Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 88.8% → 98.4%

Time: 10.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

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

Initial Program: 88.8% accurate, 1.0× speedup

Math

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

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

Alternative 1: 98.4% accurate, 0.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* (/ (sqrt x_m) (- y z)) (/ (sqrt 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) {
	return x_s * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (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 * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (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 * ((Math.sqrt(x_m) / (y - z)) * (Math.sqrt(x_m) / (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 * ((math.sqrt(x_m) / (y - z)) * (math.sqrt(x_m) / (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(Float64(sqrt(x_m) / Float64(y - z)) * Float64(sqrt(x_m) / 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 * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (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[(N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

   1. add-sqr-sqrt 40.8%

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

   2. times-frac 46.6%

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

4. Applied egg-rr 46.6%

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

Alternative 2: 70.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot \left(z - y\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.22 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* z (- z y)))))
   (*
    x_s
    (if (<= t -1.05e-77)
      (/ (/ x_m y) (- t z))
      (if (<= t 8.5e-120)
        t_1
        (if (<= t 2.22e-100)
          (/ (/ x_m t) (- y z))
          (if (<= t 8e-91)
            t_1
            (if (<= t 7e+14)
              (/ x_m (* z (- z t)))
              (/ (/ x_m (- y z)) t)))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * (z - y));
	double tmp;
	if (t <= -1.05e-77) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 8.5e-120) {
		tmp = t_1;
	} else if (t <= 2.22e-100) {
		tmp = (x_m / t) / (y - z);
	} else if (t <= 8e-91) {
		tmp = t_1;
	} else if (t <= 7e+14) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m / (z * (z - y))
    if (t <= (-1.05d-77)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 8.5d-120) then
        tmp = t_1
    else if (t <= 2.22d-100) then
        tmp = (x_m / t) / (y - z)
    else if (t <= 8d-91) then
        tmp = t_1
    else if (t <= 7d+14) then
        tmp = x_m / (z * (z - t))
    else
        tmp = (x_m / (y - z)) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * (z - y));
	double tmp;
	if (t <= -1.05e-77) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 8.5e-120) {
		tmp = t_1;
	} else if (t <= 2.22e-100) {
		tmp = (x_m / t) / (y - z);
	} else if (t <= 8e-91) {
		tmp = t_1;
	} else if (t <= 7e+14) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (z * (z - y))
	tmp = 0
	if t <= -1.05e-77:
		tmp = (x_m / y) / (t - z)
	elif t <= 8.5e-120:
		tmp = t_1
	elif t <= 2.22e-100:
		tmp = (x_m / t) / (y - z)
	elif t <= 8e-91:
		tmp = t_1
	elif t <= 7e+14:
		tmp = x_m / (z * (z - t))
	else:
		tmp = (x_m / (y - z)) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (t <= -1.05e-77)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 8.5e-120)
		tmp = t_1;
	elseif (t <= 2.22e-100)
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	elseif (t <= 8e-91)
		tmp = t_1;
	elseif (t <= 7e+14)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (z * (z - y));
	tmp = 0.0;
	if (t <= -1.05e-77)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 8.5e-120)
		tmp = t_1;
	elseif (t <= 2.22e-100)
		tmp = (x_m / t) / (y - z);
	elseif (t <= 8e-91)
		tmp = t_1;
	elseif (t <= 7e+14)
		tmp = x_m / (z * (z - t));
	else
		tmp = (x_m / (y - z)) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -1.05e-77], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-120], t$95$1, If[LessEqual[t, 2.22e-100], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-91], t$95$1, If[LessEqual[t, 7e+14], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if t < -1.05000000000000008e-77

   1. Initial program 89.3%

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

      1. associate-/r* 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around inf 62.3%

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

   if -1.05000000000000008e-77 < t < 8.50000000000000059e-120 or 2.2199999999999999e-100 < t < 8.00000000000000018e-91

   1. Initial program 90.6%

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

      1. associate-/r* 97.6%

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

      2. clear-num 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. associate-*l/ 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in x around 0 78.3%

