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

Percentage Accurate: 88.8% → 98.4%

Time: 11.9s

Alternatives: 19

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. Final simplification 46.6%

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

Alternative 2: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-217} \lor \neg \left(y \leq -3.2 \cdot 10^{-299}\right) \land y \leq 2.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -2.8e-6)
    (/ (/ x_m y) (- t z))
    (if (or (<= y -7.5e-217) (and (not (<= y -3.2e-299)) (<= y 2.2e-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 <= -2.8e-6) {
		tmp = (x_m / y) / (t - z);
	} else if ((y <= -7.5e-217) || (!(y <= -3.2e-299) && (y <= 2.2e-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 <= (-2.8d-6)) then
        tmp = (x_m / y) / (t - z)
    else if ((y <= (-7.5d-217)) .or. (.not. (y <= (-3.2d-299))) .and. (y <= 2.2d-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 <= -2.8e-6) {
		tmp = (x_m / y) / (t - z);
	} else if ((y <= -7.5e-217) || (!(y <= -3.2e-299) && (y <= 2.2e-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 <= -2.8e-6:
		tmp = (x_m / y) / (t - z)
	elif (y <= -7.5e-217) or (not (y <= -3.2e-299) and (y <= 2.2e-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 <= -2.8e-6)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif ((y <= -7.5e-217) || (!(y <= -3.2e-299) && (y <= 2.2e-155)))
		tmp = Float64(x_m / Float64(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 <= -2.8e-6)
		tmp = (x_m / y) / (t - z);
	elseif ((y <= -7.5e-217) || (~((y <= -3.2e-299)) && (y <= 2.2e-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, -2.8e-6], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -7.5e-217], And[N[Not[LessEqual[y, -3.2e-299]], $MachinePrecision], LessEqual[y, 2.2e-155]]], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $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 < -2.79999999999999987e-6

   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. add-sqr-sqrt 37.8%

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

      2. times-frac 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. associate-/r* 84.7%

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

   7. Simplified 84.7%

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

   if -2.79999999999999987e-6 < y < -7.50000000000000031e-217 or -3.20000000000000008e-299 < y < 2.1999999999999999e-155

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 80.3%

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

      1. associate-*r/ 80.3%

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

      2. neg-mul-1 80.3%

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

   5. Simplified 80.3%

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

   if -7.50000000000000031e-217 < y < -3.20000000000000008e-299 or 2.1999999999999999e-155 < y

   1. Initial program 84.7%

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

      1. associate-/l/ 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 59.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-217} \lor \neg \left(y \leq -3.2 \cdot 10^{-299}\right) \land y \leq 2.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.5× speedup

Math

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

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)
      (* (/ -1.0 (- t z)) (/ x_m z))
      (/ (/ 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 = (-1.0 / (t - z)) * (x_m / z);
	} 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 = ((-1.0d0) / (t - z)) * (x_m / z)
    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 = (-1.0 / (t - z)) * (x_m / z);
	} 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 = (-1.0 / (t - z)) * (x_m / z)
	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(-1.0 / Float64(t - z)) * Float64(x_m / z));
	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 = (-1.0 / (t - z)) * (x_m / z);
	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[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x$95$m / z), $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. add-sqr-sqrt 37.8%

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

      2. times-frac 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. associate-/r* 84.7%

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

   7. Simplified 84.7%

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

   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. Taylor expanded in x around 0 92.3%

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

      1. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

   8. Simplified 84.1%

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

      1. add-sqr-sqrt 49.7%

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

      2. sqrt-unprod 51.4%

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

      3. sqr-neg 51.4%

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

      4. sqrt-unprod 25.8%

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

      5. add-sqr-sqrt 33.9%

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

      6. *-un-lft-identity 33.9%

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

      7. associate-/l/ 34.0%

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

   10. Applied egg-rr 34.0%

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

       1. *-lft-identity 34.0%

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

       2. *-commutative 34.0%

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

   12. Simplified 34.0%

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

       1. add-sqr-sqrt 18.0%

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

       2. *-commutative 18.0%

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

       3. sqrt-unprod 51.3%

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

       4. sqr-neg 51.3%

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

       5. sqrt-unprod 43.2%

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

       6. add-sqr-sqrt 80.3%

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

       7. neg-mul-1 80.3%

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

       8. times-frac 84.1%

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

   14. Applied egg-rr 84.1%

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

   if 2.30000000000000005e-155 < y

   1. Initial program 85.1%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf 58.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-155}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 0.5× speedup

