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

Percentage Accurate: 83.8% → 96.8%

Time: 12.8s

Alternatives: 19

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: 83.8% 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: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x_m \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 3.6e-16)
    (/ (* x_m (- y z)) (- t z))
    (* (- y z) (/ x_m (- 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 (x_m <= 3.6e-16) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x_m / (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 (x_m <= 3.6d-16) then
        tmp = (x_m * (y - z)) / (t - z)
    else
        tmp = (y - z) * (x_m / (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 (x_m <= 3.6e-16) {
		tmp = (x_m * (y - z)) / (t - z);
	} else {
		tmp = (y - z) * (x_m / (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 x_m <= 3.6e-16:
		tmp = (x_m * (y - z)) / (t - z)
	else:
		tmp = (y - z) * (x_m / (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 (x_m <= 3.6e-16)
		tmp = Float64(Float64(x_m * Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / 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 (x_m <= 3.6e-16)
		tmp = (x_m * (y - z)) / (t - z);
	else
		tmp = (y - z) * (x_m / (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[LessEqual[x$95$m, 3.6e-16], N[(N[(x$95$m * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.59999999999999983e-16

   1. Initial program 85.9%

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

   if 3.59999999999999983e-16 < x

   1. Initial program 79.5%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \left(1 + \frac{t}{z}\right)\\ t_2 := x_m \cdot \frac{-y}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{-x_m}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (+ 1.0 (/ t z)))) (t_2 (* x_m (/ (- y) z))))
   (*
    x_s
    (if (<= z -1.15e+151)
      x_m
      (if (<= z -1.2e+104)
        t_2
        (if (<= z -2.8e+61)
          t_1
          (if (<= z -5.5e-51)
            (/ (- x_m) (/ t z))
            (if (<= z 7e-7) (/ (* x_m y) t) (if (<= z 4e+82) t_2 t_1)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 + (t / z));
	double t_2 = x_m * (-y / z);
	double tmp;
	if (z <= -1.15e+151) {
		tmp = x_m;
	} else if (z <= -1.2e+104) {
		tmp = t_2;
	} else if (z <= -2.8e+61) {
		tmp = t_1;
	} else if (z <= -5.5e-51) {
		tmp = -x_m / (t / z);
	} else if (z <= 7e-7) {
		tmp = (x_m * y) / t;
	} else if (z <= 4e+82) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x_m * (1.0d0 + (t / z))
    t_2 = x_m * (-y / z)
    if (z <= (-1.15d+151)) then
        tmp = x_m
    else if (z <= (-1.2d+104)) then
        tmp = t_2
    else if (z <= (-2.8d+61)) then
        tmp = t_1
    else if (z <= (-5.5d-51)) then
        tmp = -x_m / (t / z)
    else if (z <= 7d-7) then
        tmp = (x_m * y) / t
    else if (z <= 4d+82) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 + (t / z));
	double t_2 = x_m * (-y / z);
	double tmp;
	if (z <= -1.15e+151) {
		tmp = x_m;
	} else if (z <= -1.2e+104) {
		tmp = t_2;
	} else if (z <= -2.8e+61) {
		tmp = t_1;
	} else if (z <= -5.5e-51) {
		tmp = -x_m / (t / z);
	} else if (z <= 7e-7) {
		tmp = (x_m * y) / t;
	} else if (z <= 4e+82) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 + (t / z))
	t_2 = x_m * (-y / z)
	tmp = 0
	if z <= -1.15e+151:
		tmp = x_m
	elif z <= -1.2e+104:
		tmp = t_2
	elif z <= -2.8e+61:
		tmp = t_1
	elif z <= -5.5e-51:
		tmp = -x_m / (t / z)
	elif z <= 7e-7:
		tmp = (x_m * y) / t
	elif z <= 4e+82:
		tmp = t_2
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 + Float64(t / z)))
	t_2 = Float64(x_m * Float64(Float64(-y) / z))
	tmp = 0.0
	if (z <= -1.15e+151)
		tmp = x_m;
	elseif (z <= -1.2e+104)
		tmp = t_2;
	elseif (z <= -2.8e+61)
		tmp = t_1;
	elseif (z <= -5.5e-51)
		tmp = Float64(Float64(-x_m) / Float64(t / z));
	elseif (z <= 7e-7)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 4e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 + (t / z));
	t_2 = x_m * (-y / z);
	tmp = 0.0;
	if (z <= -1.15e+151)
		tmp = x_m;
	elseif (z <= -1.2e+104)
		tmp = t_2;
	elseif (z <= -2.8e+61)
		tmp = t_1;
	elseif (z <= -5.5e-51)
		tmp = -x_m / (t / z);
	elseif (z <= 7e-7)
		tmp = (x_m * y) / t;
	elseif (z <= 4e+82)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.15e+151], x$95$m, If[LessEqual[z, -1.2e+104], t$95$2, If[LessEqual[z, -2.8e+61], t$95$1, If[LessEqual[z, -5.5e-51], N[((-x$95$m) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-7], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4e+82], t$95$2, t$95$1]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.15e151

   1. Initial program 59.8%

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

      1. *-commutative 59.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.1%

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

   if -1.15e151 < z < -1.2e104 or 6.99999999999999968e-7 < z < 3.9999999999999999e82

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. div-sub 66.2%

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

      3. sub-neg 66.2%

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

      4. *-inverses 66.2%

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

      5. metadata-eval 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in y around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. associate-*r/ 54.6%

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

      3. *-commutative 54.6%

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

      4. distribute-rgt-neg-in 54.6%

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

   10. Simplified 54.6%

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

   if -1.2e104 < z < -2.8000000000000001e61 or 3.9999999999999999e82 < z

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 60.5%

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

      1. mul-1-neg 60.5%

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

      2. associate-/l* 80.5%

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

      3. distribute-neg-frac 80.5%

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

      4. div-sub 80.5%

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

      5. *-inverses 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in t around 0 62.8%

