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

Percentage Accurate: 88.6% → 97.9%

Time: 11.7s

Alternatives: 18

Speedup: 0.4×

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: 88.6% 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: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-312}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 -2e-312) t_1 (/ (/ x_m (- t z)) (- y z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-312) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m / ((y - z) * (t - z))
    if (t_1 <= (-2d-312)) then
        tmp = t_1
    else
        tmp = (x_m / (t - z)) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-312) {
		tmp = t_1;
	} else {
		tmp = (x_m / (t - z)) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = x_m / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -2e-312:
		tmp = t_1
	else:
		tmp = (x_m / (t - z)) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -2e-312)
		tmp = t_1;
	else
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -2e-312)
		tmp = t_1;
	else
		tmp = (x_m / (t - z)) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, -2e-312], t$95$1, N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -2.0000000000019e-312

   1. Initial program 98.2%

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

   if -2.0000000000019e-312 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 82.2%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

Alternative 2: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{y - z}\\ t_2 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{x\_m}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{-1}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (- y z))) (t_2 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_2 (- INFINITY))
      (/ t_1 t)
      (if (<= t_2 5e+306) (/ x_m t_2) (* t_1 (/ -1.0 z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (y - z);
	double t_2 = (y - z) * (t - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 / t;
	} else if (t_2 <= 5e+306) {
		tmp = x_m / t_2;
	} else {
		tmp = t_1 * (-1.0 / z);
	}
	return x_s * tmp;
}

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (y - z);
	double t_2 = (y - z) * (t - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 / t;
	} else if (t_2 <= 5e+306) {
		tmp = x_m / t_2;
	} else {
		tmp = t_1 * (-1.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (y - z)
	t_2 = (y - z) * (t - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 / t
	elif t_2 <= 5e+306:
		tmp = x_m / t_2
	else:
		tmp = t_1 * (-1.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(y - z))
	t_2 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 / t);
	elseif (t_2 <= 5e+306)
		tmp = Float64(x_m / t_2);
	else
		tmp = Float64(t_1 * Float64(-1.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (y - z);
	t_2 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 / t;
	elseif (t_2 <= 5e+306)
		tmp = x_m / t_2;
	else
		tmp = t_1 * (-1.0 / 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], N[(x$95$m / t$95$2), $MachinePrecision], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 67.7%

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

   3. Taylor expanded in x around 0 67.7%

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

      1. associate-/l/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 86.3%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 4.99999999999999993e306

   1. Initial program 99.1%

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

   if 4.99999999999999993e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 68.0%

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

   3. Taylor expanded in x around 0 68.0%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

      1. div-inv 99.9%

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

   7. Applied egg-rr 99.9%

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

   8. Taylor expanded in t around 0 84.3%

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

Alternative 3: 83.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.0024:\\ \;\;\;\;\frac{x\_m}{y - z} \cdot \frac{-1}{z}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.35e-77)
    (/ (/ x_m (- t z)) y)
    (if (<= t 0.0024)
      (* (/ x_m (- y z)) (/ -1.0 z))
      (if (<= t 2.2e+151) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-77) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 0.0024) {
		tmp = (x_m / (y - z)) * (-1.0 / z);
	} else if (t <= 2.2e+151) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.35d-77)) then
        tmp = (x_m / (t - z)) / y
    else if (t <= 0.0024d0) then
        tmp = (x_m / (y - z)) * ((-1.0d0) / z)
    else if (t <= 2.2d+151) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-77) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 0.0024) {
		tmp = (x_m / (y - z)) * (-1.0 / z);
	} else if (t <= 2.2e+151) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.35e-77:
		tmp = (x_m / (t - z)) / y
	elif t <= 0.0024:
		tmp = (x_m / (y - z)) * (-1.0 / z)
	elif t <= 2.2e+151:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.35e-77)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (t <= 0.0024)
		tmp = Float64(Float64(x_m / Float64(y - z)) * Float64(-1.0 / z));
	elseif (t <= 2.2e+151)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e-77)
		tmp = (x_m / (t - z)) / y;
	elseif (t <= 0.0024)
		tmp = (x_m / (y - z)) * (-1.0 / z);
	elseif (t <= 2.2e+151)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.35e-77], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.0024], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e+151], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e-77