Math

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

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 (* (- z t) (- z y)))
      (* (/ x_m (- z y)) (/ -1.0 t))))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -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[(z - t), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $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. add-sqr-sqrt 46.9%

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

      2. times-frac 51.5%

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

   4. Applied egg-rr 51.5%

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

   5. Taylor expanded in y around inf 61.2%

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

      1. associate-/r* 64.1%

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

   7. Simplified 64.1%

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

   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. *-un-lft-identity 74.0%

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

      2. frac-times 92.3%

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

      3. *-commutative 92.3%

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

   5. Applied egg-rr 92.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+121}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{-112} \lor \neg \left(y \leq 1.06 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-1}{t}\\ \end{array} \end{array} \]

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 (or (<= y -3.65e-112) (not (<= y 1.06e-119)))
    (/ (/ x_m t) y)
    (* (/ x_m z) (/ -1.0 t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((y <= -3.65e-112) || !(y <= 1.06e-119)) {
		tmp = (x_m / t) / y;
	} else {
		tmp = (x_m / z) * (-1.0 / t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.65d-112)) .or. (.not. (y <= 1.06d-119))) then
        tmp = (x_m / t) / y
    else
        tmp = (x_m / z) * ((-1.0d0) / t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((y <= -3.65e-112) || !(y <= 1.06e-119)) {
		tmp = (x_m / t) / y;
	} else {
		tmp = (x_m / z) * (-1.0 / t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (y <= -3.65e-112) or not (y <= 1.06e-119):
		tmp = (x_m / t) / y
	else:
		tmp = (x_m / z) * (-1.0 / t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((y <= -3.65e-112) || !(y <= 1.06e-119))
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(Float64(x_m / z) * Float64(-1.0 / t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((y <= -3.65e-112) || ~((y <= 1.06e-119)))
		tmp = (x_m / t) / y;
	else
		tmp = (x_m / z) * (-1.0 / t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[y, -3.65e-112], N[Not[LessEqual[y, 1.06e-119]], $MachinePrecision]], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.6499999999999999e-112 or 1.05999999999999999e-119 < y

   1. Initial program 84.1%

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

      1. add-sqr-sqrt 40.5%

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

      2. times-frac 47.3%

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

   4. Applied egg-rr 47.3%

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

   5. Taylor expanded in z around 0 48.0%

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

      1. associate-/r* 52.1%

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

   7. Simplified 52.1%

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

   if -3.6499999999999999e-112 < y < 1.05999999999999999e-119

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 59.1%

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

   4. Taylor expanded in y around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

      3. *-commutative 52.3%

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

   6. Simplified 52.3%

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

      1. neg-mul-1 52.3%

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

      2. *-commutative 52.3%

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

      3. times-frac 55.3%

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

   8. Applied egg-rr 55.3%

      \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{-112} \lor \neg \left(y \leq 1.06 \cdot 10^{-119}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+73} \lor \neg \left(z \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (or (<= z -3.8e+73) (not (<= z 1.2e+54)))
    (/ x_m (* 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 ((z <= -3.8e+73) || !(z <= 1.2e+54)) {
		tmp = x_m / (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 ((z <= (-3.8d+73)) .or. (.not. (z <= 1.2d+54))) then
        tmp = x_m / (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 ((z <= -3.8e+73) || !(z <= 1.2e+54)) {
		tmp = x_m / (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 (z <= -3.8e+73) or not (z <= 1.2e+54):
		tmp = x_m / (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 ((z <= -3.8e+73) || !(z <= 1.2e+54))
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(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 ((z <= -3.8e+73) || ~((z <= 1.2e+54)))
		tmp = x_m / (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[Or[LessEqual[z, -3.8e+73], N[Not[LessEqual[z, 1.2e+54]], $MachinePrecision]], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000022e73 or 1.19999999999999999e54 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0 77.9%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 91.1%

