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

Percentage Accurate: 85.0% → 96.7%

Time: 9.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 1.12 \cdot 10^{+156}:\\ \;\;\;\;\frac{x\_m}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z - t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

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 1.12e+156)
    (/ x_m (/ (- t z) (- y z)))
    (* (/ x_m (- z t)) (- z 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 (x_m <= 1.12e+156) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (x_m / (z - t)) * (z - 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 (x_m <= 1.12d+156) then
        tmp = x_m / ((t - z) / (y - z))
    else
        tmp = (x_m / (z - t)) * (z - 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 (x_m <= 1.12e+156) {
		tmp = x_m / ((t - z) / (y - z));
	} else {
		tmp = (x_m / (z - t)) * (z - 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 x_m <= 1.12e+156:
		tmp = x_m / ((t - z) / (y - z))
	else:
		tmp = (x_m / (z - t)) * (z - 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 (x_m <= 1.12e+156)
		tmp = Float64(x_m / Float64(Float64(t - z) / Float64(y - z)));
	else
		tmp = Float64(Float64(x_m / Float64(z - t)) * Float64(z - 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 (x_m <= 1.12e+156)
		tmp = x_m / ((t - z) / (y - z));
	else
		tmp = (x_m / (z - t)) * (z - 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[x$95$m, 1.12e+156], N[(x$95$m / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.12000000000000007e156

   1. Initial program 87.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.9%

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

      2. un-div-inv 97.1%

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

   6. Applied egg-rr 97.1%

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

   if 1.12000000000000007e156 < x

   1. Initial program 73.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 73.0%

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

      2. distribute-neg-frac2 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 99.7%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.12 \cdot 10^{+156}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;\left(-x\_m\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.65e+75)
    x_m
    (if (<= z 5.5e-39)
      (/ (* x_m y) t)
      (if (<= z 8.5e+76) (* (- x_m) (/ 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 (z <= -1.65e+75) {
		tmp = x_m;
	} else if (z <= 5.5e-39) {
		tmp = (x_m * y) / t;
	} else if (z <= 8.5e+76) {
		tmp = -x_m * (z / 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 <= (-1.65d+75)) then
        tmp = x_m
    else if (z <= 5.5d-39) then
        tmp = (x_m * y) / t
    else if (z <= 8.5d+76) then
        tmp = -x_m * (z / 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 <= -1.65e+75) {
		tmp = x_m;
	} else if (z <= 5.5e-39) {
		tmp = (x_m * y) / t;
	} else if (z <= 8.5e+76) {
		tmp = -x_m * (z / 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 <= -1.65e+75:
		tmp = x_m
	elif z <= 5.5e-39:
		tmp = (x_m * y) / t
	elif z <= 8.5e+76:
		tmp = -x_m * (z / 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 <= -1.65e+75)
		tmp = x_m;
	elseif (z <= 5.5e-39)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 8.5e+76)
		tmp = Float64(Float64(-x_m) * Float64(z / 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 <= -1.65e+75)
		tmp = x_m;
	elseif (z <= 5.5e-39)
		tmp = (x_m * y) / t;
	elseif (z <= 8.5e+76)
		tmp = -x_m * (z / 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, -1.65e+75], x$95$m, If[LessEqual[z, 5.5e-39], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 8.5e+76], N[((-x$95$m) * N[(z / t), $MachinePrecision]), $MachinePrecision], x$95$m]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999999e75 or 8.49999999999999992e76 < z

   1. Initial program 68.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 70.5%

      \[\leadsto \color{blue}{x} \]

   if -1.64999999999999999e75 < z < 5.50000000000000018e-39

   1. Initial program 96.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 68.1%

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

   if 5.50000000000000018e-39 < z < 8.49999999999999992e76

   1. Initial program 96.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 61.3%

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

   6. Taylor expanded in y around 0 49.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 49.9%

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

      2. associate-/l* 53.7%

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

      3. distribute-lft-neg-in 53.7%

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

   8. Simplified 53.7%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{z}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-62} \lor \neg \left(z \leq 1.7 \cdot 10^{-56}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{x\_m}}\\ \end{array} \end{array} \]

