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

Percentage Accurate: 88.8% → 98.4%

Time: 13.0s

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 1 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 89.7%

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

   1. add-sqr-sqrt 41.7%

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

   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: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;t_1 \leq 10^{+294}:\\ \;\;\;\;\frac{x_m}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x_m}}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m y) (- t z))
      (if (<= t_1 1e+294) (/ x_m t_1) (/ (/ -1.0 z) (/ (- t z) x_m)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / y) / (t - z);
	} else if (t_1 <= 1e+294) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / y) / (t - z);
	} else if (t_1 <= 1e+294) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / y) / (t - z)
	elif t_1 <= 1e+294:
		tmp = x_m / t_1
	else:
		tmp = (-1.0 / z) / ((t - z) / x_m)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t_1 <= 1e+294)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / y) / (t - z);
	elseif (t_1 <= 1e+294)
		tmp = x_m / t_1;
	else
		tmp = (-1.0 / z) / ((t - z) / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 69.5%

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

      1. add-sqr-sqrt 38.6%

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

      2. times-frac 60.7%

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

   4. Applied egg-rr 60.7%

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

      1. clear-num 60.7%

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

      2. un-div-inv 60.7%

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

   6. Applied egg-rr 60.7%

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

   7. Taylor expanded in y around inf 55.2%

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

      1. associate-/r* 79.6%

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

   9. Simplified 79.6%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1.00000000000000007e294

   1. Initial program 98.5%

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

   if 1.00000000000000007e294 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.5%

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

      1. clear-num 76.5%

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

      2. associate-/r/ 76.5%

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

   4. Applied egg-rr 76.5%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. associate-/r* 67.8%

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

   7. Simplified 67.8%

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

      1. associate-*l/ 85.3%

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

      2. associate-/l* 87.9%

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

   9. Applied egg-rr 87.9%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+294}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{t - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x_m}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -5.8e+123)
    (/ (- (/ x_m z)) (- t z))
    (if (<= z 5.2e+112)
      (/ x_m (* (- y z) (- t z)))
      (* (/ -1.0 (- t z)) (/ x_m z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+123) {
		tmp = -(x_m / z) / (t - z);
	} else if (z <= 5.2e+112) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x_m / z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.8d+123)) then
        tmp = -(x_m / z) / (t - z)
    else if (z <= 5.2d+112) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = ((-1.0d0) / (t - z)) * (x_m / z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+123) {
		tmp = -(x_m / z) / (t - z);
	} else if (z <= 5.2e+112) {
		tmp = x_m / ((y - z) * (t - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x_m / z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -5.8e+123:
		tmp = -(x_m / z) / (t - z)
	elif z <= 5.2e+112:
		tmp = x_m / ((y - z) * (t - z))
	else:
		tmp = (-1.0 / (t - z)) * (x_m / z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+123)
		tmp = Float64(Float64(-Float64(x_m / z)) / Float64(t - z));
	elseif (z <= 5.2e+112)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(-1.0 / Float64(t - z)) * Float64(x_m / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+123)
		tmp = -(x_m / z) / (t - z);
	elseif (z <= 5.2e+112)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = (-1.0 / (t - z)) * (x_m / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -5.8e+123], N[((-N[(x$95$m / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+112], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000019e123