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

      1. *-lft-identity 62.8%

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

      2. associate-/l* 64.9%

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

      3. associate-/r/ 64.3%

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

      4. distribute-rgt-in 64.4%

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

   10. Simplified 64.4%

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

   if -2.8000000000000001e61 < z < -5.4999999999999997e-51

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 65.4%

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

   6. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-/l* 60.9%

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

      3. distribute-neg-frac 60.9%

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

   8. Simplified 60.9%

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

   if -5.4999999999999997e-51 < z < 6.99999999999999968e-7

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 66.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-51}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{-y}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+151}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;x_m \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y) z))))
   (*
    x_s
    (if (<= z -1.85e+151)
      x_m
      (if (<= z -1.25e+104)
        t_1
        (if (<= z -2.6e+62)
          x_m
          (if (<= z -1.15e-51)
            (* x_m (/ (- z) t))
            (if (<= z 7e-6) (/ (* x_m y) t) (if (<= z 2e+80) t_1 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 = x_m * (-y / z);
	double tmp;
	if (z <= -1.85e+151) {
		tmp = x_m;
	} else if (z <= -1.25e+104) {
		tmp = t_1;
	} else if (z <= -2.6e+62) {
		tmp = x_m;
	} else if (z <= -1.15e-51) {
		tmp = x_m * (-z / t);
	} else if (z <= 7e-6) {
		tmp = (x_m * y) / t;
	} else if (z <= 2e+80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x_m * (-y / z)
    if (z <= (-1.85d+151)) then
        tmp = x_m
    else if (z <= (-1.25d+104)) then
        tmp = t_1
    else if (z <= (-2.6d+62)) then
        tmp = x_m
    else if (z <= (-1.15d-51)) then
        tmp = x_m * (-z / t)
    else if (z <= 7d-6) then
        tmp = (x_m * y) / t
    else if (z <= 2d+80) then
        tmp = t_1
    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 t_1 = x_m * (-y / z);
	double tmp;
	if (z <= -1.85e+151) {
		tmp = x_m;
	} else if (z <= -1.25e+104) {
		tmp = t_1;
	} else if (z <= -2.6e+62) {
		tmp = x_m;
	} else if (z <= -1.15e-51) {
		tmp = x_m * (-z / t);
	} else if (z <= 7e-6) {
		tmp = (x_m * y) / t;
	} else if (z <= 2e+80) {
		tmp = t_1;
	} 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):
	t_1 = x_m * (-y / z)
	tmp = 0
	if z <= -1.85e+151:
		tmp = x_m
	elif z <= -1.25e+104:
		tmp = t_1
	elif z <= -2.6e+62:
		tmp = x_m
	elif z <= -1.15e-51:
		tmp = x_m * (-z / t)
	elif z <= 7e-6:
		tmp = (x_m * y) / t
	elif z <= 2e+80:
		tmp = t_1
	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)
	t_1 = Float64(x_m * Float64(Float64(-y) / z))
	tmp = 0.0
	if (z <= -1.85e+151)
		tmp = x_m;
	elseif (z <= -1.25e+104)
		tmp = t_1;
	elseif (z <= -2.6e+62)
		tmp = x_m;
	elseif (z <= -1.15e-51)
		tmp = Float64(x_m * Float64(Float64(-z) / t));
	elseif (z <= 7e-6)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 2e+80)
		tmp = t_1;
	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)
	t_1 = x_m * (-y / z);
	tmp = 0.0;
	if (z <= -1.85e+151)
		tmp = x_m;
	elseif (z <= -1.25e+104)
		tmp = t_1;
	elseif (z <= -2.6e+62)
		tmp = x_m;
	elseif (z <= -1.15e-51)
		tmp = x_m * (-z / t);
	elseif (z <= 7e-6)
		tmp = (x_m * y) / t;
	elseif (z <= 2e+80)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.85e+151], x$95$m, If[LessEqual[z, -1.25e+104], t$95$1, If[LessEqual[z, -2.6e+62], x$95$m, If[LessEqual[z, -1.15e-51], N[(x$95$m * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-6], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2e+80], t$95$1, x$95$m]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8499999999999999e151 or -1.2499999999999999e104 < z < -2.59999999999999984e62 or 2e80 < z

   1. Initial program 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 65.4%

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

   if -1.8499999999999999e151 < z < -1.2499999999999999e104 or 6.99999999999999989e-6 < z < 2e80

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. div-sub 68.8%

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

      3. sub-neg 68.8%

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

      4. *-inverses 68.8%

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

      5. metadata-eval 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. associate-*r/ 56.7%