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 (or (<= z -3.8e-62) (not (<= z 1.7e-56)))
    (* x_m (- 1.0 (/ y 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 ((z <= -3.8e-62) || !(z <= 1.7e-56)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = 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 ((z <= (-3.8d-62)) .or. (.not. (z <= 1.7d-56))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = 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 ((z <= -3.8e-62) || !(z <= 1.7e-56)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = 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 (z <= -3.8e-62) or not (z <= 1.7e-56):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = 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 ((z <= -3.8e-62) || !(z <= 1.7e-56))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(y / 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 ((z <= -3.8e-62) || ~((z <= 1.7e-56)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = 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[Or[LessEqual[z, -3.8e-62], N[Not[LessEqual[z, 1.7e-56]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000006e-62 or 1.69999999999999991e-56 < z

   1. Initial program 77.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 53.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 53.9%

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

      2. associate-/l* 71.8%

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

      3. distribute-rgt-neg-in 71.8%

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

      4. distribute-frac-neg 71.8%

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

      5. neg-sub0 71.8%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 71.8%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 71.8%

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

      8. +-commutative 71.8%

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

      9. sub-neg 71.8%

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

      10. div-sub 71.8%

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

      11. *-inverses 71.8%

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

   7. Simplified 71.8%

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

   if -3.80000000000000006e-62 < z < 1.69999999999999991e-56

   1. Initial program 95.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 91.6%

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

      2. un-div-inv 92.1%

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

   6. Applied egg-rr 92.1%

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

   7. Taylor expanded in y around inf 87.2%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   8. Step-by-step derivation

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

   9. Simplified 85.8%

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

   10. Taylor expanded in t around inf 72.8%

       \[\leadsto y \cdot \color{blue}{\frac{x}{t}} \]
   11. Step-by-step derivation

       1. clear-num 72.7%

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

       2. un-div-inv 73.0%

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

   12. Applied egg-rr 73.0%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-62} \lor \neg \left(z \leq 1.7 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+45} \lor \neg \left(z \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

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 (or (<= z -2.75e+45) (not (<= z 7e+38)))
    (* x_m (- 1.0 (/ y z)))
    (* x_m (/ y (- t 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 <= -2.75e+45) || !(z <= 7e+38)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m * (y / (t - 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 <= (-2.75d+45)) .or. (.not. (z <= 7d+38))) then
        tmp = x_m * (1.0d0 - (y / z))
    else
        tmp = x_m * (y / (t - 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 <= -2.75e+45) || !(z <= 7e+38)) {
		tmp = x_m * (1.0 - (y / z));
	} else {
		tmp = x_m * (y / (t - 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 <= -2.75e+45) or not (z <= 7e+38):
		tmp = x_m * (1.0 - (y / z))
	else:
		tmp = x_m * (y / (t - 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 <= -2.75e+45) || !(z <= 7e+38))
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x_m * Float64(y / Float64(t - 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 <= -2.75e+45) || ~((z <= 7e+38)))
		tmp = x_m * (1.0 - (y / z));
	else
		tmp = x_m * (y / (t - 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[Or[LessEqual[z, -2.75e+45], N[Not[LessEqual[z, 7e+38]], $MachinePrecision]], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e45 or 7.00000000000000003e38 < z

   1. Initial program 71.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 55.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.6%

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

      2. associate-/l* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. distribute-frac-neg 78.2%

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

      5. neg-sub0 78.2%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 78.2%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 78.2%

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

      8. +-commutative 78.2%

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

      9. sub-neg 78.2%

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

      10. div-sub 78.2%

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

      11. *-inverses 78.2%

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

   7. Simplified 78.2%

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

   if -2.75e45 < z < 7.00000000000000003e38

   1. Initial program 96.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 82.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

      \[\leadsto \color{blue}{x \cdot \frac{y}{t - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+45} \lor \neg \left(z \leq 7 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+39}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;x\_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

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 (<= z -6.2e+39)
    (* x_m (- 1.0 (/ y z)))
    (if (<= z 4e+34) (* x_m (/ y (- t z))) (* x_m (/ z (- z 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 (z <= -6.2e+39) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4e+34) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m * (z / (z - 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 (z <= (-6.2d+39)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= 4d+34) then
        tmp = x_m * (y / (t - z))
    else
        tmp = x_m * (z / (z - 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 (z <= -6.2e+39) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4e+34) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = x_m * (z / (z - 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 z <= -6.2e+39:
		tmp = x_m * (1.0 - (y / z))
	elif z <= 4e+34:
		tmp = x_m * (y / (t - z))
	else:
		tmp = x_m * (z / (z - 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 (z <= -6.2e+39)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= 4e+34)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x_m * Float64(z / Float64(z - 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 (z <= -6.2e+39)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= 4e+34)
		tmp = x_m * (y / (t - z));
	else
		tmp = x_m * (z / (z - 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[z, -6.2e+39], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+34], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -6.2000000000000005e39