   1. Initial program 76.6%

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

      1. add-sqr-sqrt 33.3%

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

      2. times-frac 41.7%

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

   4. Applied egg-rr 41.7%

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

   5. Taylor expanded in y around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. associate-/r* 93.6%

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

      3. distribute-neg-frac 93.6%

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

      4. distribute-frac-neg 93.6%

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

   7. Simplified 93.6%

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

   if -5.80000000000000019e123 < z < 5.2000000000000001e112

   1. Initial program 94.3%

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

   if 5.2000000000000001e112 < z

   1. Initial program 79.1%

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

      1. add-sqr-sqrt 48.9%

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

      2. times-frac 62.8%

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

   4. Applied egg-rr 62.8%

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

   5. Taylor expanded in y around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-/r* 96.3%

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

      3. distribute-neg-frac 96.3%

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

      4. distribute-frac-neg 96.3%

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

   7. Simplified 96.3%

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

      1. associate-/l/ 79.1%

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

      2. neg-mul-1 79.1%

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

      3. times-frac 96.5%

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

   9. Applied egg-rr 96.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+123}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{-t}}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.3e-85)
    (/ (/ x_m y) t)
    (if (<= t 2.4e-172)
      (/ (- x_m) (* y z))
      (if (<= t 5e+258) (/ (/ 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 (t <= -1.3e-85) {
		tmp = (x_m / y) / t;
	} else if (t <= 2.4e-172) {
		tmp = -x_m / (y * z);
	} else if (t <= 5e+258) {
		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 (t <= (-1.3d-85)) then
        tmp = (x_m / y) / t
    else if (t <= 2.4d-172) then
        tmp = -x_m / (y * z)
    else if (t <= 5d+258) 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 (t <= -1.3e-85) {
		tmp = (x_m / y) / t;
	} else if (t <= 2.4e-172) {
		tmp = -x_m / (y * z);
	} else if (t <= 5e+258) {
		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 t <= -1.3e-85:
		tmp = (x_m / y) / t
	elif t <= 2.4e-172:
		tmp = -x_m / (y * z)
	elif t <= 5e+258:
		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 (t <= -1.3e-85)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (t <= 2.4e-172)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (t <= 5e+258)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(Float64(x_m / Float64(-t)) / z);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.3e-85)
		tmp = (x_m / y) / t;
	elseif (t <= 2.4e-172)
		tmp = -x_m / (y * z);
	elseif (t <= 5e+258)
		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[LessEqual[t, -1.3e-85], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.4e-172], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+258], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / (-t)), $MachinePrecision] / z), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.30000000000000006e-85

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 49.6%

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

      1. *-un-lft-identity 49.6%

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

      2. times-frac 53.0%

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

   5. Applied egg-rr 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-un-lft-identity 53.0%

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

   7. Applied egg-rr 53.0%

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

   if -1.30000000000000006e-85 < t < 2.4000000000000001e-172

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-/r* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in t around 0 54.0%

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

      1. associate-*r/ 54.0%

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

      2. neg-mul-1 54.0%

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

      3. *-commutative 54.0%

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

   8. Simplified 54.0%

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

   if 2.4000000000000001e-172 < t < 5e258

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-/r* 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around inf 50.4%

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

   if 5e258 < t

   1. Initial program 69.0%

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

      1. add-sqr-sqrt 43.6%

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

      2. times-frac 66.5%

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

   4. Applied egg-rr 66.5%

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

   5. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. associate-/r* 75.9%

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

      3. distribute-neg-frac 75.9%

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

      4. distribute-frac-neg 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in z around 0 45.4%