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

      3. *-commutative 56.7%

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

      4. distribute-rgt-neg-in 56.7%

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

   10. Simplified 56.7%

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

   if -2.59999999999999984e62 < z < -1.15000000000000001e-51

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 65.4%

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

   6. Taylor expanded in y around 0 60.9%

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

      1. neg-mul-1 60.9%

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

      2. distribute-neg-frac 60.9%

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

   8. Simplified 60.9%

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

   if -1.15000000000000001e-51 < z < 6.99999999999999989e-6

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 66.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{-y}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-51}:\\ \;\;\;\;\frac{-x_m}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- y) z))))
   (*
    x_s
    (if (<= z -1.15e+151)
      x_m
      (if (<= z -1.25e+104)
        t_1
        (if (<= z -1.4e+62)
          x_m
          (if (<= z -4e-51)
            (/ (- x_m) (/ t z))
            (if (<= z 2.2e-7)
              (/ (* x_m y) t)
              (if (<= z 2.1e+79) t_1 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 = x_m * (-y / z);
	double tmp;
	if (z <= -1.15e+151) {
		tmp = x_m;
	} else if (z <= -1.25e+104) {
		tmp = t_1;
	} else if (z <= -1.4e+62) {
		tmp = x_m;
	} else if (z <= -4e-51) {
		tmp = -x_m / (t / z);
	} else if (z <= 2.2e-7) {
		tmp = (x_m * y) / t;
	} else if (z <= 2.1e+79) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x_m * (-y / z)
    if (z <= (-1.15d+151)) then
        tmp = x_m
    else if (z <= (-1.25d+104)) then
        tmp = t_1
    else if (z <= (-1.4d+62)) then
        tmp = x_m
    else if (z <= (-4d-51)) then
        tmp = -x_m / (t / z)
    else if (z <= 2.2d-7) then
        tmp = (x_m * y) / t
    else if (z <= 2.1d+79) then
        tmp = t_1
    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 t_1 = x_m * (-y / z);
	double tmp;
	if (z <= -1.15e+151) {
		tmp = x_m;
	} else if (z <= -1.25e+104) {
		tmp = t_1;
	} else if (z <= -1.4e+62) {
		tmp = x_m;
	} else if (z <= -4e-51) {
		tmp = -x_m / (t / z);
	} else if (z <= 2.2e-7) {
		tmp = (x_m * y) / t;
	} else if (z <= 2.1e+79) {
		tmp = t_1;
	} 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):
	t_1 = x_m * (-y / z)
	tmp = 0
	if z <= -1.15e+151:
		tmp = x_m
	elif z <= -1.25e+104:
		tmp = t_1
	elif z <= -1.4e+62:
		tmp = x_m
	elif z <= -4e-51:
		tmp = -x_m / (t / z)
	elif z <= 2.2e-7:
		tmp = (x_m * y) / t
	elif z <= 2.1e+79:
		tmp = t_1
	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)
	t_1 = Float64(x_m * Float64(Float64(-y) / z))
	tmp = 0.0
	if (z <= -1.15e+151)
		tmp = x_m;
	elseif (z <= -1.25e+104)
		tmp = t_1;
	elseif (z <= -1.4e+62)
		tmp = x_m;
	elseif (z <= -4e-51)
		tmp = Float64(Float64(-x_m) / Float64(t / z));
	elseif (z <= 2.2e-7)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 2.1e+79)
		tmp = t_1;
	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)
	t_1 = x_m * (-y / z);
	tmp = 0.0;
	if (z <= -1.15e+151)
		tmp = x_m;
	elseif (z <= -1.25e+104)
		tmp = t_1;
	elseif (z <= -1.4e+62)
		tmp = x_m;
	elseif (z <= -4e-51)
		tmp = -x_m / (t / z);
	elseif (z <= 2.2e-7)
		tmp = (x_m * y) / t;
	elseif (z <= 2.1e+79)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x$95$m * N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.15e+151], x$95$m, If[LessEqual[z, -1.25e+104], t$95$1, If[LessEqual[z, -1.4e+62], x$95$m, If[LessEqual[z, -4e-51], N[((-x$95$m) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-7], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e+79], t$95$1, x$95$m]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e151 or -1.2499999999999999e104 < z < -1.40000000000000007e62 or 2.10000000000000008e79 < z

   1. Initial program 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 65.4%

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

   if -1.15e151 < z < -1.2499999999999999e104 or 2.2000000000000001e-7 < z < 2.10000000000000008e79

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. div-sub 68.8%

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

      3. sub-neg 68.8%

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

      4. *-inverses 68.8%

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

      5. metadata-eval 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. associate-*r/ 56.7%

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

      3. *-commutative 56.7%

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

      4. distribute-rgt-neg-in 56.7%

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

   10. Simplified 56.7%

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

   if -1.40000000000000007e62 < z < -4e-51

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 65.4%

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

   6. Taylor expanded in y around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. associate-/l* 60.9%

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

      3. distribute-neg-frac 60.9%

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

   8. Simplified 60.9%

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

   if -4e-51 < z < 2.2000000000000001e-7

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 66.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-51}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{z}{z - t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ z (- z t)))))
   (*
    x_s
    (if (<= z -5.8e+148)
      t_1
      (if (<= z -1.55e+102)
        (* x_m (- 1.0 (/ y z)))
        (if (<= z -4.3e-51)
          t_1
          (if (<= z 2e-161)
            (* (- y z) (/ x_m t))
            (if (<= z 3.6e+32) (* x_m (/ y (- t z))) t_1))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -5.8e+148) {
		tmp = t_1;
	} else if (z <= -1.55e+102) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -4.3e-51) {
		tmp = t_1;
	} else if (z <= 2e-161) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 3.6e+32) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (z / (z - t))
    if (z <= (-5.8d+148)) then
        tmp = t_1
    else if (z <= (-1.55d+102)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= (-4.3d-51)) then
        tmp = t_1
    else if (z <= 2d-161) then
        tmp = (y - z) * (x_m / t)
    else if (z <= 3.6d+32) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -5.8e+148) {
		tmp = t_1;
	} else if (z <= -1.55e+102) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -4.3e-51) {
		tmp = t_1;
	} else if (z <= 2e-161) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 3.6e+32) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (z / (z - t))
	tmp = 0
	if z <= -5.8e+148:
		tmp = t_1
	elif z <= -1.55e+102:
		tmp = x_m * (1.0 - (y / z))
	elif z <= -4.3e-51:
		tmp = t_1
	elif z <= 2e-161:
		tmp = (y - z) * (x_m / t)
	elif z <= 3.6e+32:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -5.8e+148)
		tmp = t_1;
	elseif (z <= -1.55e+102)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= -4.3e-51)
		tmp = t_1;
	elseif (z <= 2e-161)
		tmp = Float64(Float64(y - z) * Float64(x_m / t));
	elseif (z <= 3.6e+32)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (z / (z - t));
	tmp = 0.0;
	if (z <= -5.8e+148)
		tmp = t_1;
	elseif (z <= -1.55e+102)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= -4.3e-51)
		tmp = t_1;
	elseif (z <= 2e-161)
		tmp = (y - z) * (x_m / t);
	elseif (z <= 3.6e+32)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -5.8e+148], t$95$1, If[LessEqual[z, -1.55e+102], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.3e-51], t$95$1, If[LessEqual[z, 2e-161], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+32], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if z < -5.7999999999999999e148 or -1.54999999999999993e102 < z < -4.2999999999999997e-51 or 3.5999999999999997e32 < z

