac{t}{x\_m}}\\ \end{array} \end{array} \end{array} \]

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 (/ (* (/ -2.0 t) x_m) z)))
   (*
    x_s
    (if (<= t -2.4e+18)
      t_1
      (if (<= t 4e-185)
        (/ (/ (* x_m 2.0) z) y)
        (if (<= t 8.5e-168)
          t_1
          (if (<= t 66000000.0)
            (/ (* x_m 2.0) (* y z))
            (/ (/ -2.0 z) (/ 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 t_1 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2.4e+18) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = ((x_m * 2.0) / z) / y;
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 66000000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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) :: t_1
    real(8) :: tmp
    t_1 = (((-2.0d0) / t) * x_m) / z
    if (t <= (-2.4d+18)) then
        tmp = t_1
    else if (t <= 4d-185) then
        tmp = ((x_m * 2.0d0) / z) / y
    else if (t <= 8.5d-168) then
        tmp = t_1
    else if (t <= 66000000.0d0) then
        tmp = (x_m * 2.0d0) / (y * z)
    else
        tmp = ((-2.0d0) / z) / (t / 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 t_1 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2.4e+18) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = ((x_m * 2.0) / z) / y;
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 66000000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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):
	t_1 = ((-2.0 / t) * x_m) / z
	tmp = 0
	if t <= -2.4e+18:
		tmp = t_1
	elif t <= 4e-185:
		tmp = ((x_m * 2.0) / z) / y
	elif t <= 8.5e-168:
		tmp = t_1
	elif t <= 66000000.0:
		tmp = (x_m * 2.0) / (y * z)
	else:
		tmp = (-2.0 / z) / (t / 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)
	t_1 = Float64(Float64(Float64(-2.0 / t) * x_m) / z)
	tmp = 0.0
	if (t <= -2.4e+18)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = Float64(Float64(Float64(x_m * 2.0) / z) / y);
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 66000000.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(y * z));
	else
		tmp = Float64(Float64(-2.0 / z) / Float64(t / 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)
	t_1 = ((-2.0 / t) * x_m) / z;
	tmp = 0.0;
	if (t <= -2.4e+18)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = ((x_m * 2.0) / z) / y;
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 66000000.0)
		tmp = (x_m * 2.0) / (y * z);
	else
		tmp = (-2.0 / z) / (t / 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_] := Block[{t$95$1 = N[(N[(N[(-2.0 / t), $MachinePrecision] * x$95$m), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -2.4e+18], t$95$1, If[LessEqual[t, 4e-185], N[(N[(N[(x$95$m * 2.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 8.5e-168], t$95$1, If[LessEqual[t, 66000000.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 / z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4e18 or 4e-185 < t < 8.4999999999999994e-168

   1. Initial program 89.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.4e18 < t < 4e-185

   1. Initial program 93.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 8.4999999999999994e-168 < t < 6.6e7

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 6.6e7 < t

   1. Initial program 83.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

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

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{-2}{t} \cdot x\_m}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-185}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 21000:\\ \;\;\;\;\frac{x\_m \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{z}}{\frac{t}{x\_m}}\\ \end{array} \end{array} \end{array} \]