   1. Initial program 60.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.1%

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

      2. associate-/l* 81.9%

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

      3. distribute-rgt-neg-in 81.9%

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

      4. distribute-frac-neg 81.9%

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

      5. neg-sub0 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.9%

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

      8. +-commutative 81.9%

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

      9. sub-neg 81.9%

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

      10. div-sub 81.9%

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

      11. *-inverses 81.9%

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

   7. Simplified 81.9%

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

   if -6.2000000000000005e39 < z < 3.99999999999999978e34

   1. Initial program 96.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.0%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   6. Step-by-step derivation

      1. associate-/l* 79.7%

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

   7. Simplified 79.7%

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

   if 3.99999999999999978e34 < z

   1. Initial program 80.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 69.7%

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

      2. distribute-neg-frac2 69.7%

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

      3. neg-sub0 69.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 69.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 69.7%

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

      6. +-commutative 69.7%

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

      7. sub-neg 69.7%

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

      8. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x\_m}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

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 (<= z -2.5e+47)
    (* x_m (- 1.0 (/ y z)))
    (if (<= z 1.3e-27) (* y (/ x_m (- t z))) (* x_m (/ z (- z 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 (z <= -2.5e+47) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 1.3e-27) {
		tmp = y * (x_m / (t - z));
	} else {
		tmp = x_m * (z / (z - 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 (z <= (-2.5d+47)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= 1.3d-27) then
        tmp = y * (x_m / (t - z))
    else
        tmp = x_m * (z / (z - 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 (z <= -2.5e+47) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 1.3e-27) {
		tmp = y * (x_m / (t - z));
	} else {
		tmp = x_m * (z / (z - 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 z <= -2.5e+47:
		tmp = x_m * (1.0 - (y / z))
	elif z <= 1.3e-27:
		tmp = y * (x_m / (t - z))
	else:
		tmp = x_m * (z / (z - 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 (z <= -2.5e+47)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.3e-27)
		tmp = Float64(y * Float64(x_m / Float64(t - z)));
	else
		tmp = Float64(x_m * Float64(z / Float64(z - 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 (z <= -2.5e+47)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= 1.3e-27)
		tmp = y * (x_m / (t - z));
	else
		tmp = x_m * (z / (z - 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[z, -2.5e+47], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-27], N[(y * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000011e47

   1. Initial program 60.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.1%

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

      2. associate-/l* 81.9%

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

      3. distribute-rgt-neg-in 81.9%

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

      4. distribute-frac-neg 81.9%

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

      5. neg-sub0 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.9%

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

      8. +-commutative 81.9%

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

      9. sub-neg 81.9%

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

      10. div-sub 81.9%

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

      11. *-inverses 81.9%

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

   7. Simplified 81.9%

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

   if -2.50000000000000011e47 < z < 1.30000000000000009e-27

   1. Initial program 96.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 92.1%

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

      2. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in y around inf 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   8. Step-by-step derivation

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

   9. Simplified 82.3%

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

   if 1.30000000000000009e-27 < z

   1. Initial program 83.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 67.9%

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

      2. distribute-neg-frac2 67.9%

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

      3. neg-sub0 67.9%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 67.9%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 67.9%

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

      6. +-commutative 67.9%

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

      7. sub-neg 67.9%

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

      8. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x\_m}}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