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-neg-frac 81.0%

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

   7. Simplified 81.0%

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

      1. *-commutative 81.0%

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

      2. frac-2neg 81.0%

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

      3. remove-double-neg 81.0%

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

      4. associate-*l/ 60.0%

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

      5. sub-neg 60.0%

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

      6. distribute-neg-in 60.0%

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

      7. remove-double-neg 60.0%

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

   9. Applied egg-rr 60.0%

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

       1. associate-/l* 63.2%

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

       2. associate-/r/ 81.0%

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

       3. +-commutative 81.0%

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

       4. unsub-neg 81.0%

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

   11. Simplified 81.0%

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

   if -5.7999999999999999e148 < z < -1.54999999999999993e102

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. div-sub 87.3%

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

      3. sub-neg 87.3%

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

      4. *-inverses 87.3%

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

      5. metadata-eval 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 87.3%

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

   if -4.2999999999999997e-51 < z < 2.00000000000000006e-161

   1. Initial program 92.9%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 86.5%

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

   if 2.00000000000000006e-161 < z < 3.5999999999999997e32

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.8%

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

      3. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 74.5%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+102}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{z}{z - t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+150}:\\ \;\;\;\;\frac{x_m}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ z (- z t)))))
   (*
    x_s
    (if (<= z -2.65e+150)
      (/ x_m (- 1.0 (/ t z)))
      (if (<= z -1.1e+96)
        (* x_m (- 1.0 (/ y z)))
        (if (<= z -4.6e-52)
          t_1
          (if (<= z 8.5e-162)
            (* (- y z) (/ x_m t))
            (if (<= z 8e+35) (* x_m (/ y (- t z))) t_1))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -2.65e+150) {
		tmp = x_m / (1.0 - (t / z));
	} else if (z <= -1.1e+96) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -4.6e-52) {
		tmp = t_1;
	} else if (z <= 8.5e-162) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 8e+35) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (z / (z - t))
    if (z <= (-2.65d+150)) then
        tmp = x_m / (1.0d0 - (t / z))
    else if (z <= (-1.1d+96)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= (-4.6d-52)) then
        tmp = t_1
    else if (z <= 8.5d-162) then
        tmp = (y - z) * (x_m / t)
    else if (z <= 8d+35) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -2.65e+150) {
		tmp = x_m / (1.0 - (t / z));
	} else if (z <= -1.1e+96) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -4.6e-52) {
		tmp = t_1;
	} else if (z <= 8.5e-162) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 8e+35) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (z / (z - t))
	tmp = 0
	if z <= -2.65e+150:
		tmp = x_m / (1.0 - (t / z))
	elif z <= -1.1e+96:
		tmp = x_m * (1.0 - (y / z))
	elif z <= -4.6e-52:
		tmp = t_1
	elif z <= 8.5e-162:
		tmp = (y - z) * (x_m / t)
	elif z <= 8e+35:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -2.65e+150)
		tmp = Float64(x_m / Float64(1.0 - Float64(t / z)));
	elseif (z <= -1.1e+96)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= -4.6e-52)
		tmp = t_1;
	elseif (z <= 8.5e-162)
		tmp = Float64(Float64(y - z) * Float64(x_m / t));
	elseif (z <= 8e+35)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (z / (z - t));
	tmp = 0.0;
	if (z <= -2.65e+150)
		tmp = x_m / (1.0 - (t / z));
	elseif (z <= -1.1e+96)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= -4.6e-52)
		tmp = t_1;
	elseif (z <= 8.5e-162)
		tmp = (y - z) * (x_m / t);
	elseif (z <= 8e+35)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.65e+150], N[(x$95$m / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e+96], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.6e-52], t$95$1, If[LessEqual[z, 8.5e-162], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+35], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if z < -2.65000000000000007e150

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 89.2%

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

      3. distribute-neg-frac 89.2%

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

      4. div-sub 89.2%

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

      5. *-inverses 89.2%

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

   7. Simplified 89.2%

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

      1. frac-2neg 89.2%

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

      2. div-inv 89.1%

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

      3. remove-double-neg 89.1%

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

      4. sub-neg 89.1%

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

      5. metadata-eval 89.1%

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

      6. distribute-neg-in 89.1%

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

      7. metadata-eval 89.1%

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

   9. Applied egg-rr 89.1%

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

       1. associate-*r/ 89.2%

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

       2. *-rgt-identity 89.2%

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

       3. +-commutative 89.2%

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

       4. unsub-neg 89.2%

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

   11. Simplified 89.2%

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

   if -2.65000000000000007e150 < z < -1.0999999999999999e96

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. div-sub 87.3%

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

      3. sub-neg 87.3%

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

      4. *-inverses 87.3%

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

      5. metadata-eval 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 87.3%

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

   if -1.0999999999999999e96 < z < -4.59999999999999989e-52 or 7.9999999999999997e35 < z