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 (/ (* (/ -2.0 t) x_m) z)))
   (*
    x_s
    (if (<= t -2e+19)
      t_1
      (if (<= t 4e-185)
        (* (/ x_m z) (/ 2.0 y))
        (if (<= t 8.5e-168)
          t_1
          (if (<= t 21000.0)
            (/ (* x_m 2.0) (* y z))
            (/ (/ -2.0 z) (/ 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 t_1 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2e+19) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = (x_m / z) * (2.0 / y);
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 21000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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) :: t_1
    real(8) :: tmp
    t_1 = (((-2.0d0) / t) * x_m) / z
    if (t <= (-2d+19)) then
        tmp = t_1
    else if (t <= 4d-185) then
        tmp = (x_m / z) * (2.0d0 / y)
    else if (t <= 8.5d-168) then
        tmp = t_1
    else if (t <= 21000.0d0) then
        tmp = (x_m * 2.0d0) / (y * z)
    else
        tmp = ((-2.0d0) / z) / (t / 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 t_1 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2e+19) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = (x_m / z) * (2.0 / y);
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 21000.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (-2.0 / z) / (t / 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):
	t_1 = ((-2.0 / t) * x_m) / z
	tmp = 0
	if t <= -2e+19:
		tmp = t_1
	elif t <= 4e-185:
		tmp = (x_m / z) * (2.0 / y)
	elif t <= 8.5e-168:
		tmp = t_1
	elif t <= 21000.0:
		tmp = (x_m * 2.0) / (y * z)
	else:
		tmp = (-2.0 / z) / (t / 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)
	t_1 = Float64(Float64(Float64(-2.0 / t) * x_m) / z)
	tmp = 0.0
	if (t <= -2e+19)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / y));
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 21000.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(y * z));
	else
		tmp = Float64(Float64(-2.0 / z) / Float64(t / 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)
	t_1 = ((-2.0 / t) * x_m) / z;
	tmp = 0.0;
	if (t <= -2e+19)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = (x_m / z) * (2.0 / y);
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 21000.0)
		tmp = (x_m * 2.0) / (y * z);
	else
		tmp = (-2.0 / z) / (t / 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_] := Block[{t$95$1 = N[(N[(N[(-2.0 / t), $MachinePrecision] * x$95$m), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -2e+19], t$95$1, If[LessEqual[t, 4e-185], N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-168], t$95$1, If[LessEqual[t, 21000.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(-2.0 / z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if t < -2e19 or 4e-185 < t < 8.4999999999999994e-168

   1. Initial program 89.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2e19 < t < 4e-185

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 8.4999999999999994e-168 < t < 21000

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 21000 < t

   1. Initial program 83.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

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

Alternative 5: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{-2}{t} \cdot x\_m}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-185}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 215000:\\ \;\;\;\;\frac{x\_m \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (/ (* (/ -2.0 t) x_m) z)))
   (*
    x_s
    (if (<= t -2.15e+20)
      t_1
      (if (<= t 4e-185)
        (* (/ x_m z) (/ 2.0 y))
        (if (<= t 8.5e-168)
          t_1
          (if (<= t 215000.0) (/ (* x_m 2.0) (* y 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 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2.15e+20) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = (x_m / z) * (2.0 / y);
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 215000.0) {
		tmp = (x_m * 2.0) / (y * 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 = (((-2.0d0) / t) * x_m) / z
    if (t <= (-2.15d+20)) then
        tmp = t_1
    else if (t <= 4d-185) then
        tmp = (x_m / z) * (2.0d0 / y)
    else if (t <= 8.5d-168) then
        tmp = t_1
    else if (t <= 215000.0d0) then
        tmp = (x_m * 2.0d0) / (y * 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 = ((-2.0 / t) * x_m) / z;
	double tmp;
	if (t <= -2.15e+20) {
		tmp = t_1;
	} else if (t <= 4e-185) {
		tmp = (x_m / z) * (2.0 / y);
	} else if (t <= 8.5e-168) {
		tmp = t_1;
	} else if (t <= 215000.0) {
		tmp = (x_m * 2.0) / (y * 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 = ((-2.0 / t) * x_m) / z
	tmp = 0
	if t <= -2.15e+20:
		tmp = t_1
	elif t <= 4e-185:
		tmp = (x_m / z) * (2.0 / y)
	elif t <= 8.5e-168:
		tmp = t_1
	elif t <= 215000.0:
		tmp = (x_m * 2.0) / (y * 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(Float64(Float64(-2.0 / t) * x_m) / z)
	tmp = 0.0
	if (t <= -2.15e+20)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / y));
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 215000.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(y * 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 = ((-2.0 / t) * x_m) / z;
	tmp = 0.0;
	if (t <= -2.15e+20)
		tmp = t_1;
	elseif (t <= 4e-185)
		tmp = (x_m / z) * (2.0 / y);
	elseif (t <= 8.5e-168)
		tmp = t_1;
	elseif (t <= 215000.0)
		tmp = (x_m * 2.0) / (y * 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[(N[(N[(-2.0 / t), $MachinePrecision] * x$95$m), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -2.15e+20], t$95$1, If[LessEqual[t, 4e-185], N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-168], t$95$1, If[LessEqual[t, 215000.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -2.15e20 or 4e-185 < t < 8.4999999999999994e-168 or 215000 < t