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

      1. associate-/r* 84.0%

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

      2. associate-*r/ 84.0%

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

      3. metadata-eval 84.0%

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

      4. times-frac 84.0%

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

      5. *-lft-identity 84.0%

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

      6. neg-mul-1 84.0%

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

   10. Simplified 84.0%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{x_m}{-t}}{z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -1.4e+164)
    (/ (/ x_m (- t)) z)
    (if (<= z -8.8e-55)
      (/ (- (/ x_m z)) y)
      (if (<= z 5.6e-35) (/ (/ x_m t) y) (/ (- x_m) (* 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 <= -1.4e+164) {
		tmp = (x_m / -t) / z;
	} else if (z <= -8.8e-55) {
		tmp = -(x_m / z) / y;
	} else if (z <= 5.6e-35) {
		tmp = (x_m / t) / y;
	} else {
		tmp = -x_m / (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 <= (-1.4d+164)) then
        tmp = (x_m / -t) / z
    else if (z <= (-8.8d-55)) then
        tmp = -(x_m / z) / y
    else if (z <= 5.6d-35) then
        tmp = (x_m / t) / y
    else
        tmp = -x_m / (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 <= -1.4e+164) {
		tmp = (x_m / -t) / z;
	} else if (z <= -8.8e-55) {
		tmp = -(x_m / z) / y;
	} else if (z <= 5.6e-35) {
		tmp = (x_m / t) / y;
	} else {
		tmp = -x_m / (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 <= -1.4e+164:
		tmp = (x_m / -t) / z
	elif z <= -8.8e-55:
		tmp = -(x_m / z) / y
	elif z <= 5.6e-35:
		tmp = (x_m / t) / y
	else:
		tmp = -x_m / (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 <= -1.4e+164)
		tmp = Float64(Float64(x_m / Float64(-t)) / z);
	elseif (z <= -8.8e-55)
		tmp = Float64(Float64(-Float64(x_m / z)) / y);
	elseif (z <= 5.6e-35)
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e+164)
		tmp = (x_m / -t) / z;
	elseif (z <= -8.8e-55)
		tmp = -(x_m / z) / y;
	elseif (z <= 5.6e-35)
		tmp = (x_m / t) / y;
	else
		tmp = -x_m / (z * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.4e+164], N[(N[(x$95$m / (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.8e-55], N[((-N[(x$95$m / z), $MachinePrecision]) / y), $MachinePrecision], If[LessEqual[z, 5.6e-35], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[((-x$95$m) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e164

   1. Initial program 69.9%

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

      1. add-sqr-sqrt 27.8%

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

      2. times-frac 39.8%

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

   4. Applied egg-rr 39.8%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/r* 93.9%

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

      3. distribute-neg-frac 93.9%

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

      4. distribute-frac-neg 93.9%

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

   7. Simplified 93.9%

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

   8. Taylor expanded in z around 0 49.2%

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

      1. associate-/r* 55.0%

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

      2. associate-*r/ 55.0%

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

      3. metadata-eval 55.0%

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

      4. times-frac 55.0%

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

      5. *-lft-identity 55.0%

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

      6. neg-mul-1 55.0%

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

   10. Simplified 55.0%

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

   if -1.4000000000000001e164 < z < -8.7999999999999998e-55

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-/r* 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in t around 0 36.8%

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

      1. associate-*r/ 36.8%

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

      2. neg-mul-1 36.8%

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

   8. Simplified 36.8%

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

   if -8.7999999999999998e-55 < z < 5.5999999999999999e-35

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-/r* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in t around inf 69.1%

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

   if 5.5999999999999999e-35 < z

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 52.6%

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

      1. distribute-lft-out 52.6%

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

      2. mul-1-neg 52.6%

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

      3. distribute-rgt-neg-in 52.6%

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

      4. unsub-neg 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in y around 0 31.9%

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

      1. associate-*r/ 31.9%

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

      2. neg-mul-1 31.9%

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

   8. Simplified 31.9%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+164}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-55}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-215}:\\ \;\;\;\;\frac{-x_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -8.5e-66)
    (/ (/ x_m y) (- t z))
    (if (<= y 1.55e-215) (/ (- 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 <= -8.5e-66) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.55e-215) {
		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 <= (-8.5d-66)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 1.55d-215) 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 <= -8.5e-66) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.55e-215) {
		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 <= -8.5e-66:
		tmp = (x_m / y) / (t - z)
	elif y <= 1.55e-215:
		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 <= -8.5e-66)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 1.55e-215)
		tmp = Float64(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 <= -8.5e-66)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 1.55e-215)
		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, -8.5e-66], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-215], 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 < -8.49999999999999966e-66

   1. Initial program 91.3%

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

      1. add-sqr-sqrt 43.7%

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

      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. Step-by-step derivation

      1. clear-num 47.6%

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

      2. un-div-inv 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in y around inf 85.8%