   1. Initial program 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   7. Simplified 77.8%

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

      1. *-commutative 77.8%

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

      2. frac-2neg 77.8%

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

      3. remove-double-neg 77.8%

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

      4. associate-*l/ 61.7%

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

      5. sub-neg 61.7%

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

      6. distribute-neg-in 61.7%

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

      7. remove-double-neg 61.7%

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

   9. Applied egg-rr 61.7%

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

       1. associate-/l* 64.9%

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

       2. associate-/r/ 77.8%

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

       3. +-commutative 77.8%

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

       4. unsub-neg 77.8%

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

   11. Simplified 77.8%

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

   if -4.59999999999999989e-52 < z < 8.49999999999999955e-162

   1. Initial program 92.9%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 86.5%

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

   if 8.49999999999999955e-162 < z < 7.9999999999999997e35

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.8%

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

      3. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 74.5%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-162}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{z}{z - t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+148}:\\ \;\;\;\;\frac{x_m}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+103}:\\ \;\;\;\;x_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-161}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x_m}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+30}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ z (- z t)))))
   (*
    x_s
    (if (<= z -6.4e+148)
      (/ x_m (- 1.0 (/ t z)))
      (if (<= z -1.02e+103)
        (* x_m (- 1.0 (/ y z)))
        (if (<= z -1.7e-51)
          t_1
          (if (<= z 2.7e-161)
            (/ (- y z) (/ t x_m))
            (if (<= z 5e+30) (* x_m (/ y (- t z))) t_1))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -6.4e+148) {
		tmp = x_m / (1.0 - (t / z));
	} else if (z <= -1.02e+103) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -1.7e-51) {
		tmp = t_1;
	} else if (z <= 2.7e-161) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 5e+30) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (z / (z - t))
    if (z <= (-6.4d+148)) then
        tmp = x_m / (1.0d0 - (t / z))
    else if (z <= (-1.02d+103)) then
        tmp = x_m * (1.0d0 - (y / z))
    else if (z <= (-1.7d-51)) then
        tmp = t_1
    else if (z <= 2.7d-161) then
        tmp = (y - z) / (t / x_m)
    else if (z <= 5d+30) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (z / (z - t));
	double tmp;
	if (z <= -6.4e+148) {
		tmp = x_m / (1.0 - (t / z));
	} else if (z <= -1.02e+103) {
		tmp = x_m * (1.0 - (y / z));
	} else if (z <= -1.7e-51) {
		tmp = t_1;
	} else if (z <= 2.7e-161) {
		tmp = (y - z) / (t / x_m);
	} else if (z <= 5e+30) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (z / (z - t))
	tmp = 0
	if z <= -6.4e+148:
		tmp = x_m / (1.0 - (t / z))
	elif z <= -1.02e+103:
		tmp = x_m * (1.0 - (y / z))
	elif z <= -1.7e-51:
		tmp = t_1
	elif z <= 2.7e-161:
		tmp = (y - z) / (t / x_m)
	elif z <= 5e+30:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -6.4e+148)
		tmp = Float64(x_m / Float64(1.0 - Float64(t / z)));
	elseif (z <= -1.02e+103)
		tmp = Float64(x_m * Float64(1.0 - Float64(y / z)));
	elseif (z <= -1.7e-51)
		tmp = t_1;
	elseif (z <= 2.7e-161)
		tmp = Float64(Float64(y - z) / Float64(t / x_m));
	elseif (z <= 5e+30)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (z / (z - t));
	tmp = 0.0;
	if (z <= -6.4e+148)
		tmp = x_m / (1.0 - (t / z));
	elseif (z <= -1.02e+103)
		tmp = x_m * (1.0 - (y / z));
	elseif (z <= -1.7e-51)
		tmp = t_1;
	elseif (z <= 2.7e-161)
		tmp = (y - z) / (t / x_m);
	elseif (z <= 5e+30)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6.4e+148], N[(x$95$m / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.02e+103], N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-51], t$95$1, If[LessEqual[z, 2.7e-161], N[(N[(y - z), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+30], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if z < -6.3999999999999999e148

   1. Initial program 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. associate-/l* 89.2%

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

      3. distribute-neg-frac 89.2%

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

      4. div-sub 89.2%

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

      5. *-inverses 89.2%

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

   7. Simplified 89.2%

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

      1. frac-2neg 89.2%

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

      2. div-inv 89.1%

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

      3. remove-double-neg 89.1%

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

      4. sub-neg 89.1%

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

      5. metadata-eval 89.1%

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

      6. distribute-neg-in 89.1%

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

      7. metadata-eval 89.1%

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

   9. Applied egg-rr 89.1%

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

       1. associate-*r/ 89.2%

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

       2. *-rgt-identity 89.2%

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

       3. +-commutative 89.2%

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

       4. unsub-neg 89.2%

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

   11. Simplified 89.2%

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

   if -6.3999999999999999e148 < z < -1.01999999999999991e103

   1. Initial program 87.4%

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

      1. *-commutative 87.4%

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

      2. associate-*l/ 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. div-sub 87.3%

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

      3. sub-neg 87.3%

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

      4. *-inverses 87.3%

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

      5. metadata-eval 87.3%

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

   7. Simplified 87.3%

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

   8. Taylor expanded in x around 0 87.3%

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

   if -1.01999999999999991e103 < z < -1.70000000000000001e-51 or 4.9999999999999998e30 < z

   1. Initial program 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   7. Simplified 77.8%

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

      1. *-commutative 77.8%

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

      2. frac-2neg 77.8%

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

      3. remove-double-neg 77.8%

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

      4. associate-*l/ 61.7%

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

      5. sub-neg 61.7%

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

      6. distribute-neg-in 61.7%

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

      7. remove-double-neg 61.7%

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

   9. Applied egg-rr 61.7%

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

       1. associate-/l* 64.9%

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

       2. associate-/r/ 77.8%

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

       3. +-commutative 77.8%

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

       4. unsub-neg 77.8%

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

   11. Simplified 77.8%

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

   if -1.70000000000000001e-51 < z < 2.6999999999999999e-161

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l/ 88.3%

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

      3. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around 0 92.9%

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

      1. associate-*r/ 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-/r/ 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in t around inf 86.5%

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

   if 2.6999999999999999e-161 < z < 4.9999999999999998e30

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.8%

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

      3. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around inf 74.5%

      \[\leadsto x \cdot \color{blue}{\frac{y}{t - z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-161}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \frac{-z}{t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ (- z) t))))
   (*
    x_s
    (if (<= z -1.8e+63)
      x_m
      (if (<= z -4.6e-51)
        t_1
        (if (<= z 5.2e-45) (/ (* x_m y) t) (if (<= z 1.4e+83) t_1 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 = x_m * (-z / t);
	double tmp;
	if (z <= -1.8e+63) {
		tmp = x_m;
	} else if (z <= -4.6e-51) {
		tmp = t_1;
	} else if (z <= 5.2e-45) {
		tmp = (x_m * y) / t;
	} else if (z <= 1.4e+83) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x_m * (-z / t)
    if (z <= (-1.8d+63)) then
        tmp = x_m
    else if (z <= (-4.6d-51)) then
        tmp = t_1
    else if (z <= 5.2d-45) then
        tmp = (x_m * y) / t
    else if (z <= 1.4d+83) then
        tmp = t_1
    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 t_1 = x_m * (-z / t);
	double tmp;
	if (z <= -1.8e+63) {
		tmp = x_m;
	} else if (z <= -4.6e-51) {
		tmp = t_1;
	} else if (z <= 5.2e-45) {
		tmp = (x_m * y) / t;
	} else if (z <= 1.4e+83) {
		tmp = t_1;
	} 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):
	t_1 = x_m * (-z / t)
	tmp = 0
	if z <= -1.8e+63:
		tmp = x_m
	elif z <= -4.6e-51:
		tmp = t_1
	elif z <= 5.2e-45:
		tmp = (x_m * y) / t
	elif z <= 1.4e+83:
		tmp = t_1
	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)
	t_1 = Float64(x_m * Float64(Float64(-z) / t))
	tmp = 0.0
	if (z <= -1.8e+63)
		tmp = x_m;
	elseif (z <= -4.6e-51)
		tmp = t_1;
	elseif (z <= 5.2e-45)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 1.4e+83)
		tmp = t_1;
	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)
	t_1 = x_m * (-z / t);
	tmp = 0.0;
	if (z <= -1.8e+63)
		tmp = x_m;
	elseif (z <= -4.6e-51)
		tmp = t_1;
	elseif (z <= 5.2e-45)
		tmp = (x_m * y) / t;
	elseif (z <= 1.4e+83)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x$95$m * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.8e+63], x$95$m, If[LessEqual[z, -4.6e-51], t$95$1, If[LessEqual[z, 5.2e-45], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.4e+83], t$95$1, x$95$m]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999999e63 or 1.4e83 < z