   1. Initial program 86.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -2.15e20 < t < 4e-185

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 8.4999999999999994e-168 < t < 215000

   1. Initial program 98.0%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 6: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -5000000:\\ \;\;\;\;\frac{-2 \cdot x\_m}{t \cdot z}\\ \mathbf{elif}\;t \leq 1200:\\ \;\;\;\;\frac{x\_m \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

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 (<= t -5000000.0)
    (/ (* -2.0 x_m) (* t z))
    (if (<= t 1200.0) (/ (* x_m 2.0) (* y z)) (* (/ x_m z) (/ -2.0 t))))))

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 (t <= -5000000.0) {
		tmp = (-2.0 * x_m) / (t * z);
	} else if (t <= 1200.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (x_m / z) * (-2.0 / t);
	}
	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 (t <= (-5000000.0d0)) then
        tmp = ((-2.0d0) * x_m) / (t * z)
    else if (t <= 1200.0d0) then
        tmp = (x_m * 2.0d0) / (y * z)
    else
        tmp = (x_m / z) * ((-2.0d0) / t)
    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 (t <= -5000000.0) {
		tmp = (-2.0 * x_m) / (t * z);
	} else if (t <= 1200.0) {
		tmp = (x_m * 2.0) / (y * z);
	} else {
		tmp = (x_m / z) * (-2.0 / t);
	}
	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 t <= -5000000.0:
		tmp = (-2.0 * x_m) / (t * z)
	elif t <= 1200.0:
		tmp = (x_m * 2.0) / (y * z)
	else:
		tmp = (x_m / z) * (-2.0 / t)
	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 (t <= -5000000.0)
		tmp = Float64(Float64(-2.0 * x_m) / Float64(t * z));
	elseif (t <= 1200.0)
		tmp = Float64(Float64(x_m * 2.0) / Float64(y * z));
	else
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	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 (t <= -5000000.0)
		tmp = (-2.0 * x_m) / (t * z);
	elseif (t <= 1200.0)
		tmp = (x_m * 2.0) / (y * z);
	else
		tmp = (x_m / z) * (-2.0 / t);
	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[t, -5000000.0], N[(N[(-2.0 * x$95$m), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1200.0], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -5e6

   1. Initial program 89.4%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -5e6 < t < 1200

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1200 < t

   1. Initial program 83.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 7: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -50000000:\\ \;\;\;\;\frac{-2 \cdot x\_m}{t \cdot z}\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;\frac{\frac{2}{z}}{y} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

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 (<= t -50000000.0)
    (/ (* -2.0 x_m) (* t z))
    (if (<= t 10500.0) (* (/ (/ 2.0 z) y) x_m) (* (/ x_m z) (/ -2.0 t))))))

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 (t <= -50000000.0) {
		tmp = (-2.0 * x_m) / (t * z);
	} else if (t <= 10500.0) {
		tmp = ((2.0 / z) / y) * x_m;
	} else {
		tmp = (x_m / z) * (-2.0 / t);
	}
	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 (t <= (-50000000.0d0)) then
        tmp = ((-2.0d0) * x_m) / (t * z)
    else if (t <= 10500.0d0) then
        tmp = ((2.0d0 / z) / y) * x_m
    else
        tmp = (x_m / z) * ((-2.0d0) / t)
    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 (t <= -50000000.0) {
		tmp = (-2.0 * x_m) / (t * z);
	} else if (t <= 10500.0) {
		tmp = ((2.0 / z) / y) * x_m;
	} else {
		tmp = (x_m / z) * (-2.0 / t);
	}
	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 t <= -50000000.0:
		tmp = (-2.0 * x_m) / (t * z)
	elif t <= 10500.0:
		tmp = ((2.0 / z) / y) * x_m
	else:
		tmp = (x_m / z) * (-2.0 / t)
	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 (t <= -50000000.0)
		tmp = Float64(Float64(-2.0 * x_m) / Float64(t * z));
	elseif (t <= 10500.0)
		tmp = Float64(Float64(Float64(2.0 / z) / y) * x_m);
	else
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	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 (t <= -50000000.0)
		tmp = (-2.0 * x_m) / (t * z);
	elseif (t <= 10500.0)
		tmp = ((2.0 / z) / y) * x_m;
	else
		tmp = (x_m / z) * (-2.0 / t);
	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[t, -50000000.0], N[(N[(-2.0 * x$95$m), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 10500.0], N[(N[(N[(2.0 / z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -5e7