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

      1. mul-1-neg 91.1%

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

   8. Simplified 91.1%

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

      1. add-sqr-sqrt 56.3%

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

      2. sqrt-unprod 75.8%

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

      3. sqr-neg 75.8%

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

      4. sqrt-unprod 49.3%

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

      5. add-sqr-sqrt 63.9%

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

      6. *-un-lft-identity 63.9%

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

      7. associate-/l/ 64.2%

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

   10. Applied egg-rr 64.2%

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

       1. *-lft-identity 64.2%

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

       2. *-commutative 64.2%

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

   12. Simplified 64.2%

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

   if -3.80000000000000022e73 < z < 1.19999999999999999e54

   1. Initial program 92.7%

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

   3. Taylor expanded in t around inf 68.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+73} \lor \neg \left(z \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x\_m}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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 -2.8e-109)
    (* (/ x_m y) (/ 1.0 t))
    (if (<= y 3.7e-119) (* (/ x_m z) (/ -1.0 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 <= -2.8e-109) {
		tmp = (x_m / y) * (1.0 / t);
	} else if (y <= 3.7e-119) {
		tmp = (x_m / z) * (-1.0 / 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 <= (-2.8d-109)) then
        tmp = (x_m / y) * (1.0d0 / t)
    else if (y <= 3.7d-119) then
        tmp = (x_m / z) * ((-1.0d0) / 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 <= -2.8e-109) {
		tmp = (x_m / y) * (1.0 / t);
	} else if (y <= 3.7e-119) {
		tmp = (x_m / z) * (-1.0 / 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 <= -2.8e-109:
		tmp = (x_m / y) * (1.0 / t)
	elif y <= 3.7e-119:
		tmp = (x_m / z) * (-1.0 / 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 <= -2.8e-109)
		tmp = Float64(Float64(x_m / y) * Float64(1.0 / t));
	elseif (y <= 3.7e-119)
		tmp = Float64(Float64(x_m / z) * Float64(-1.0 / 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 <= -2.8e-109)
		tmp = (x_m / y) * (1.0 / t);
	elseif (y <= 3.7e-119)
		tmp = (x_m / z) * (-1.0 / 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, -2.8e-109], N[(N[(x$95$m / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-119], N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999979e-109

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 49.9%

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

      1. *-un-lft-identity 49.9%

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

      2. times-frac 56.4%

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

   5. Applied egg-rr 56.4%

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

   if -2.79999999999999979e-109 < y < 3.7000000000000001e-119

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 59.1%

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

   4. Taylor expanded in y around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

      3. *-commutative 52.3%

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

   6. Simplified 52.3%

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

      1. neg-mul-1 52.3%

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

      2. *-commutative 52.3%

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

      3. times-frac 55.3%

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

   8. Applied egg-rr 55.3%

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

   if 3.7000000000000001e-119 < y

   1. Initial program 84.2%

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

      1. add-sqr-sqrt 39.8%

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

      2. times-frac 47.4%

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

   4. Applied egg-rr 47.4%

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

   5. Taylor expanded in z around 0 46.4%

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

      1. associate-/r* 49.3%

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

   7. Simplified 49.3%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-113}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x\_m}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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-113)
    (/ 1.0 (* t (/ y x_m)))
    (if (<= y 2.8e-119) (* (/ x_m z) (/ -1.0 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-113) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= 2.8e-119) {
		tmp = (x_m / z) * (-1.0 / 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-113)) then
        tmp = 1.0d0 / (t * (y / x_m))
    else if (y <= 2.8d-119) then
        tmp = (x_m / z) * ((-1.0d0) / 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-113) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= 2.8e-119) {
		tmp = (x_m / z) * (-1.0 / 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-113:
		tmp = 1.0 / (t * (y / x_m))
	elif y <= 2.8e-119:
		tmp = (x_m / z) * (-1.0 / 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-113)
		tmp = Float64(1.0 / Float64(t * Float64(y / x_m)));
	elseif (y <= 2.8e-119)
		tmp = Float64(Float64(x_m / z) * Float64(-1.0 / 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-113)
		tmp = 1.0 / (t * (y / x_m));
	elseif (y <= 2.8e-119)
		tmp = (x_m / z) * (-1.0 / 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-113], N[(1.0 / N[(t * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-119], N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e-113