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

      1. associate-/r* 86.2%

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

   9. Simplified 86.2%

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

   if -8.49999999999999966e-66 < y < 1.54999999999999997e-215

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. neg-mul-1 85.1%

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

   5. Simplified 85.1%

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

   if 1.54999999999999997e-215 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf 52.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-215}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -6.2e-66)
    (/ (/ x_m y) (- t z))
    (if (<= y 1.25e-217) (/ (- (/ 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 <= -6.2e-66) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.25e-217) {
		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 <= (-6.2d-66)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 1.25d-217) 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 <= -6.2e-66) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1.25e-217) {
		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 <= -6.2e-66:
		tmp = (x_m / y) / (t - z)
	elif y <= 1.25e-217:
		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 <= -6.2e-66)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 1.25e-217)
		tmp = Float64(Float64(-Float64(x_m / 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 <= -6.2e-66)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 1.25e-217)
		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, -6.2e-66], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-217], N[((-N[(x$95$m / z), $MachinePrecision]) / N[(t - 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 y < -6.1999999999999995e-66

   1. Initial program 91.3%

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

      1. add-sqr-sqrt 43.7%

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

      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. Step-by-step derivation

      1. clear-num 47.6%

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

      2. un-div-inv 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in y around inf 85.8%

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

      1. associate-/r* 86.2%

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

   9. Simplified 86.2%

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

   if -6.1999999999999995e-66 < y < 1.2500000000000001e-217

   1. Initial program 93.3%

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

      1. add-sqr-sqrt 47.8%

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

      2. times-frac 50.4%

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

   4. Applied egg-rr 50.4%

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

   5. Taylor expanded in y around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/r* 89.9%

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

      3. distribute-neg-frac 89.9%

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

      4. distribute-frac-neg 89.9%

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

   7. Simplified 89.9%

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

   if 1.2500000000000001e-217 < y

   1. Initial program 86.6%

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

   3. Taylor expanded in t around inf 52.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\frac{x_m}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -5e-139)
    (/ (/ x_m y) (- t z))
    (if (<= t 5.4e+26) (/ (- (/ x_m z)) (- 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 <= -5e-139) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 5.4e+26) {
		tmp = -(x_m / z) / (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 <= (-5d-139)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 5.4d+26) then
        tmp = -(x_m / z) / (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 <= -5e-139) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 5.4e+26) {
		tmp = -(x_m / z) / (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 <= -5e-139:
		tmp = (x_m / y) / (t - z)
	elif t <= 5.4e+26:
		tmp = -(x_m / z) / (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 <= -5e-139)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 5.4e+26)
		tmp = Float64(Float64(-Float64(x_m / z)) / Float64(y - 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 <= -5e-139)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 5.4e+26)
		tmp = -(x_m / z) / (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, -5e-139], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+26], N[((-N[(x$95$m / z), $MachinePrecision]) / 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 < -5.00000000000000034e-139

   1. Initial program 88.5%

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

      1. add-sqr-sqrt 43.0%

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

      2. times-frac 48.2%

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

   4. Applied egg-rr 48.2%

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

      1. clear-num 48.1%

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

      2. un-div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   7. Taylor expanded in y around inf 58.8%

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

      1. associate-/r* 63.7%

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

   9. Simplified 63.7%

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

   if -5.00000000000000034e-139 < t < 5.4e26

   1. Initial program 91.6%

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

      1. add-sqr-sqrt 39.5%

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

      2. times-frac 42.3%

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

   4. Applied egg-rr 42.3%

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

   5. Taylor expanded in t around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. associate-/r* 77.5%

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

      3. distribute-neg-frac 77.5%

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

      4. distribute-frac-neg 77.5%

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

   7. Simplified 77.5%

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

   if 5.4e26 < t

   1. Initial program 88.5%

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

   3. Taylor expanded in t around inf 82.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-139}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{-\frac{x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -6.5e-83)
    (/ (/ x_m y) t)
    (if (<= t 4.2e-150) (/ (- 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 <= -6.5e-83) {
		tmp = (x_m / y) / t;
	} else if (t <= 4.2e-150) {
		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 <= (-6.5d-83)) then
        tmp = (x_m / y) / t
    else if (t <= 4.2d-150) 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 <= -6.5e-83) {
		tmp = (x_m / y) / t;
	} else if (t <= 4.2e-150) {
		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 <= -6.5e-83:
		tmp = (x_m / y) / t
	elif t <= 4.2e-150:
		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 <= -6.5e-83)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (t <= 4.2e-150)
		tmp = Float64(Float64(-x_m) / Float64(y * 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 <= -6.5e-83)
		tmp = (x_m / y) / t;
	elseif (t <= 4.2e-150)
		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, -6.5e-83], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 4.2e-150], 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 < -6.5e-83