   1. Initial program 89.4%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -5e7 < t < 10500

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 10500 < t

   1. Initial program 83.8%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

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

Alternative 8: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -0.9:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2050000:\\ \;\;\;\;\frac{\frac{2}{z}}{y} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 z) (/ -2.0 t))))
   (*
    x_s
    (if (<= t -0.9) t_1 (if (<= t 2050000.0) (* (/ (/ 2.0 z) y) x_m) 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 / z) * (-2.0 / t);
	double tmp;
	if (t <= -0.9) {
		tmp = t_1;
	} else if (t <= 2050000.0) {
		tmp = ((2.0 / z) / y) * x_m;
	} 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 / z) * ((-2.0d0) / t)
    if (t <= (-0.9d0)) then
        tmp = t_1
    else if (t <= 2050000.0d0) then
        tmp = ((2.0d0 / z) / y) * x_m
    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 / z) * (-2.0 / t);
	double tmp;
	if (t <= -0.9) {
		tmp = t_1;
	} else if (t <= 2050000.0) {
		tmp = ((2.0 / z) / y) * x_m;
	} 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 / z) * (-2.0 / t)
	tmp = 0
	if t <= -0.9:
		tmp = t_1
	elif t <= 2050000.0:
		tmp = ((2.0 / z) / y) * x_m
	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(Float64(x_m / z) * Float64(-2.0 / t))
	tmp = 0.0
	if (t <= -0.9)
		tmp = t_1;
	elseif (t <= 2050000.0)
		tmp = Float64(Float64(Float64(2.0 / z) / y) * x_m);
	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 / z) * (-2.0 / t);
	tmp = 0.0;
	if (t <= -0.9)
		tmp = t_1;
	elseif (t <= 2050000.0)
		tmp = ((2.0 / z) / y) * x_m;
	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[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -0.9], t$95$1, If[LessEqual[t, 2050000.0], N[(N[(N[(2.0 / z), $MachinePrecision] / y), $MachinePrecision] * x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.900000000000000022 or 2.05e6 < t

   1. Initial program 86.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -0.900000000000000022 < t < 2.05e6

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

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

Alternative 9: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z} \cdot \frac{-2}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -530000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 450000000:\\ \;\;\;\;\frac{2}{z \cdot y} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 z) (/ -2.0 t))))
   (*
    x_s
    (if (<= t -530000000.0)
      t_1
      (if (<= t 450000000.0) (* (/ 2.0 (* z y)) x_m) 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 / z) * (-2.0 / t);
	double tmp;
	if (t <= -530000000.0) {
		tmp = t_1;
	} else if (t <= 450000000.0) {
		tmp = (2.0 / (z * y)) * x_m;
	} 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 / z) * ((-2.0d0) / t)
    if (t <= (-530000000.0d0)) then
        tmp = t_1
    else if (t <= 450000000.0d0) then
        tmp = (2.0d0 / (z * y)) * x_m
    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 / z) * (-2.0 / t);
	double tmp;
	if (t <= -530000000.0) {
		tmp = t_1;
	} else if (t <= 450000000.0) {
		tmp = (2.0 / (z * y)) * x_m;
	} 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 / z) * (-2.0 / t)
	tmp = 0
	if t <= -530000000.0:
		tmp = t_1
	elif t <= 450000000.0:
		tmp = (2.0 / (z * y)) * x_m
	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(Float64(x_m / z) * Float64(-2.0 / t))
	tmp = 0.0
	if (t <= -530000000.0)
		tmp = t_1;
	elseif (t <= 450000000.0)
		tmp = Float64(Float64(2.0 / Float64(z * y)) * x_m);
	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 / z) * (-2.0 / t);
	tmp = 0.0;
	if (t <= -530000000.0)
		tmp = t_1;
	elseif (t <= 450000000.0)
		tmp = (2.0 / (z * y)) * x_m;
	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[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -530000000.0], t$95$1, If[LessEqual[t, 450000000.0], N[(N[(2.0 / N[(z * y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.3e8 or 4.5e8 < t