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 61.6%

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

   if -1.79999999999999999e63 < z < -4.60000000000000004e-51 or 5.19999999999999973e-45 < z < 1.4e83

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 61.0%

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

   6. Taylor expanded in y around 0 51.3%

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

      1. neg-mul-1 51.3%

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

      2. distribute-neg-frac 51.3%

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

   8. Simplified 51.3%

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

   if -4.60000000000000004e-51 < z < 5.19999999999999973e-45

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l/ 89.8%

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

      3. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in z around 0 68.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-54}:\\ \;\;\;\;x_m \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{-x_m}{t}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -5.5e+59)
    x_m
    (if (<= z -3.2e-54)
      (* x_m (/ (- z) t))
      (if (<= z 4.2e-45)
        (/ (* x_m y) t)
        (if (<= z 3.6e+82) (* z (/ (- x_m) 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 <= -5.5e+59) {
		tmp = x_m;
	} else if (z <= -3.2e-54) {
		tmp = x_m * (-z / t);
	} else if (z <= 4.2e-45) {
		tmp = (x_m * y) / t;
	} else if (z <= 3.6e+82) {
		tmp = z * (-x_m / 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 <= (-5.5d+59)) then
        tmp = x_m
    else if (z <= (-3.2d-54)) then
        tmp = x_m * (-z / t)
    else if (z <= 4.2d-45) then
        tmp = (x_m * y) / t
    else if (z <= 3.6d+82) then
        tmp = z * (-x_m / 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 <= -5.5e+59) {
		tmp = x_m;
	} else if (z <= -3.2e-54) {
		tmp = x_m * (-z / t);
	} else if (z <= 4.2e-45) {
		tmp = (x_m * y) / t;
	} else if (z <= 3.6e+82) {
		tmp = z * (-x_m / 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 <= -5.5e+59:
		tmp = x_m
	elif z <= -3.2e-54:
		tmp = x_m * (-z / t)
	elif z <= 4.2e-45:
		tmp = (x_m * y) / t
	elif z <= 3.6e+82:
		tmp = z * (-x_m / 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 <= -5.5e+59)
		tmp = x_m;
	elseif (z <= -3.2e-54)
		tmp = Float64(x_m * Float64(Float64(-z) / t));
	elseif (z <= 4.2e-45)
		tmp = Float64(Float64(x_m * y) / t);
	elseif (z <= 3.6e+82)
		tmp = Float64(z * Float64(Float64(-x_m) / 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 <= -5.5e+59)
		tmp = x_m;
	elseif (z <= -3.2e-54)
		tmp = x_m * (-z / t);
	elseif (z <= 4.2e-45)
		tmp = (x_m * y) / t;
	elseif (z <= 3.6e+82)
		tmp = z * (-x_m / 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, -5.5e+59], x$95$m, If[LessEqual[z, -3.2e-54], N[(x$95$m * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-45], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.6e+82], N[(z * N[((-x$95$m) / t), $MachinePrecision]), $MachinePrecision], x$95$m]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -5.4999999999999999e59 or 3.60000000000000014e82 < z

   1. Initial program 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 61.6%

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

   if -5.4999999999999999e59 < z < -3.19999999999999998e-54

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 65.4%

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

   6. Taylor expanded in y around 0 60.9%

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

      1. neg-mul-1 60.9%

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

      2. distribute-neg-frac 60.9%

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

   8. Simplified 60.9%

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

   if -3.19999999999999998e-54 < z < 4.1999999999999999e-45

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l/ 89.8%

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

      3. *-commutative 89.8%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in z around 0 68.3%

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

   if 4.1999999999999999e-45 < z < 3.60000000000000014e82

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 57.3%

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

   6. Taylor expanded in y around 0 39.3%

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

      1. mul-1-neg 39.3%

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

      2. associate-/l* 43.3%

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

      3. distribute-neg-frac 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in x around 0 39.3%