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 49.9%

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

      1. clear-num 50.3%

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

      2. inv-pow 50.3%

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

      3. associate-/l* 60.0%

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

   5. Applied egg-rr 60.0%

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

      1. unpow-1 60.0%

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

   7. Simplified 60.0%

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

   if -3.0000000000000001e-113 < y < 2.8e-119

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 59.1%

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

   4. Taylor expanded in y around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

      3. *-commutative 52.3%

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

   6. Simplified 52.3%

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

      1. neg-mul-1 52.3%

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

      2. *-commutative 52.3%

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

      3. times-frac 55.3%

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

   8. Applied egg-rr 55.3%

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

   if 2.8e-119 < y

   1. Initial program 84.2%

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

      1. add-sqr-sqrt 39.8%

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

      2. times-frac 47.4%

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

   4. Applied egg-rr 47.4%

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

   5. Taylor expanded in z around 0 46.4%

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

      1. associate-/r* 49.3%

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

   7. Simplified 49.3%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-113}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x\_m}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -3.2e-97)
    (/ 1.0 (* t (/ y x_m)))
    (if (<= t 1.4e-121) (/ x_m (* y (- 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 <= -3.2e-97) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (t <= 1.4e-121) {
		tmp = x_m / (y * -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 <= (-3.2d-97)) then
        tmp = 1.0d0 / (t * (y / x_m))
    else if (t <= 1.4d-121) then
        tmp = x_m / (y * -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 <= -3.2e-97) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (t <= 1.4e-121) {
		tmp = x_m / (y * -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 <= -3.2e-97:
		tmp = 1.0 / (t * (y / x_m))
	elif t <= 1.4e-121:
		tmp = x_m / (y * -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 <= -3.2e-97)
		tmp = Float64(1.0 / Float64(t * Float64(y / x_m)));
	elseif (t <= 1.4e-121)
		tmp = Float64(x_m / Float64(y * Float64(-z)));
	else
		tmp = Float64(x_m / Float64(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 <= -3.2e-97)
		tmp = 1.0 / (t * (y / x_m));
	elseif (t <= 1.4e-121)
		tmp = x_m / (y * -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, -3.2e-97], N[(1.0 / N[(t * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-121], N[(x$95$m / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -3.1999999999999998e-97

   1. Initial program 89.8%

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

   3. Taylor expanded in z around 0 54.4%

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

      1. clear-num 54.7%

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

      2. inv-pow 54.7%

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

      3. associate-/l* 57.5%

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

   5. Applied egg-rr 57.5%

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

      1. unpow-1 57.5%

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

   7. Simplified 57.5%

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

   if -3.1999999999999998e-97 < t < 1.4000000000000001e-121

   1. Initial program 89.6%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.3%

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

      2. associate-/r/ 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in t around 0 87.0%

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

   8. Taylor expanded in z around 0 44.7%

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

      1. associate-*r/ 44.7%

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

      2. mul-1-neg 44.7%

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

   10. Simplified 44.7%

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

   if 1.4000000000000001e-121 < t

   1. Initial program 81.6%

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

   3. Taylor expanded in t around inf 69.9%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-118}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= y -2e-118)
    (/ x_m (* y (- t z)))
    (if (<= y -1.9e-194) (/ x_m (* 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 (y <= -2e-118) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -1.9e-194) {
		tmp = x_m / (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 (y <= (-2d-118)) then
        tmp = x_m / (y * (t - z))
    else if (y <= (-1.9d-194)) then
        tmp = x_m / (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 (y <= -2e-118) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -1.9e-194) {
		tmp = x_m / (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 y <= -2e-118:
		tmp = x_m / (y * (t - z))
	elif y <= -1.9e-194:
		tmp = x_m / (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 (y <= -2e-118)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= -1.9e-194)
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(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 (y <= -2e-118)
		tmp = x_m / (y * (t - z));
	elseif (y <= -1.9e-194)
		tmp = x_m / (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[y, -2e-118], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-194], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999997e-118