   1. Initial program 87.4%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 55.5%

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

   if -1.35e-77 < t < 0.00239999999999999979

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0 87.2%

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

      1. associate-/l/ 97.1%

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

   5. Simplified 97.1%

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

      1. div-inv 97.0%

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

   7. Applied egg-rr 97.0%

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

   8. Taylor expanded in t around 0 85.4%

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

   if 0.00239999999999999979 < t < 2.20000000000000007e151

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 83.6%

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

   if 2.20000000000000007e151 < t

   1. Initial program 70.0%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 91.8%

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

Alternative 4: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{elif}\;t \leq 0.0036:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -2.2e-80)
    (/ (/ x_m (- t z)) y)
    (if (<= t 0.0036)
      (/ (/ x_m z) (- z y))
      (if (<= t 3.6e+149) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e-80) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 0.0036) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.6e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.2d-80)) then
        tmp = (x_m / (t - z)) / y
    else if (t <= 0.0036d0) then
        tmp = (x_m / z) / (z - y)
    else if (t <= 3.6d+149) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e-80) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 0.0036) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.6e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -2.2e-80:
		tmp = (x_m / (t - z)) / y
	elif t <= 0.0036:
		tmp = (x_m / z) / (z - y)
	elif t <= 3.6e+149:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -2.2e-80)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (t <= 0.0036)
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	elseif (t <= 3.6e+149)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -2.2e-80)
		tmp = (x_m / (t - z)) / y;
	elseif (t <= 0.0036)
		tmp = (x_m / z) / (z - y);
	elseif (t <= 3.6e+149)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -2.2e-80], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.0036], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+149], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -2.2000000000000001e-80

   1. Initial program 87.4%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around inf 55.5%

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

   if -2.2000000000000001e-80 < t < 0.0035999999999999999

   1. Initial program 87.2%

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

   3. Taylor expanded in t around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. associate-/r* 85.9%

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

      3. distribute-neg-frac2 85.9%

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

      4. neg-sub0 85.9%

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

      5. sub-neg 85.9%

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

      6. +-commutative 85.9%

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

      7. associate--r+ 85.9%

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

      8. neg-sub0 85.9%

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

      9. remove-double-neg 85.9%

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

   5. Simplified 85.9%

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

   if 0.0035999999999999999 < t < 3.59999999999999995e149

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 83.6%

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

   if 3.59999999999999995e149 < t

   1. Initial program 70.0%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 91.8%

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

Alternative 5: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-151}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 0.004:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -9e-151)
    (/ (/ x_m y) (- t z))
    (if (<= t 0.004)
      (/ (/ x_m z) (- z y))
      (if (<= t 3.2e+151) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -9e-151) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 0.004) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.2e+151) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-9d-151)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 0.004d0) then
        tmp = (x_m / z) / (z - y)
    else if (t <= 3.2d+151) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -9e-151) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 0.004) {
		tmp = (x_m / z) / (z - y);
	} else if (t <= 3.2e+151) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -9e-151:
		tmp = (x_m / y) / (t - z)
	elif t <= 0.004:
		tmp = (x_m / z) / (z - y)
	elif t <= 3.2e+151:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -9e-151)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 0.004)
		tmp = Float64(Float64(x_m / z) / Float64(z - y));
	elseif (t <= 3.2e+151)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -9e-151)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 0.004)
		tmp = (x_m / z) / (z - y);
	elseif (t <= 3.2e+151)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -9e-151], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.004], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+151], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -9.0000000000000005e-151