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 49.6%

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

      1. *-un-lft-identity 49.6%

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

      2. times-frac 53.0%

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

   5. Applied egg-rr 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-un-lft-identity 53.0%

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

   7. Applied egg-rr 53.0%

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

   if -6.5e-83 < t < 4.2000000000000002e-150

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-/r* 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in t around 0 52.4%

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

      1. associate-*r/ 52.4%

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

      2. neg-mul-1 52.4%

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

      3. *-commutative 52.4%

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

   8. Simplified 52.4%

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

   if 4.2000000000000002e-150 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 69.7%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-43} \lor \neg \left(z \leq 6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{-x_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.2e-43) (not (<= z 6e-35)))
    (/ (- 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 <= -2.2e-43) || !(z <= 6e-35)) {
		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 <= (-2.2d-43)) .or. (.not. (z <= 6d-35))) 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 <= -2.2e-43) || !(z <= 6e-35)) {
		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 <= -2.2e-43) or not (z <= 6e-35):
		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 <= -2.2e-43) || !(z <= 6e-35))
		tmp = Float64(Float64(-x_m) / Float64(z * t));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e-43) || ~((z <= 6e-35)))
		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, -2.2e-43], N[Not[LessEqual[z, 6e-35]], $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 < -2.19999999999999997e-43 or 5.99999999999999978e-35 < z

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 56.9%

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

      1. distribute-lft-out 56.9%

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

      2. mul-1-neg 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

      4. unsub-neg 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in y around 0 36.7%

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

      1. associate-*r/ 36.7%

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

      2. neg-mul-1 36.7%

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

   8. Simplified 36.7%

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

   if -2.19999999999999997e-43 < z < 5.99999999999999978e-35

   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 inf 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-/r* 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in t around inf 69.0%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-43} \lor \neg \left(z \leq 6 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{-x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.1e-82)
    (/ (/ x_m y) t)
    (if (<= t 2.4e-172) (/ (- x_m) (* y z)) (/ (/ 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 (t <= -1.1e-82) {
		tmp = (x_m / y) / t;
	} else if (t <= 2.4e-172) {
		tmp = -x_m / (y * z);
	} 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 (t <= (-1.1d-82)) then
        tmp = (x_m / y) / t
    else if (t <= 2.4d-172) then
        tmp = -x_m / (y * z)
    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 (t <= -1.1e-82) {
		tmp = (x_m / y) / t;
	} else if (t <= 2.4e-172) {
		tmp = -x_m / (y * z);
	} 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 t <= -1.1e-82:
		tmp = (x_m / y) / t
	elif t <= 2.4e-172:
		tmp = -x_m / (y * z)
	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 (t <= -1.1e-82)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (t <= 2.4e-172)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	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 (t <= -1.1e-82)
		tmp = (x_m / y) / t;
	elseif (t <= 2.4e-172)
		tmp = -x_m / (y * z);
	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[t, -1.1e-82], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.4e-172], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.09999999999999993e-82

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 49.6%

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

      1. *-un-lft-identity 49.6%

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

      2. times-frac 53.0%

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

   5. Applied egg-rr 53.0%

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

      1. associate-*l/ 53.0%

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

      2. *-un-lft-identity 53.0%

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

   7. Applied egg-rr 53.0%

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

   if -1.09999999999999993e-82 < t < 2.4000000000000001e-172

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-/r* 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in t around 0 54.0%