   1. Initial program 84.1%

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

   3. Taylor expanded in y around inf 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -1.99999999999999997e-118 < y < -1.9000000000000001e-194

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 93.6%

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

      1. mul-1-neg 93.6%

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

   8. Simplified 93.6%

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

      1. add-sqr-sqrt 68.2%

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

      2. sqrt-unprod 81.9%

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

      3. sqr-neg 81.9%

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

      4. sqrt-unprod 38.0%

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

      5. add-sqr-sqrt 52.0%

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

      6. *-un-lft-identity 52.0%

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

      7. associate-/l/ 52.0%

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

   10. Applied egg-rr 52.0%

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

       1. *-lft-identity 52.0%

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

       2. *-commutative 52.0%

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

   12. Simplified 52.0%

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

   if -1.9000000000000001e-194 < y

   1. Initial program 87.0%

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

   3. Taylor expanded in t around inf 55.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -2.3e-119)
    (/ x_m (* y (- t z)))
    (if (<= y -4.8e-195) (/ x_m (* z (- t z))) (/ (/ 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 <= -2.3e-119) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -4.8e-195) {
		tmp = x_m / (z * (t - z));
	} 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 <= (-2.3d-119)) then
        tmp = x_m / (y * (t - z))
    else if (y <= (-4.8d-195)) then
        tmp = x_m / (z * (t - z))
    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 <= -2.3e-119) {
		tmp = x_m / (y * (t - z));
	} else if (y <= -4.8e-195) {
		tmp = x_m / (z * (t - z));
	} 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 <= -2.3e-119:
		tmp = x_m / (y * (t - z))
	elif y <= -4.8e-195:
		tmp = x_m / (z * (t - z))
	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 <= -2.3e-119)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= -4.8e-195)
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	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 <= -2.3e-119)
		tmp = x_m / (y * (t - z));
	elseif (y <= -4.8e-195)
		tmp = x_m / (z * (t - z));
	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, -2.3e-119], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-195], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $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 < -2.29999999999999993e-119

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf 69.1%

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

      1. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   if -2.29999999999999993e-119 < y < -4.8e-195

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 93.2%

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

      1. mul-1-neg 93.2%

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

   8. Simplified 93.2%

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

      1. add-sqr-sqrt 66.2%

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

      2. sqrt-unprod 80.8%

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

      3. sqr-neg 80.8%

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

      4. sqrt-unprod 40.5%

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

      5. add-sqr-sqrt 55.2%

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

      6. *-un-lft-identity 55.2%

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

      7. associate-/l/ 55.2%

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

   10. Applied egg-rr 55.2%

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

       1. *-lft-identity 55.2%

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

       2. *-commutative 55.2%

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

   12. Simplified 55.2%

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

   if -4.8e-195 < y

   1. Initial program 87.0%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 57.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -3.2e-119)
    (/ (/ x_m y) (- t z))
    (if (<= y -1.9e-194) (/ x_m (* z (- t z))) (/ (/ 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 <= -3.2e-119) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -1.9e-194) {
		tmp = x_m / (z * (t - z));
	} 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 <= (-3.2d-119)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= (-1.9d-194)) then
        tmp = x_m / (z * (t - z))
    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 <= -3.2e-119) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -1.9e-194) {
		tmp = x_m / (z * (t - z));
	} 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 <= -3.2e-119:
		tmp = (x_m / y) / (t - z)
	elif y <= -1.9e-194:
		tmp = x_m / (z * (t - z))
	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 <= -3.2e-119)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= -1.9e-194)
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	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 <= -3.2e-119)
		tmp = (x_m / y) / (t - z);
	elseif (y <= -1.9e-194)
		tmp = x_m / (z * (t - z));
	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, -3.2e-119], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-194], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $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 < -3.19999999999999993e-119