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 52.2%

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

      1. associate-/r* 52.1%

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

   5. Simplified 52.1%

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

   if -9.0000000000000005e-151 < t < 0.0040000000000000001

   1. Initial program 87.6%

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

   3. Taylor expanded in t around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. associate-/r* 87.1%

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

      3. distribute-neg-frac2 87.1%

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

      4. neg-sub0 87.1%

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

      5. sub-neg 87.1%

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

      6. +-commutative 87.1%

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

      7. associate--r+ 87.1%

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

      8. neg-sub0 87.1%

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

      9. remove-double-neg 87.1%

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

   5. Simplified 87.1%

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

   if 0.0040000000000000001 < t < 3.19999999999999994e151

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 83.6%

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

   if 3.19999999999999994e151 < t

   1. Initial program 70.0%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 91.8%

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

Alternative 6: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -1.12e+190)
    (/ (/ x_m y) (- t z))
    (if (<= y -2.8e-17)
      (/ x_m (* y (- t z)))
      (if (<= y 7.5e-18) (/ (/ x_m z) (- z t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+190) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -2.8e-17) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 7.5e-18) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.12d+190)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= (-2.8d-17)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 7.5d-18) then
        tmp = (x_m / z) / (z - t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+190) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= -2.8e-17) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 7.5e-18) {
		tmp = (x_m / z) / (z - t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -1.12e+190:
		tmp = (x_m / y) / (t - z)
	elif y <= -2.8e-17:
		tmp = x_m / (y * (t - z))
	elif y <= 7.5e-18:
		tmp = (x_m / z) / (z - t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+190)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= -2.8e-17)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 7.5e-18)
		tmp = Float64(Float64(x_m / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -1.12e+190)
		tmp = (x_m / y) / (t - z);
	elseif (y <= -2.8e-17)
		tmp = x_m / (y * (t - z));
	elseif (y <= 7.5e-18)
		tmp = (x_m / z) / (z - t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -1.12e+190], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-17], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-18], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -1.12000000000000003e190

   1. Initial program 77.3%

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

   3. Taylor expanded in y around inf 77.3%

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

      1. associate-/r* 93.3%

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

   5. Simplified 93.3%

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

   if -1.12000000000000003e190 < y < -2.7999999999999999e-17

   1. Initial program 91.8%

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

      1. clear-num 91.6%

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

      2. associate-/r/ 91.7%

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

   4. Applied egg-rr 91.7%

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

      1. associate-*l/ 91.8%

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

      2. times-frac 94.3%

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

      3. *-commutative 94.3%

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

      4. clear-num 94.3%

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

      5. associate-*l/ 95.4%

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

      6. *-un-lft-identity 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in y around inf 89.0%

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

   if -2.7999999999999999e-17 < y < 7.50000000000000015e-18

   1. Initial program 88.7%

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

   3. Taylor expanded in y around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-/r* 84.1%

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

      3. distribute-neg-frac2 84.1%

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

      4. sub-neg 84.1%

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

      5. +-commutative 84.1%

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

      6. distribute-neg-in 84.1%

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

      7. remove-double-neg 84.1%

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

      8. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   if 7.50000000000000015e-18 < y

   1. Initial program 81.8%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around inf 47.3%

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

Alternative 7: 79.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-250}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t \leq 0.0012:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+149}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.4e-250)
    (/ (/ x_m y) (- t z))
    (if (<= t 0.0012)
      (/ x_m (* z (- z y)))
      (if (<= t 5.2e+149) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-250) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 0.0012) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.2e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.4d-250)) then
        tmp = (x_m / y) / (t - z)
    else if (t <= 0.0012d0) then
        tmp = x_m / (z * (z - y))
    else if (t <= 5.2d+149) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-250) {
		tmp = (x_m / y) / (t - z);
	} else if (t <= 0.0012) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 5.2e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.4e-250:
		tmp = (x_m / y) / (t - z)
	elif t <= 0.0012:
		tmp = x_m / (z * (z - y))
	elif t <= 5.2e+149:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-250)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t <= 0.0012)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 5.2e+149)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-250)
		tmp = (x_m / y) / (t - z);
	elseif (t <= 0.0012)
		tmp = x_m / (z * (z - y));
	elseif (t <= 5.2e+149)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.4e-250], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0012], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+149], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.40000000000000014e-250