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

   if 8.50000000000000059e-120 < t < 2.2199999999999999e-100

   1. Initial program 89.2%

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

   3. Taylor expanded in t around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/r* 89.0%

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

   5. Simplified 89.0%

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

      1. associate-/l/ 78.5%

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

      2. associate-/r* 79.1%

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

   7. Applied egg-rr 79.1%

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

   if 8.00000000000000018e-91 < t < 7e14

   1. Initial program 94.7%

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

   3. Taylor expanded in y around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-neg-frac2 48.6%

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

      3. distribute-rgt-neg-in 48.6%

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

      4. neg-sub0 48.6%

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

      5. associate--r- 48.6%

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

      6. neg-sub0 48.6%

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

      7. mul-1-neg 48.6%

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

      8. +-commutative 48.6%

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

      9. mul-1-neg 48.6%

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

      10. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   if 7e14 < t

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/r* 81.7%

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

   5. Simplified 81.7%

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

Alternative 3: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-215}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-299} \lor \neg \left(y \leq 6 \cdot 10^{-156}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.25e-7)
    (/ (/ x_m y) (- t z))
    (if (<= y -9.5e-215)
      (/ x_m (* z (- z y)))
      (if (or (<= y -3.2e-299) (not (<= y 6e-156)))
        (/ (/ x_m t) (- y z))
        (/ x_m (* z (- z t))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-7) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -9.5e-215) {
		tmp = x_m / (z * (z - y));
	} else if ((y <= -3.2e-299) || !(y <= 6e-156)) {
		tmp = (x_m / t) / (y - z);
	} else {
		tmp = x_m / (z * (z - t));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.25d-7)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= (-9.5d-215)) then
        tmp = x_m / (z * (z - y))
    else if ((y <= (-3.2d-299)) .or. (.not. (y <= 6d-156))) then
        tmp = (x_m / t) / (y - z)
    else
        tmp = x_m / (z * (z - t))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-7) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -9.5e-215) {
		tmp = x_m / (z * (z - y));
	} else if ((y <= -3.2e-299) || !(y <= 6e-156)) {
		tmp = (x_m / t) / (y - z);
	} else {
		tmp = x_m / (z * (z - t));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.25e-7:
		tmp = (x_m / y) / (t - z)
	elif y <= -9.5e-215:
		tmp = x_m / (z * (z - y))
	elif (y <= -3.2e-299) or not (y <= 6e-156):
		tmp = (x_m / t) / (y - z)
	else:
		tmp = x_m / (z * (z - t))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-7)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= -9.5e-215)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif ((y <= -3.2e-299) || !(y <= 6e-156))
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	else
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-7)
		tmp = (x_m / y) / (t - z);
	elseif (y <= -9.5e-215)
		tmp = x_m / (z * (z - y));
	elseif ((y <= -3.2e-299) || ~((y <= 6e-156)))
		tmp = (x_m / t) / (y - z);
	else
		tmp = x_m / (z * (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.25e-7], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-215], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.2e-299], N[Not[LessEqual[y, 6e-156]], $MachinePrecision]], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -2.2499999999999999e-7

   1. Initial program 81.3%

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

      1. associate-/r* 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in y around inf 84.7%

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

   if -2.2499999999999999e-7 < y < -9.5000000000000007e-215

   1. Initial program 94.7%

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

      1. associate-/r* 97.7%

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

      2. clear-num 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. associate-*l/ 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in x around 0 57.9%

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

   if -9.5000000000000007e-215 < y < -3.20000000000000008e-299 or 6e-156 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/r* 63.6%

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

   5. Simplified 63.6%

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

      1. associate-/l/ 54.9%

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

      2. associate-/r* 59.8%

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

   7. Applied egg-rr 59.8%

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

   if -3.20000000000000008e-299 < y < 6e-156

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-neg-frac2 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. neg-sub0 86.5%