   1. Initial program 84.3%

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

      1. add-sqr-sqrt 40.3%

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

      2. times-frac 46.1%

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

   4. Applied egg-rr 46.1%

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

   5. Taylor expanded in y around inf 69.1%

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

      1. associate-/r* 73.2%

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

   7. Simplified 73.2%

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

   if -3.19999999999999993e-119 < y < -1.9000000000000001e-194

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 93.2%

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

      1. mul-1-neg 93.2%

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

   8. Simplified 93.2%

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

      1. add-sqr-sqrt 66.2%

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

      2. sqrt-unprod 80.8%

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

      3. sqr-neg 80.8%

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

      4. sqrt-unprod 40.5%

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

      5. add-sqr-sqrt 55.2%

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

      6. *-un-lft-identity 55.2%

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

      7. associate-/l/ 55.2%

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

   10. Applied egg-rr 55.2%

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

       1. *-lft-identity 55.2%

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

       2. *-commutative 55.2%

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

   12. Simplified 55.2%

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

   if -1.9000000000000001e-194 < y

   1. Initial program 87.0%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around inf 57.6%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-119}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

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 -4e-7)
    (/ (/ x_m y) (- t z))
    (if (<= y 6.5e-156) (/ (/ 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 <= -4e-7) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 6.5e-156) {
		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 <= (-4d-7)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 6.5d-156) 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 <= -4e-7) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 6.5e-156) {
		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 <= -4e-7:
		tmp = (x_m / y) / (t - z)
	elif y <= 6.5e-156:
		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 <= -4e-7)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 6.5e-156)
		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 <= -4e-7)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 6.5e-156)
		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, -4e-7], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-156], 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 < -3.9999999999999998e-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. add-sqr-sqrt 37.8%

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

      2. times-frac 46.2%

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

   4. Applied egg-rr 46.2%

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

   5. Taylor expanded in y around inf 77.9%

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

      1. associate-/r* 84.7%

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

   7. Simplified 84.7%

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

   if -3.9999999999999998e-7 < y < 6.5000000000000002e-156

   1. Initial program 92.3%

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

   3. Taylor expanded in x around 0 92.3%

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

      1. associate-/l/ 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

   8. Simplified 84.1%

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

   if 6.5000000000000002e-156 < y

   1. Initial program 85.1%

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

      1. associate-/l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around inf 58.7%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-112} \lor \neg \left(y \leq 5 \cdot 10^{-120}\right):\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= y -1.05e-112) (not (<= y 5e-120)))
    (/ (/ x_m t) y)
    (/ 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 ((y <= -1.05e-112) || !(y <= 5e-120)) {
		tmp = (x_m / t) / y;
	} else {
		tmp = 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 ((y <= (-1.05d-112)) .or. (.not. (y <= 5d-120))) then
        tmp = (x_m / t) / y
    else
        tmp = 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 ((y <= -1.05e-112) || !(y <= 5e-120)) {
		tmp = (x_m / t) / y;
	} else {
		tmp = 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 (y <= -1.05e-112) or not (y <= 5e-120):
		tmp = (x_m / t) / y
	else:
		tmp = 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 ((y <= -1.05e-112) || !(y <= 5e-120))
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(x_m / Float64(t * Float64(-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 <= -1.05e-112) || ~((y <= 5e-120)))
		tmp = (x_m / t) / y;
	else
		tmp = 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[Or[LessEqual[y, -1.05e-112], N[Not[LessEqual[y, 5e-120]], $MachinePrecision]], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(t * (-z)), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-112 or 5.00000000000000007e-120 < y

   1. Initial program 84.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 47.6%

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

   4. Applied egg-rr 47.6%

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

   5. Taylor expanded in z around 0 48.2%

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

      1. associate-/r* 52.4%

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

   7. Simplified 52.4%

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

   if -1.05e-112 < y < 5.00000000000000007e-120

   1. Initial program 93.6%

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

      1. associate-/l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around inf 54.8%

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

   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%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-112} \lor \neg \left(y \leq 5 \cdot 10^{-120}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3500 \lor \neg \left(z \leq 1.8 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