   1. Initial program 86.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in t around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if -5.3e8 < t < 4.5e8

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 10: 96.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 4 \cdot 10^{-54}:\\ \;\;\;\;\frac{-2}{z \cdot \left(t - y\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x\_m}}\\ \end{array} \end{array} \]

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 2.0) 4e-54)
    (* (/ -2.0 (* z (- t y))) x_m)
    (/ (/ 2.0 z) (/ (- 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 ((x_m * 2.0) <= 4e-54) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (2.0 / z) / ((y - t) / 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 * 2.0d0) <= 4d-54) then
        tmp = ((-2.0d0) / (z * (t - y))) * x_m
    else
        tmp = (2.0d0 / z) / ((y - t) / 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 * 2.0) <= 4e-54) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (2.0 / z) / ((y - t) / 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 * 2.0) <= 4e-54:
		tmp = (-2.0 / (z * (t - y))) * x_m
	else:
		tmp = (2.0 / z) / ((y - t) / 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 (Float64(x_m * 2.0) <= 4e-54)
		tmp = Float64(Float64(-2.0 / Float64(z * Float64(t - y))) * x_m);
	else
		tmp = Float64(Float64(2.0 / z) / Float64(Float64(y - t) / 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 * 2.0) <= 4e-54)
		tmp = (-2.0 / (z * (t - y))) * x_m;
	else
		tmp = (2.0 / z) / ((y - t) / 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[N[(x$95$m * 2.0), $MachinePrecision], 4e-54], N[(N[(-2.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 4.0000000000000001e-54

   1. Initial program 92.2%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.0000000000000001e-54 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 84.9%

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

   4. Applied egg-rr 0

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

Alternative 11: 96.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 10^{-46}:\\ \;\;\;\;\frac{-2}{z \cdot \left(t - y\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{t - y} \cdot x\_m}{z}\\ \end{array} \end{array} \]

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 2.0) 1e-46)
    (* (/ -2.0 (* z (- t y))) x_m)
    (/ (* (/ -2.0 (- t y)) x_m) 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 * 2.0) <= 1e-46) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = ((-2.0 / (t - y)) * x_m) / 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 * 2.0d0) <= 1d-46) then
        tmp = ((-2.0d0) / (z * (t - y))) * x_m
    else
        tmp = (((-2.0d0) / (t - y)) * x_m) / 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 * 2.0) <= 1e-46) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = ((-2.0 / (t - y)) * x_m) / 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 * 2.0) <= 1e-46:
		tmp = (-2.0 / (z * (t - y))) * x_m
	else:
		tmp = ((-2.0 / (t - y)) * x_m) / 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 (Float64(x_m * 2.0) <= 1e-46)
		tmp = Float64(Float64(-2.0 / Float64(z * Float64(t - y))) * x_m);
	else
		tmp = Float64(Float64(Float64(-2.0 / Float64(t - y)) * x_m) / 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 * 2.0) <= 1e-46)
		tmp = (-2.0 / (z * (t - y))) * x_m;
	else
		tmp = ((-2.0 / (t - y)) * x_m) / 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[N[(x$95$m * 2.0), $MachinePrecision], 1e-46], N[(N[(-2.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 1.00000000000000002e-46

   1. Initial program 92.3%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.00000000000000002e-46 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 84.5%

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

   4. Applied egg-rr 0

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

Alternative 12: 96.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 5 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \left(t - y\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