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

      5. associate--r- 86.5%

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

      6. neg-sub0 86.5%

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

      7. mul-1-neg 86.5%

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

      8. +-commutative 86.5%

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

      9. mul-1-neg 86.5%

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

      10. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-299} \lor \neg \left(y \leq 6 \cdot 10^{-156}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-215}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-301} \lor \neg \left(y \leq 4.2 \cdot 10^{-155}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.25e-7)
    (/ x_m (* y (- t z)))
    (if (<= y -4.6e-215)
      (/ x_m (* z (- z y)))
      (if (or (<= y -1.2e-301) (not (<= y 4.2e-155)))
        (/ (/ x_m t) (- y z))
        (/ x_m (* z (- z t))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -4.6e-215) {
		tmp = x_m / (z * (z - y));
	} else if ((y <= -1.2e-301) || !(y <= 4.2e-155)) {
		tmp = (x_m / t) / (y - z);
	} else {
		tmp = x_m / (z * (z - t));
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.25d-7)) then
        tmp = x_m / (y * (t - z))
    else if (y <= (-4.6d-215)) then
        tmp = x_m / (z * (z - y))
    else if ((y <= (-1.2d-301)) .or. (.not. (y <= 4.2d-155))) then
        tmp = (x_m / t) / (y - z)
    else
        tmp = x_m / (z * (z - t))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -4.6e-215) {
		tmp = x_m / (z * (z - y));
	} else if ((y <= -1.2e-301) || !(y <= 4.2e-155)) {
		tmp = (x_m / t) / (y - z);
	} else {
		tmp = x_m / (z * (z - t));
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.25e-7:
		tmp = x_m / (y * (t - z))
	elif y <= -4.6e-215:
		tmp = x_m / (z * (z - y))
	elif (y <= -1.2e-301) or not (y <= 4.2e-155):
		tmp = (x_m / t) / (y - z)
	else:
		tmp = x_m / (z * (z - t))
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-7)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= -4.6e-215)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif ((y <= -1.2e-301) || !(y <= 4.2e-155))
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	else
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-7)
		tmp = x_m / (y * (t - z));
	elseif (y <= -4.6e-215)
		tmp = x_m / (z * (z - y));
	elseif ((y <= -1.2e-301) || ~((y <= 4.2e-155)))
		tmp = (x_m / t) / (y - z);
	else
		tmp = x_m / (z * (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.25e-7], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-215], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.2e-301], N[Not[LessEqual[y, 4.2e-155]], $MachinePrecision]], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -2.2499999999999999e-7

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -2.2499999999999999e-7 < y < -4.5999999999999998e-215

   1. Initial program 94.7%

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

      1. associate-/r* 97.7%

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

      2. clear-num 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. associate-*l/ 61.9%

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

      3. distribute-rgt-neg-in 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in x around 0 57.9%

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

   if -4.5999999999999998e-215 < y < -1.19999999999999996e-301 or 4.2000000000000003e-155 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf 54.9%

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

      1. *-commutative 54.9%

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

      2. associate-/r* 63.6%

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

   5. Simplified 63.6%

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

      1. associate-/l/ 54.9%

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

      2. associate-/r* 59.8%

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

   7. Applied egg-rr 59.8%

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

   if -1.19999999999999996e-301 < y < 4.2000000000000003e-155

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-neg-frac2 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. neg-sub0 86.5%

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

      5. associate--r- 86.5%

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

      6. neg-sub0 86.5%

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

      7. mul-1-neg 86.5%

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

      8. +-commutative 86.5%

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

      9. mul-1-neg 86.5%

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

      10. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-301} \lor \neg \left(y \leq 4.2 \cdot 10^{-155}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot \left(z - t\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-68} \lor \neg \left(z \leq 1.25 \cdot 10^{-52}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* z (- z t)))))
   (*
    x_s
    (if (<= z -1.5e-62)
      t_1
      (if (<= z 6.8e-113)
        (/ (/ x_m y) t)
        (if (or (<= z 4.5e-68) (not (<= z 1.25e-52))) t_1 (/ x_m (* y t))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * (z - t));
	double tmp;
	if (z <= -1.5e-62) {
		tmp = t_1;
	} else if (z <= 6.8e-113) {
		tmp = (x_m / y) / t;
	} else if ((z <= 4.5e-68) || !(z <= 1.25e-52)) {
		tmp = t_1;
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m / (z * (z - t))
    if (z <= (-1.5d-62)) then
        tmp = t_1
    else if (z <= 6.8d-113) then
        tmp = (x_m / y) / t
    else if ((z <= 4.5d-68) .or. (.not. (z <= 1.25d-52))) then
        tmp = t_1
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (z * (z - t));
	double tmp;
	if (z <= -1.5e-62) {
		tmp = t_1;
	} else if (z <= 6.8e-113) {
		tmp = (x_m / y) / t;
	} else if ((z <= 4.5e-68) || !(z <= 1.25e-52)) {
		tmp = t_1;
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (z * (z - t))
	tmp = 0
	if z <= -1.5e-62:
		tmp = t_1
	elif z <= 6.8e-113:
		tmp = (x_m / y) / t
	elif (z <= 4.5e-68) or not (z <= 1.25e-52):
		tmp = t_1
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -1.5e-62)
		tmp = t_1;
	elseif (z <= 6.8e-113)
		tmp = Float64(Float64(x_m / y) / t);
	elseif ((z <= 4.5e-68) || !(z <= 1.25e-52))
		tmp = t_1;
	else
		tmp = Float64(x_m / Float64(y * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (z * (z - t));
	tmp = 0.0;
	if (z <= -1.5e-62)
		tmp = t_1;
	elseif (z <= 6.8e-113)
		tmp = (x_m / y) / t;
	elseif ((z <= 4.5e-68) || ~((z <= 1.25e-52)))
		tmp = t_1;
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -1.5e-62], t$95$1, If[LessEqual[z, 6.8e-113], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[z, 4.5e-68], N[Not[LessEqual[z, 1.25e-52]], $MachinePrecision]], t$95$1, N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e-62 or 6.8000000000000005e-113 < z < 4.49999999999999999e-68 or 1.25e-52 < z