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

       1. mul-1-neg 39.3%

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

       2. associate-*l/ 43.3%

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

       3. distribute-rgt-neg-out 43.3%

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

   11. Simplified 43.3%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot \left(-z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-45}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+82}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \left(1 - \frac{y}{z}\right)\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{-x_m}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -7.2e+50)
      t_1
      (if (<= z -2.2e-55)
        (/ (- x_m) (/ t z))
        (if (<= z 2.5e-8) (/ (* x_m y) t) t_1))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -7.2e+50) {
		tmp = t_1;
	} else if (z <= -2.2e-55) {
		tmp = -x_m / (t / z);
	} else if (z <= 2.5e-8) {
		tmp = (x_m * y) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (1.0d0 - (y / z))
    if (z <= (-7.2d+50)) then
        tmp = t_1
    else if (z <= (-2.2d-55)) then
        tmp = -x_m / (t / z)
    else if (z <= 2.5d-8) then
        tmp = (x_m * y) / t
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -7.2e+50) {
		tmp = t_1;
	} else if (z <= -2.2e-55) {
		tmp = -x_m / (t / z);
	} else if (z <= 2.5e-8) {
		tmp = (x_m * y) / t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -7.2e+50:
		tmp = t_1
	elif z <= -2.2e-55:
		tmp = -x_m / (t / z)
	elif z <= 2.5e-8:
		tmp = (x_m * y) / t
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -7.2e+50)
		tmp = t_1;
	elseif (z <= -2.2e-55)
		tmp = Float64(Float64(-x_m) / Float64(t / z));
	elseif (z <= 2.5e-8)
		tmp = Float64(Float64(x_m * y) / t);
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -7.2e+50)
		tmp = t_1;
	elseif (z <= -2.2e-55)
		tmp = -x_m / (t / z);
	elseif (z <= 2.5e-8)
		tmp = (x_m * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -7.2e+50], t$95$1, If[LessEqual[z, -2.2e-55], N[((-x$95$m) / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-8], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -7.19999999999999972e50 or 2.4999999999999999e-8 < z

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. div-sub 73.8%

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

      3. sub-neg 73.8%

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

      4. *-inverses 73.8%

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

      5. metadata-eval 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around 0 73.8%

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

   if -7.19999999999999972e50 < z < -2.2e-55

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 66.8%

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

   6. Taylor expanded in y around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. associate-/l* 62.0%

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

      3. distribute-neg-frac 62.0%

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

   8. Simplified 62.0%

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

   if -2.2e-55 < z < 2.4999999999999999e-8

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*l/ 90.4%

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

      3. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in z around 0 66.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{-x}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \left(1 - \frac{y}{z}\right)\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-163}:\\ \;\;\;\;x_m \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -1.22e+64)
      t_1
      (if (<= z -1.1e-163)
        (* x_m (/ (- y z) t))
        (if (<= z 3.5e+82) (* x_m (/ y (- t z))) t_1))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -1.22e+64) {
		tmp = t_1;
	} else if (z <= -1.1e-163) {
		tmp = x_m * ((y - z) / t);
	} else if (z <= 3.5e+82) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (1.0d0 - (y / z))
    if (z <= (-1.22d+64)) then
        tmp = t_1
    else if (z <= (-1.1d-163)) then
        tmp = x_m * ((y - z) / t)
    else if (z <= 3.5d+82) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -1.22e+64) {
		tmp = t_1;
	} else if (z <= -1.1e-163) {
		tmp = x_m * ((y - z) / t);
	} else if (z <= 3.5e+82) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -1.22e+64:
		tmp = t_1
	elif z <= -1.1e-163:
		tmp = x_m * ((y - z) / t)
	elif z <= 3.5e+82:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.22e+64)
		tmp = t_1;
	elseif (z <= -1.1e-163)
		tmp = Float64(x_m * Float64(Float64(y - z) / t));
	elseif (z <= 3.5e+82)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.22e+64)
		tmp = t_1;
	elseif (z <= -1.1e-163)
		tmp = x_m * ((y - z) / t);
	elseif (z <= 3.5e+82)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.22e+64], t$95$1, If[LessEqual[z, -1.1e-163], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+82], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999994e64 or 3.5e82 < z

   1. Initial program 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. div-sub 77.0%

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

      3. sub-neg 77.0%

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

      4. *-inverses 77.0%

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

      5. metadata-eval 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in x around 0 77.0%

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

   if -1.21999999999999994e64 < z < -1.10000000000000005e-163

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around inf 72.3%

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

   if -1.10000000000000005e-163 < z < 3.5e82

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-*l/ 91.7%

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

      3. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in y around inf 76.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x_m \cdot \left(1 - \frac{y}{z}\right)\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- 1.0 (/ y z)))))
   (*
    x_s
    (if (<= z -6e+65)
      t_1
      (if (<= z 1.45e-161)
        (* (- y z) (/ x_m t))
        (if (<= z 3.5e+82) (* x_m (/ y (- t z))) t_1))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -6e+65) {
		tmp = t_1;
	} else if (z <= 1.45e-161) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 3.5e+82) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (1.0d0 - (y / z))
    if (z <= (-6d+65)) then
        tmp = t_1
    else if (z <= 1.45d-161) then
        tmp = (y - z) * (x_m / t)
    else if (z <= 3.5d+82) then
        tmp = x_m * (y / (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (1.0 - (y / z));
	double tmp;
	if (z <= -6e+65) {
		tmp = t_1;
	} else if (z <= 1.45e-161) {
		tmp = (y - z) * (x_m / t);
	} else if (z <= 3.5e+82) {
		tmp = x_m * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (1.0 - (y / z))
	tmp = 0
	if z <= -6e+65:
		tmp = t_1
	elif z <= 1.45e-161:
		tmp = (y - z) * (x_m / t)
	elif z <= 3.5e+82:
		tmp = x_m * (y / (t - z))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6e+65)
		tmp = t_1;
	elseif (z <= 1.45e-161)
		tmp = Float64(Float64(y - z) * Float64(x_m / t));
	elseif (z <= 3.5e+82)
		tmp = Float64(x_m * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6e+65)
		tmp = t_1;
	elseif (z <= 1.45e-161)
		tmp = (y - z) * (x_m / t);
	elseif (z <= 3.5e+82)
		tmp = x_m * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -6e+65], t$95$1, If[LessEqual[z, 1.45e-161], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+82], N[(x$95$m * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000004e65 or 3.5e82 < z

   1. Initial program 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. div-sub 77.0%

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

      3. sub-neg 77.0%

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

      4. *-inverses 77.0%

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

      5. metadata-eval 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in x around 0 77.0%