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 (<= z -2.1e+40)
    (* x_m (- 1.0 (/ y z)))
    (if (<= z 4.8e-25) (/ y (/ (- t z) x_m)) (* x_m (/ z (- z 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 (z <= -2.1e+40) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4.8e-25) {
		tmp = y / ((t - z) / x_m);
	} else {
		tmp = x_m * (z / (z - 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 (z <= (-2.1d+40)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= 4.8d-25) then
        tmp = y / ((t - z) / x_m)
    else
        tmp = x_m * (z / (z - 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 (z <= -2.1e+40) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4.8e-25) {
		tmp = y / ((t - z) / x_m);
	} else {
		tmp = x_m * (z / (z - 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 z <= -2.1e+40:
		tmp = x_m * (1.0 - (y / z))
	elif z <= 4.8e-25:
		tmp = y / ((t - z) / x_m)
	else:
		tmp = x_m * (z / (z - 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 (z <= -2.1e+40)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= 4.8e-25)
		tmp = Float64(y / Float64(Float64(t - z) / x_m));
	else
		tmp = Float64(x_m * Float64(z / Float64(z - 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 (z <= -2.1e+40)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= 4.8e-25)
		tmp = y / ((t - z) / x_m);
	else
		tmp = x_m * (z / (z - 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[z, -2.1e+40], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-25], N[(y / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -2.1000000000000001e40

   1. Initial program 60.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.1%

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

      2. associate-/l* 81.9%

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

      3. distribute-rgt-neg-in 81.9%

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

      4. distribute-frac-neg 81.9%

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

      5. neg-sub0 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.9%

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

      8. +-commutative 81.9%

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

      9. sub-neg 81.9%

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

      10. div-sub 81.9%

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

      11. *-inverses 81.9%

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

   7. Simplified 81.9%

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

   if -2.1000000000000001e40 < z < 4.80000000000000018e-25

   1. Initial program 96.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 92.1%

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

      2. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]
   7. Step-by-step derivation

      1. *-un-lft-identity 92.5%

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

      2. div-inv 92.4%

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

      3. times-frac 96.1%

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

   8. Applied egg-rr 96.1%

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

   9. Taylor expanded in y around inf 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t - z}} \]
   10. Step-by-step derivation

       1. *-commutative 84.1%

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

       2. *-rgt-identity 84.1%

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

       3. times-frac 80.6%

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

       4. /-rgt-identity 80.6%

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

       5. associate-/r/ 82.5%

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

   11. Simplified 82.5%

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

   if 4.80000000000000018e-25 < z

   1. Initial program 83.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 67.9%

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

      2. distribute-neg-frac2 67.9%

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

      3. neg-sub0 67.9%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 67.9%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 67.9%

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

      6. +-commutative 67.9%

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

      7. sub-neg 67.9%

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

      8. associate-/l* 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;x\_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{x\_m \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

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 (<= z -3.3e+49)
    (* x_m (- 1.0 (/ y z)))
    (if (<= z 4.6e+34) (/ (* x_m y) (- t z)) (* x_m (/ z (- z 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 (z <= -3.3e+49) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4.6e+34) {
		tmp = (x_m * y) / (t - z);
	} else {
		tmp = x_m * (z / (z - 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 (z <= (-3.3d+49)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= 4.6d+34) then
        tmp = (x_m * y) / (t - z)
    else
        tmp = x_m * (z / (z - 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 (z <= -3.3e+49) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= 4.6e+34) {
		tmp = (x_m * y) / (t - z);
	} else {
		tmp = x_m * (z / (z - 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 z <= -3.3e+49:
		tmp = x_m * (1.0 - (y / z))
	elif z <= 4.6e+34:
		tmp = (x_m * y) / (t - z)
	else:
		tmp = x_m * (z / (z - 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 (z <= -3.3e+49)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= 4.6e+34)
		tmp = Float64(Float64(x_m * y) / Float64(t - z));
	else
		tmp = Float64(x_m * Float64(z / Float64(z - 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 (z <= -3.3e+49)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= 4.6e+34)
		tmp = (x_m * y) / (t - z);
	else
		tmp = x_m * (z / (z - 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[z, -3.3e+49], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+34], N[(N[(x$95$m * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999998e49

   1. Initial program 60.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 49.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.1%

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

      2. associate-/l* 81.9%

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

      3. distribute-rgt-neg-in 81.9%

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

      4. distribute-frac-neg 81.9%

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

      5. neg-sub0 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 81.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 81.9%

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

      8. +-commutative 81.9%

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

      9. sub-neg 81.9%

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

      10. div-sub 81.9%

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

      11. *-inverses 81.9%

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

   7. Simplified 81.9%

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

   if -3.2999999999999998e49 < z < 4.5999999999999996e34

   1. Initial program 96.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.0%

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

   if 4.5999999999999996e34 < z

   1. Initial program 80.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t - z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 69.7%