   1. Initial program 83.4%

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

   3. Taylor expanded in y around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-neg-frac2 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. neg-sub0 69.3%

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

      5. associate--r- 69.3%

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

      6. neg-sub0 69.3%

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

      7. mul-1-neg 69.3%

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

      8. +-commutative 69.3%

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

      9. mul-1-neg 69.3%

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

      10. unsub-neg 69.3%

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

   5. Simplified 69.3%

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

   if -1.5000000000000001e-62 < z < 6.8000000000000005e-113

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-/r* 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in y around inf 78.4%

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

   if 4.49999999999999999e-68 < z < 1.25e-52

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 75.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-68} \lor \neg \left(z \leq 1.25 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+121}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -2.8e+22)
    (/ (/ x_m y) (- t z))
    (if (<= t 2.7e+121) (/ x_m (* (- y z) (- t z))) (/ (/ x_m (- y z)) t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e+22) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 2.7e+121) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.8d+22)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 2.7d+121) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = (x_m / (y - z)) / t
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e+22) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 2.7e+121) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (x_m / (y - z)) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -2.8e+22:
		tmp = (x_m / y) / (t - z)
	elif t <= 2.7e+121:
		tmp = x_m / ((y - z) * (t - z))
	else:
		tmp = (x_m / (y - z)) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -2.8e+22)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 2.7e+121)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -2.8e+22)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 2.7e+121)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = (x_m / (y - z)) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -2.8e+22], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e+121], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e22

   1. Initial program 88.4%

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

      1. associate-/r* 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf 64.1%

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

   if -2.8e22 < t < 2.7000000000000002e121

   1. Initial program 89.3%

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

   if 2.7000000000000002e121 < t

   1. Initial program 74.0%

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

   3. Taylor expanded in t around inf 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-/r* 92.2%

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

   5. Simplified 92.2%

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

Alternative 7: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-155}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.15e-5)
    (/ (/ x_m y) (- t z))
    (if (<= y 2.3e-155) (/ (/ x_m z) (- z t)) (/ (/ x_m t) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-5) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 2.3e-155) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.15d-5)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 2.3d-155) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-5) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 2.3e-155) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.15e-5:
		tmp = (x_m / y) / (t - z)
	elif y <= 2.3e-155:
		tmp = (x_m / z) / (z - t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.15e-5)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 2.3e-155)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.15e-5)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 2.3e-155)
		tmp = (x_m / z) / (z - t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.15e-5], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-155], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.1500000000000001e-5

   1. Initial program 81.3%

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

      1. associate-/r* 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in y around inf 84.7%

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

   if -2.1500000000000001e-5 < y < 2.30000000000000005e-155

   1. Initial program 92.3%

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

      1. associate-/r* 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in y around 0 84.1%

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

      1. associate-*r/ 84.1%

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

      2. neg-mul-1 84.1%

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

   7. Simplified 84.1%

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

   if 2.30000000000000005e-155 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in t around inf 54.2%