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

   if -6.0000000000000004e65 < z < 1.45e-161

   1. Initial program 93.4%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in t around inf 80.7%

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

   if 1.45e-161 < z < 3.5e82

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 96.3%

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

      3. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around inf 70.6%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+63} \lor \neg \left(z \leq 3.5 \cdot 10^{+82}\right):\\ \;\;\;\;x_m \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -7.8e+63) (not (<= z 3.5e+82)))
    (* 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 <= -7.8e+63) || !(z <= 3.5e+82)) {
		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 <= (-7.8d+63)) .or. (.not. (z <= 3.5d+82))) 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 <= -7.8e+63) || !(z <= 3.5e+82)) {
		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 <= -7.8e+63) or not (z <= 3.5e+82):
		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 <= -7.8e+63) || !(z <= 3.5e+82))
		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 <= -7.8e+63) || ~((z <= 3.5e+82)))
		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, -7.8e+63], N[Not[LessEqual[z, 3.5e+82]], $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 < -7.8e63 or 3.5e82 < z

   1. Initial program 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. div-sub 77.0%

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

      3. sub-neg 77.0%

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

      4. *-inverses 77.0%

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

      5. metadata-eval 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in x around 0 77.0%

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

   if -7.8e63 < z < 3.5e82

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 92.7%

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

      3. *-commutative 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 y around inf 71.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+63} \lor \neg \left(z \leq 3.5 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;x_m \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x_m}{t - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 3.9e-69)
    (* x_m (/ (- y z) (- t z)))
    (* (- y z) (/ x_m (- 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 (x_m <= 3.9e-69) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (x_m / (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 (x_m <= 3.9d-69) then
        tmp = x_m * ((y - z) / (t - z))
    else
        tmp = (y - z) * (x_m / (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 (x_m <= 3.9e-69) {
		tmp = x_m * ((y - z) / (t - z));
	} else {
		tmp = (y - z) * (x_m / (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 x_m <= 3.9e-69:
		tmp = x_m * ((y - z) / (t - z))
	else:
		tmp = (y - z) * (x_m / (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 (x_m <= 3.9e-69)
		tmp = Float64(x_m * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x_m / 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 (x_m <= 3.9e-69)
		tmp = x_m * ((y - z) / (t - z));
	else
		tmp = (y - z) * (x_m / (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[LessEqual[x$95$m, 3.9e-69], N[(x$95$m * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 3.89999999999999981e-69

   1. Initial program 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 97.7%

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

      3. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   if 3.89999999999999981e-69 < x

   1. Initial program 84.0%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+54}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+46}:\\ \;\;\;\;x_m \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -6.6e+54) x_m (if (<= z 2.06e+46) (* 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 <= -6.6e+54) {
		tmp = x_m;
	} else if (z <= 2.06e+46) {
		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 <= (-6.6d+54)) then
        tmp = x_m
    else if (z <= 2.06d+46) 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 <= -6.6e+54) {
		tmp = x_m;
	} else if (z <= 2.06e+46) {
		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 <= -6.6e+54:
		tmp = x_m
	elif z <= 2.06e+46:
		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 <= -6.6e+54)
		tmp = x_m;
	elseif (z <= 2.06e+46)
		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 <= -6.6e+54)
		tmp = x_m;
	elseif (z <= 2.06e+46)
		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, -6.6e+54], x$95$m, If[LessEqual[z, 2.06e+46], N[(x$95$m * N[(y / t), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e54 or 2.0600000000000001e46 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.8%

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

   if -6.6e54 < z < 2.0600000000000001e46

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 92.3%

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

      3. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 57.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{x_m}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -1.95e+54) x_m (if (<= z 2.8e+43) (/ x_m (/ 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) {
	double tmp;
	if (z <= -1.95e+54) {
		tmp = x_m;
	} else if (z <= 2.8e+43) {
		tmp = x_m / (t / y);
	} 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 <= (-1.95d+54)) then
        tmp = x_m
    else if (z <= 2.8d+43) then
        tmp = x_m / (t / y)
    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 <= -1.95e+54) {
		tmp = x_m;
	} else if (z <= 2.8e+43) {
		tmp = x_m / (t / y);
	} 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 <= -1.95e+54:
		tmp = x_m
	elif z <= 2.8e+43:
		tmp = x_m / (t / y)
	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 <= -1.95e+54)
		tmp = x_m;
	elseif (z <= 2.8e+43)
		tmp = Float64(x_m / Float64(t / y));
	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 <= -1.95e+54)
		tmp = x_m;
	elseif (z <= 2.8e+43)
		tmp = x_m / (t / y);
	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, -1.95e+54], x$95$m, If[LessEqual[z, 2.8e+43], N[(x$95$m / N[(t / y), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e54 or 2.80000000000000019e43 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.8%

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

   if -1.9500000000000001e54 < z < 2.80000000000000019e43

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 92.3%

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

      3. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 58.9%

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

      1. associate-/l* 58.0%

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

   7. Simplified 58.0%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+55}:\\ \;\;\;\;x_m\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x_m \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= z -9e+55) x_m (if (<= z 6.2e+41) (/ (* 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 <= -9e+55) {
		tmp = x_m;
	} else if (z <= 6.2e+41) {
		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 <= (-9d+55)) then
        tmp = x_m
    else if (z <= 6.2d+41) 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 <= -9e+55) {
		tmp = x_m;
	} else if (z <= 6.2e+41) {
		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 <= -9e+55:
		tmp = x_m
	elif z <= 6.2e+41:
		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 <= -9e+55)
		tmp = x_m;
	elseif (z <= 6.2e+41)
		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 <= -9e+55)
		tmp = x_m;
	elseif (z <= 6.2e+41)
		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, -9e+55], x$95$m, If[LessEqual[z, 6.2e+41], N[(N[(x$95$m * y), $MachinePrecision] / t), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999996e55 or 6.2e41 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.8%

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

   if -8.99999999999999996e55 < z < 6.2e41

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 92.3%

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

      3. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 58.9%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 97.0% 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 1 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 84.4%

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

   1. *-commutative 84.4%

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

   2. associate-*l/ 95.5%

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

   3. *-commutative 95.5%

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

3. Simplified 95.5%

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

5. Final simplification 95.5%

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

Alternative 19: 35.5% 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 1 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 84.4%

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

   1. *-commutative 84.4%

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

   2. associate-*l/ 95.5%

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

   3. *-commutative 95.5%

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

3. Simplified 95.5%

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

5. Taylor expanded in z around inf 30.8%

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

6. Final simplification 30.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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