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

      2. distribute-neg-frac2 69.7%

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

      3. neg-sub0 69.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{0 - \left(t - z\right)}} \]

      4. associate--r- 69.7%

         \[\leadsto \frac{x \cdot z}{\color{blue}{\left(0 - t\right) + z}} \]

      5. neg-sub0 69.7%

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

      6. +-commutative 69.7%

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

      7. sub-neg 69.7%

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

      8. associate-/l* 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+75}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x\_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.35e+75) x_m (if (<= z 3.5e+82) (* 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 <= -1.35e+75) {
		tmp = x_m;
	} else if (z <= 3.5e+82) {
		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 <= (-1.35d+75)) then
        tmp = x_m
    else if (z <= 3.5d+82) 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 <= -1.35e+75) {
		tmp = x_m;
	} else if (z <= 3.5e+82) {
		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 <= -1.35e+75:
		tmp = x_m
	elif z <= 3.5e+82:
		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 <= -1.35e+75)
		tmp = x_m;
	elseif (z <= 3.5e+82)
		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 <= -1.35e+75)
		tmp = x_m;
	elseif (z <= 3.5e+82)
		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, -1.35e+75], x$95$m, If[LessEqual[z, 3.5e+82], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999999e75 or 3.5e82 < z

   1. Initial program 67.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{x} \]

   if -1.34999999999999999e75 < z < 3.5e82

   1. Initial program 96.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.4%

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

   7. Simplified 61.4%

      \[\leadsto \color{blue}{x \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+81}:\\ \;\;\;\;\frac{x\_m \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

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 -1.05e+75) x_m (if (<= z 9e+81) (/ (* 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 <= -1.05e+75) {
		tmp = x_m;
	} else if (z <= 9e+81) {
		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 <= (-1.05d+75)) then
        tmp = x_m
    else if (z <= 9d+81) 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 <= -1.05e+75) {
		tmp = x_m;
	} else if (z <= 9e+81) {
		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 <= -1.05e+75:
		tmp = x_m
	elif z <= 9e+81:
		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 <= -1.05e+75)
		tmp = x_m;
	elseif (z <= 9e+81)
		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 <= -1.05e+75)
		tmp = x_m;
	elseif (z <= 9e+81)
		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, -1.05e+75], x$95$m, If[LessEqual[z, 9e+81], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999999e75 or 9.00000000000000034e81 < z

   1. Initial program 67.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{x} \]

   if -1.04999999999999999e75 < z < 9.00000000000000034e81

   1. Initial program 96.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+81}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 9 \cdot 10^{+156}:\\ \;\;\;\;x\_m \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z - t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

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 9e+156)
    (* x_m (/ (- y z) (- t z)))
    (* (/ x_m (- z t)) (- z 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 (x_m <= 9e+156) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (x_m / (z - t)) * (z - 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 (x_m <= 9d+156) then
        tmp = x_m * ((y - z) / (t - z))
    else
        tmp = (x_m / (z - t)) * (z - 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 (x_m <= 9e+156) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (x_m / (z - t)) * (z - 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 x_m <= 9e+156:
		tmp = x_m * ((y - z) / (t - z))
	else:
		tmp = (x_m / (z - t)) * (z - 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 (x_m <= 9e+156)
		tmp = Float64(x_m * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / Float64(z - t)) * Float64(z - 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 (x_m <= 9e+156)
		tmp = x_m * ((y - z) / (t - z));
	else
		tmp = (x_m / (z - t)) * (z - 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[x$95$m, 9e+156], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 9.00000000000000061e156

   1. Initial program 87.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   if 9.00000000000000061e156 < x

   1. Initial program 73.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 73.0%

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

      2. distribute-neg-frac2 73.0%

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

      3. *-commutative 73.0%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 99.7%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9 \cdot 10^{+156}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.1% accurate, 1.0× speedup

Math

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

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 (* x_m (/ (- y z) (- t 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) {
	return x_s * (x_m * ((y - z) / (t - z)));
}

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 * ((y - z) / (t - z)))
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 * ((y - z) / (t - z)));
}

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

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

Derivation

1. Initial program 85.9%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Final simplification 96.0%

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

Alternative 13: 34.6% 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 85.9%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 32.8%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 32.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.1% 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 2024080 
(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)))