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

      1. associate-*r/ 54.0%

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

      2. neg-mul-1 54.0%

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

      3. *-commutative 54.0%

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

   8. Simplified 54.0%

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

   if 2.4000000000000001e-172 < t

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/r* 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in t around inf 49.6%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-172}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+16} \lor \neg \left(z \leq 8.8 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3.6e+16) (not (<= z 8.8e+90)))
    (/ x_m (* y z))
    (/ 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 <= -3.6e+16) || !(z <= 8.8e+90)) {
		tmp = x_m / (y * z);
	} 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 <= (-3.6d+16)) .or. (.not. (z <= 8.8d+90))) then
        tmp = x_m / (y * z)
    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 <= -3.6e+16) || !(z <= 8.8e+90)) {
		tmp = x_m / (y * z);
	} 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 <= -3.6e+16) or not (z <= 8.8e+90):
		tmp = x_m / (y * z)
	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 <= -3.6e+16) || !(z <= 8.8e+90))
		tmp = Float64(x_m / Float64(y * z));
	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 <= -3.6e+16) || ~((z <= 8.8e+90)))
		tmp = x_m / (y * z);
	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, -3.6e+16], N[Not[LessEqual[z, 8.8e+90]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e16 or 8.79999999999999961e90 < z

   1. Initial program 81.3%

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

   3. Taylor expanded in y around inf 39.0%

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

      1. *-commutative 39.0%

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

      2. associate-/r* 47.9%

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

   5. Simplified 47.9%

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

   6. Taylor expanded in t around 0 42.3%

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

      1. associate-*r/ 42.3%

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

      2. neg-mul-1 42.3%

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

   8. Simplified 42.3%

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

      1. expm1-log1p-u 41.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{y}\right)\right)} \]

      2. expm1-udef 53.3%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{y}\right)} - 1} \]

      3. associate-/l/ 53.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{y \cdot z}}\right)} - 1 \]

      4. add-sqr-sqrt 28.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y \cdot z}\right)} - 1 \]

      5. sqrt-unprod 49.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y \cdot z}\right)} - 1 \]

      6. sqr-neg 49.1%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{y \cdot z}\right)} - 1 \]

      7. sqrt-unprod 25.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y \cdot z}\right)} - 1 \]

      8. add-sqr-sqrt 53.4%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{y \cdot z}\right)} - 1 \]

   10. Applied egg-rr 53.4%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 35.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)\right)} \]

       2. expm1-log1p 35.5%

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

       3. *-commutative 35.5%

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

   12. Simplified 35.5%

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

   if -3.6e16 < z < 8.79999999999999961e90

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 52.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+16} \lor \neg \left(z \leq 8.8 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+105} \lor \neg \left(z \leq 8.2 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x_m}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -8.2e+105) (not (<= z 8.2e+90)))
    (/ x_m (* y z))
    (/ (/ 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 <= -8.2e+105) || !(z <= 8.2e+90)) {
		tmp = x_m / (y * z);
	} 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 <= (-8.2d+105)) .or. (.not. (z <= 8.2d+90))) then
        tmp = x_m / (y * z)
    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 <= -8.2e+105) || !(z <= 8.2e+90)) {
		tmp = x_m / (y * z);
	} 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 <= -8.2e+105) or not (z <= 8.2e+90):
		tmp = x_m / (y * z)
	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 <= -8.2e+105) || !(z <= 8.2e+90))
		tmp = Float64(x_m / Float64(y * z));
	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 <= -8.2e+105) || ~((z <= 8.2e+90)))
		tmp = x_m / (y * z);
	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, -8.2e+105], N[Not[LessEqual[z, 8.2e+90]], $MachinePrecision]], N[(x$95$m / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000005e105 or 8.20000000000000083e90 < z

   1. Initial program 79.2%

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

   3. Taylor expanded in y around inf 40.8%

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

      1. *-commutative 40.8%

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

      2. associate-/r* 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in t around 0 46.9%

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

      1. associate-*r/ 46.9%

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

      2. neg-mul-1 46.9%

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

   8. Simplified 46.9%

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

      1. expm1-log1p-u 46.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{-x}{z}}{y}\right)\right)} \]

      2. expm1-udef 62.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{-x}{z}}{y}\right)} - 1} \]

      3. associate-/l/ 62.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-x}{y \cdot z}}\right)} - 1 \]

      4. add-sqr-sqrt 30.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y \cdot z}\right)} - 1 \]

      5. sqrt-unprod 57.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y \cdot z}\right)} - 1 \]