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

      1. *-commutative 54.2%

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

      2. associate-/r* 62.8%

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

   5. Simplified 62.8%

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

      1. associate-/l/ 54.2%

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

      2. associate-/r* 58.7%

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

   7. Applied egg-rr 58.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-155}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -4e-7)
    (/ x_m (* y (- t z)))
    (if (<= y 5.2e-119) (/ x_m (* z (- z t))) (/ (/ 1.0 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 (y <= -4e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 5.2e-119) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (1.0 / y) / (t / x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d-7)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 5.2d-119) then
        tmp = x_m / (z * (z - t))
    else
        tmp = (1.0d0 / y) / (t / x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 5.2e-119) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (1.0 / y) / (t / x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -4e-7:
		tmp = x_m / (y * (t - z))
	elif y <= 5.2e-119:
		tmp = x_m / (z * (z - t))
	else:
		tmp = (1.0 / y) / (t / x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -4e-7)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 5.2e-119)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(1.0 / y) / Float64(t / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -4e-7)
		tmp = x_m / (y * (t - z));
	elseif (y <= 5.2e-119)
		tmp = x_m / (z * (z - t));
	else
		tmp = (1.0 / y) / (t / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -4e-7], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-119], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] / N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999998e-7

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -3.9999999999999998e-7 < y < 5.20000000000000023e-119

   1. Initial program 92.8%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-neg-frac2 80.5%

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

      3. distribute-rgt-neg-in 80.5%

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

      4. neg-sub0 80.5%

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

      5. associate--r- 80.5%

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

      6. neg-sub0 80.5%

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

      7. mul-1-neg 80.5%

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

      8. +-commutative 80.5%

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

      9. mul-1-neg 80.5%

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

      10. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if 5.20000000000000023e-119 < y

   1. Initial program 84.2%

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

   3. Taylor expanded in z around 0 46.4%

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

      1. associate-/r* 49.3%

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

   5. Applied egg-rr 49.3%

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

      1. div-inv 49.3%

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

      2. clear-num 49.2%

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

      3. associate-*l/ 50.2%

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

      4. *-un-lft-identity 50.2%

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

   7. Applied egg-rr 50.2%

      \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.3e-7)
    (/ x_m (* y (- t z)))
    (if (<= y 8.2e-121) (/ x_m (* z (- z t))) (/ (/ x_m t) y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 8.2e-121) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.3d-7)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 8.2d-121) then
        tmp = x_m / (z * (z - t))
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e-7) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 8.2e-121) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.3e-7:
		tmp = x_m / (y * (t - z))
	elif y <= 8.2e-121:
		tmp = x_m / (z * (z - t))
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.3e-7)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 8.2e-121)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.3e-7)
		tmp = x_m / (y * (t - z));
	elseif (y <= 8.2e-121)
		tmp = x_m / (z * (z - t));
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.3e-7], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-121], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999995e-7

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

   if -2.29999999999999995e-7 < y < 8.19999999999999965e-121

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. distribute-neg-frac2 81.3%

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

      3. distribute-rgt-neg-in 81.3%

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

      4. neg-sub0 81.3%

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

      5. associate--r- 81.3%

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

      6. neg-sub0 81.3%

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

      7. mul-1-neg 81.3%

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

      8. +-commutative 81.3%

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

      9. mul-1-neg 81.3%

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

      10. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

   if 8.19999999999999965e-121 < y

   1. Initial program 84.4%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. associate-/r* 49.8%

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

   5. Applied egg-rr 49.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{x\_m}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -4.05e-109)
    (/ (/ x_m y) t)
    (if (<= y 4e-121) (/ (/ x_m (- z)) t) (/ (/ x_m t) y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.05e-109) {
		tmp = (x_m / y) / t;
	} else if (y <= 4e-121) {
		tmp = (x_m / -z) / t;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.05d-109)) then
        tmp = (x_m / y) / t
    else if (y <= 4d-121) then
        tmp = (x_m / -z) / t
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.05e-109) {
		tmp = (x_m / y) / t;
	} else if (y <= 4e-121) {
		tmp = (x_m / -z) / t;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -4.05e-109:
		tmp = (x_m / y) / t
	elif y <= 4e-121:
		tmp = (x_m / -z) / t
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -4.05e-109)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (y <= 4e-121)
		tmp = Float64(Float64(x_m / Float64(-z)) / t);
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -4.05e-109)
		tmp = (x_m / y) / t;
	elseif (y <= 4e-121)
		tmp = (x_m / -z) / t;
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -4.05e-109], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 4e-121], N[(N[(x$95$m / (-z)), $MachinePrecision] / t), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -4.0500000000000001e-109