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 (or (<= z -3500.0) (not (<= z 1.8e+124)))
    (/ x_m (* z t))
    (/ 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 tmp;
	if ((z <= -3500.0) || !(z <= 1.8e+124)) {
		tmp = x_m / (z * t);
	} 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) :: tmp
    if ((z <= (-3500.0d0)) .or. (.not. (z <= 1.8d+124))) then
        tmp = x_m / (z * t)
    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 tmp;
	if ((z <= -3500.0) || !(z <= 1.8e+124)) {
		tmp = x_m / (z * t);
	} 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):
	tmp = 0
	if (z <= -3500.0) or not (z <= 1.8e+124):
		tmp = x_m / (z * t)
	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)
	tmp = 0.0
	if ((z <= -3500.0) || !(z <= 1.8e+124))
		tmp = Float64(x_m / Float64(z * t));
	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)
	tmp = 0.0;
	if ((z <= -3500.0) || ~((z <= 1.8e+124)))
		tmp = x_m / (z * t);
	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_] := N[(x$95$s * If[Or[LessEqual[z, -3500.0], N[Not[LessEqual[z, 1.8e+124]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3500 or 1.79999999999999993e124 < z

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

   8. Simplified 87.0%

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

      1. add-sqr-sqrt 51.0%

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

      2. sqrt-unprod 69.5%

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

      3. sqr-neg 69.5%

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

      4. sqrt-unprod 45.4%

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

      5. add-sqr-sqrt 56.7%

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

      6. *-un-lft-identity 56.7%

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

      7. associate-/l/ 57.0%

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

   10. Applied egg-rr 57.0%

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

       1. *-lft-identity 57.0%

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

       2. *-commutative 57.0%

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

   12. Simplified 57.0%

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

   13. Taylor expanded in z around 0 31.8%

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

       1. *-commutative 31.8%

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

   15. Simplified 31.8%

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

   if -3500 < z < 1.79999999999999993e124

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 57.0%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3500 \lor \neg \left(z \leq 1.8 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+112} \lor \neg \left(z \leq 2.6 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

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 (or (<= z -7e+112) (not (<= z 2.6e+147)))
    (/ 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 ((z <= -7e+112) || !(z <= 2.6e+147)) {
		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 ((z <= (-7d+112)) .or. (.not. (z <= 2.6d+147))) 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 ((z <= -7e+112) || !(z <= 2.6e+147)) {
		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 (z <= -7e+112) or not (z <= 2.6e+147):
		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 ((z <= -7e+112) || !(z <= 2.6e+147))
		tmp = 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 ((z <= -7e+112) || ~((z <= 2.6e+147)))
		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[Or[LessEqual[z, -7e+112], N[Not[LessEqual[z, 2.6e+147]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999994e112 or 2.5999999999999999e147 < z

   1. Initial program 78.4%

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

   3. Taylor expanded in x around 0 78.4%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 96.8%

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

      1. mul-1-neg 96.8%

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

   8. Simplified 96.8%

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

      1. add-sqr-sqrt 60.6%

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

      2. sqrt-unprod 83.6%

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

      3. sqr-neg 83.6%

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

      4. sqrt-unprod 61.8%

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

      5. add-sqr-sqrt 74.0%

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

      6. *-un-lft-identity 74.0%

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

      7. associate-/l/ 74.4%

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

   10. Applied egg-rr 74.4%

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

       1. *-lft-identity 74.4%

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

       2. *-commutative 74.4%

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

   12. Simplified 74.4%

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

   13. Taylor expanded in z around 0 42.5%

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

       1. *-commutative 42.5%

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

   15. Simplified 42.5%

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

   if -6.99999999999999994e112 < z < 2.5999999999999999e147

   1. Initial program 90.2%

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

      1. add-sqr-sqrt 41.2%

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

      2. times-frac 44.9%

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

   4. Applied egg-rr 44.9%

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

   5. Taylor expanded in z around 0 48.3%

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

      1. associate-/r* 54.8%

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

   7. Simplified 54.8%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+112} \lor \neg \left(z \leq 2.6 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 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. Step-by-step derivation

   1. associate-/l/ 97.2%

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

3. Simplified 97.2%

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

5. Final simplification 97.2%

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

Alternative 18: 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. 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-/l/ 98.2%

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

5. Simplified 98.2%

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

6. Final simplification 98.2%

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

Alternative 19: 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))))