      6. sqr-neg 57.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{y \cdot z}\right)} - 1 \]

      7. sqrt-unprod 31.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y \cdot z}\right)} - 1 \]

      8. add-sqr-sqrt 62.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{y \cdot z}\right)} - 1 \]

   10. Applied egg-rr 62.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 39.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)\right)} \]

       2. expm1-log1p 39.9%

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

       3. *-commutative 39.9%

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

   12. Simplified 39.9%

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

   if -8.2000000000000005e105 < z < 8.20000000000000083e90

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-/r* 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in t around inf 51.8%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+105} \lor \neg \left(z \leq 8.2 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{x_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 5.2e-150) (/ x_m (* y (- t z))) (/ x_m (* (- y z) t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e-150) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 5.2d-150) then
        tmp = x_m / (y * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e-150) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 5.2e-150:
		tmp = x_m / (y * (t - z))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 5.2e-150)
		tmp = Float64(x_m / Float64(y * 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 (t <= 5.2e-150)
		tmp = x_m / (y * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 5.2e-150], N[(x$95$m / N[(y * 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 t < 5.1999999999999995e-150

   1. Initial program 90.7%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if 5.1999999999999995e-150 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 69.7%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{x_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 5.2e-150) (/ (/ x_m y) (- t z)) (/ x_m (* (- y z) t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e-150) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 5.2d-150) then
        tmp = (x_m / y) / (t - z)
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 5.2e-150) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 5.2e-150:
		tmp = (x_m / y) / (t - z)
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 5.2e-150)
		tmp = Float64(Float64(x_m / y) / 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 (t <= 5.2e-150)
		tmp = (x_m / y) / (t - z);
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 5.2e-150], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 5.1999999999999995e-150

   1. Initial program 90.7%

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

      1. add-sqr-sqrt 41.1%

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

      2. times-frac 45.4%

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

   4. Applied egg-rr 45.4%

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

      1. clear-num 45.4%

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

      2. un-div-inv 45.4%

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

   6. Applied egg-rr 45.4%

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

   7. Taylor expanded in y around inf 60.4%

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

      1. associate-/r* 61.1%

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

   9. Simplified 61.1%

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

   if 5.1999999999999995e-150 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 69.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{x_m}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 8e-103) (/ (/ x_m (- t z)) y) (/ 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 <= 8e-103) {
		tmp = (x_m / (t - z)) / y;
	} 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 <= 8d-103) then
        tmp = (x_m / (t - z)) / y
    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 <= 8e-103) {
		tmp = (x_m / (t - z)) / y;
	} 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 <= 8e-103:
		tmp = (x_m / (t - z)) / y
	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 <= 8e-103)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	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 <= 8e-103)
		tmp = (x_m / (t - z)) / y;
	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, 8e-103], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 7.99999999999999966e-103

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-/r* 64.2%

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

   5. Simplified 64.2%

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

   if 7.99999999999999966e-103 < t

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf 74.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8 \cdot 10^{-103}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
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 1 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 89.7%

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

   1. add-sqr-sqrt 41.7%

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

   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. Step-by-step derivation

   1. frac-times 41.7%

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

   2. add-sqr-sqrt 89.7%

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

   3. *-commutative 89.7%

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

   4. associate-/r* 97.8%

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

6. Applied egg-rr 97.8%

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

7. Final simplification 97.8%

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

Alternative 18: 96.8% 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 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (/ (/ x_m (- y z)) (- t z))))

C

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

Fortran

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

Java

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

Python

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

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(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 89.7%

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

   1. add-sqr-sqrt 41.7%

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

   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. Step-by-step derivation

   1. associate-*r/ 46.3%

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

   2. associate-*l/ 46.2%

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

   3. add-sqr-sqrt 97.1%

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

6. Applied egg-rr 97.1%

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

7. Final simplification 97.1%

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

Alternative 19: 38.5% 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 1 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 89.7%

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

3. Taylor expanded in z around 0 39.1%

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

4. Final simplification 39.1%

   \[\leadsto \frac{x}{y \cdot t} \]
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 2024010 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (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))))