   1. Initial program 83.9%

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

   3. Taylor expanded in t around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-/r* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 56.4%

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

   if -4.0500000000000001e-109 < y < 3.9999999999999999e-121

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-/r* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around 0 56.1%

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

      1. associate-*r/ 90.5%

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

      2. neg-mul-1 90.5%

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

   8. Simplified 56.1%

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

   if 3.9999999999999999e-121 < y

   1. Initial program 84.4%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. associate-/r* 49.8%

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

   5. Applied egg-rr 49.8%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.05 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -1.06e-108)
    (/ (/ x_m y) t)
    (if (<= y 5.4e-121) (/ (- x_m) (* z t)) (/ (/ x_m t) y)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e-108) {
		tmp = (x_m / y) / t;
	} else if (y <= 5.4e-121) {
		tmp = -x_m / (z * t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.06d-108)) then
        tmp = (x_m / y) / t
    else if (y <= 5.4d-121) then
        tmp = -x_m / (z * t)
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.06e-108) {
		tmp = (x_m / y) / t;
	} else if (y <= 5.4e-121) {
		tmp = -x_m / (z * t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -1.06e-108:
		tmp = (x_m / y) / t
	elif y <= 5.4e-121:
		tmp = -x_m / (z * t)
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -1.06e-108)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (y <= 5.4e-121)
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -1.06e-108)
		tmp = (x_m / y) / t;
	elseif (y <= 5.4e-121)
		tmp = -x_m / (z * t);
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -1.06e-108], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 5.4e-121], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e-108

   1. Initial program 83.9%

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

   3. Taylor expanded in t around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-/r* 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around inf 56.4%

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

   if -1.06e-108 < y < 5.4000000000000004e-121

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-/r* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in y around 0 53.0%

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

      1. associate-*r/ 53.0%

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

      2. neg-mul-1 53.0%

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

   8. Simplified 53.0%

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

   if 5.4000000000000004e-121 < y

   1. Initial program 84.4%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. associate-/r* 49.8%

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

   5. Applied egg-rr 49.8%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= y -3e-92) (/ (/ x_m y) t) (/ (/ x_m t) y))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -3e-92) {
		tmp = (x_m / y) / t;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d-92)) then
        tmp = (x_m / y) / t
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -3e-92) {
		tmp = (x_m / y) / t;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -3e-92:
		tmp = (x_m / y) / t
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -3e-92)
		tmp = Float64(Float64(x_m / y) / t);
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -3e-92)
		tmp = (x_m / y) / t;
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -3e-92], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000013e-92

   1. Initial program 83.5%

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

   3. Taylor expanded in t around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/r* 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in y around inf 56.4%

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

   if -3.00000000000000013e-92 < y

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 34.9%

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

      1. associate-/r* 40.5%

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

   5. Applied egg-rr 40.5%

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

Alternative 13: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(Float64(x_m / 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[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

   1. associate-/r* 98.2%

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

4. Applied egg-rr 98.2%

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

Alternative 14: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((x_m / (t - z)) / (y - 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 / (t - z)) / (y - 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 / (t - z)) / (y - 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 / (t - z)) / (y - 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(Float64(x_m / Float64(t - z)) / Float64(y - 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 / (t - z)) / (y - 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[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in x around 0 86.9%

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

   1. associate-/r* 97.2%

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

5. Simplified 97.2%

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

Alternative 15: 43.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 / t) / y)
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 / t) / y);
}

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 / t) / y)

Julia

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in z around 0 39.3%

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

   1. associate-/r* 44.8%

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

5. Applied egg-rr 44.8%

   \[\leadsto \color{blue}{\frac{\frac{x}{t}}{y}} \]
6. Add Preprocessing

Alternative 16: 39.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 * t))
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 * t));
}

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 * t))

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(y * t)))
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 * t));
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[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in z around 0 39.3%

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

4. Final simplification 39.3%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 87.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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