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 2.0) 5e-86)
    (* (/ -2.0 (* z (- t y))) x_m)
    (* (/ x_m (- y t)) (/ 2.0 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 * 2.0) <= 5e-86) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (x_m / (y - t)) * (2.0 / 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 * 2.0d0) <= 5d-86) then
        tmp = ((-2.0d0) / (z * (t - y))) * x_m
    else
        tmp = (x_m / (y - t)) * (2.0d0 / 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 * 2.0) <= 5e-86) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (x_m / (y - t)) * (2.0 / 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 * 2.0) <= 5e-86:
		tmp = (-2.0 / (z * (t - y))) * x_m
	else:
		tmp = (x_m / (y - t)) * (2.0 / 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 (Float64(x_m * 2.0) <= 5e-86)
		tmp = Float64(Float64(-2.0 / Float64(z * Float64(t - y))) * x_m);
	else
		tmp = Float64(Float64(x_m / Float64(y - t)) * Float64(2.0 / 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 * 2.0) <= 5e-86)
		tmp = (-2.0 / (z * (t - y))) * x_m;
	else
		tmp = (x_m / (y - t)) * (2.0 / 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[N[(x$95$m * 2.0), $MachinePrecision], 5e-86], N[(N[(-2.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(x$95$m / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 4.9999999999999999e-86

   1. Initial program 91.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 4.9999999999999999e-86 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.3%

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

   4. Applied egg-rr 0

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

Alternative 13: 94.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{-2}{z \cdot \left(t - y\right)} \cdot x\_m\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t - y}\\ \end{array} \end{array} \]

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 7.5e-21)
    (* (/ -2.0 (* z (- t y))) x_m)
    (* (/ x_m z) (/ -2.0 (- t y))))))

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 <= 7.5e-21) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (x_m / z) * (-2.0 / (t - y));
	}
	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 <= 7.5d-21) then
        tmp = ((-2.0d0) / (z * (t - y))) * x_m
    else
        tmp = (x_m / z) * ((-2.0d0) / (t - y))
    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 <= 7.5e-21) {
		tmp = (-2.0 / (z * (t - y))) * x_m;
	} else {
		tmp = (x_m / z) * (-2.0 / (t - y));
	}
	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 <= 7.5e-21:
		tmp = (-2.0 / (z * (t - y))) * x_m
	else:
		tmp = (x_m / z) * (-2.0 / (t - y))
	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 <= 7.5e-21)
		tmp = Float64(Float64(-2.0 / Float64(z * Float64(t - y))) * x_m);
	else
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / Float64(t - y)));
	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 <= 7.5e-21)
		tmp = (-2.0 / (z * (t - y))) * x_m;
	else
		tmp = (x_m / z) * (-2.0 / (t - y));
	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, 7.5e-21], N[(N[(-2.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 7.50000000000000072e-21

   1. Initial program 90.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   if 7.50000000000000072e-21 < z

   1. Initial program 90.1%

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

   4. Applied egg-rr 0

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

Alternative 14: 91.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(\frac{-2}{z \cdot \left(t - y\right)} \cdot x\_m\right) \end{array} \]

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 (* (/ -2.0 (* z (- t y))) 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 * ((-2.0 / (z * (t - y))) * 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 * (((-2.0d0) / (z * (t - y))) * 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 * ((-2.0 / (z * (t - y))) * 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 * ((-2.0 / (z * (t - y))) * 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 * Float64(Float64(-2.0 / Float64(z * Float64(t - y))) * 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 * ((-2.0 / (z * (t - y))) * 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 * N[(N[(-2.0 / N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 15: 53.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(\frac{2}{z \cdot y} \cdot x\_m\right) \end{array} \]

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 (* (/ 2.0 (* z y)) 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 * ((2.0 / (z * y)) * 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 * ((2.0d0 / (z * y)) * 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 * ((2.0 / (z * y)) * 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 * ((2.0 / (z * y)) * 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 * Float64(Float64(2.0 / Float64(z * y)) * 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 * ((2.0 / (z * y)) * 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 * N[(N[(2.0 / N[(z * y), $MachinePrecision]), $MachinePrecision] * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

3. Taylor expanded in y around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

9. Applied egg-rr 0

   \[\leadsto expr\]
10. Add Preprocessing

Developer target: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t\_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - 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) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - 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 / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))