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf 51.9%

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

      1. associate-/r* 51.8%

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

   5. Simplified 51.8%

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

   if -1.40000000000000014e-250 < t < 0.00119999999999999989

   1. Initial program 88.4%

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

   3. Taylor expanded in t around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. distribute-rgt-neg-in 78.4%

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

      3. neg-sub0 78.4%

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

      4. sub-neg 78.4%

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

      5. +-commutative 78.4%

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

      6. associate--r+ 78.4%

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

      7. neg-sub0 78.4%

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

      8. remove-double-neg 78.4%

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

   5. Simplified 78.4%

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

   if 0.00119999999999999989 < t < 5.19999999999999957e149

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 83.6%

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

   if 5.19999999999999957e149 < t

   1. Initial program 70.0%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 91.8%

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

Alternative 8: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-209}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.0039:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{+149}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.15e-209)
    (/ x_m (* y (- t z)))
    (if (<= t 0.0039)
      (/ x_m (* z (- z y)))
      (if (<= t 7.3e+149) (/ x_m (* (- y z) t)) (/ (/ x_m t) (- y z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e-209) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 0.0039) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 7.3e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.15d-209)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 0.0039d0) then
        tmp = x_m / (z * (z - y))
    else if (t <= 7.3d+149) then
        tmp = x_m / ((y - z) * t)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e-209) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 0.0039) {
		tmp = x_m / (z * (z - y));
	} else if (t <= 7.3e+149) {
		tmp = x_m / ((y - z) * t);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.15e-209:
		tmp = x_m / (y * (t - z))
	elif t <= 0.0039:
		tmp = x_m / (z * (z - y))
	elif t <= 7.3e+149:
		tmp = x_m / ((y - z) * t)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.15e-209)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 0.0039)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (t <= 7.3e+149)
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.15e-209)
		tmp = x_m / (y * (t - z));
	elseif (t <= 0.0039)
		tmp = x_m / (z * (z - y));
	elseif (t <= 7.3e+149)
		tmp = x_m / ((y - z) * t);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.15e-209], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0039], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.3e+149], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if t < -1.15e-209

   1. Initial program 87.4%

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

      1. clear-num 87.3%

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

      2. associate-/r/ 87.3%

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

   4. Applied egg-rr 87.3%

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

      1. associate-*l/ 87.4%

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

      2. times-frac 95.8%

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

      3. *-commutative 95.8%

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

      4. clear-num 95.6%

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

      5. associate-*l/ 96.2%

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

      6. *-un-lft-identity 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around inf 53.0%

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

   if -1.15e-209 < t < 0.0038999999999999998

   1. Initial program 87.2%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-in 77.8%

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

      3. neg-sub0 77.8%

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

      4. sub-neg 77.8%

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

      5. +-commutative 77.8%

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

      6. associate--r+ 77.8%

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

      7. neg-sub0 77.8%

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

      8. remove-double-neg 77.8%

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

   5. Simplified 77.8%

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

   if 0.0038999999999999998 < t < 7.2999999999999997e149

   1. Initial program 96.2%

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

   3. Taylor expanded in t around inf 83.6%

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

   if 7.2999999999999997e149 < t

   1. Initial program 70.0%

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

      1. associate-/l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in t around inf 91.8%

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

Alternative 9: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+120}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -1.35e+154)
    (/ (/ x_m z) z)
    (if (<= z -1.5e-43)
      (/ x_m (* z (- z y)))
      (if (<= z 4e+120) (/ x_m (* y (- t z))) (* (/ x_m z) (/ 1.0 z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+154) {
		tmp = (x_m / z) / z;
	} else if (z <= -1.5e-43) {
		tmp = x_m / (z * (z - y));
	} else if (z <= 4e+120) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.35d+154)) then
        tmp = (x_m / z) / z
    else if (z <= (-1.5d-43)) then
        tmp = x_m / (z * (z - y))
    else if (z <= 4d+120) then
        tmp = x_m / (y * (t - z))
    else
        tmp = (x_m / z) * (1.0d0 / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+154) {
		tmp = (x_m / z) / z;
	} else if (z <= -1.5e-43) {
		tmp = x_m / (z * (z - y));
	} else if (z <= 4e+120) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -1.35e+154:
		tmp = (x_m / z) / z
	elif z <= -1.5e-43:
		tmp = x_m / (z * (z - y))
	elif z <= 4e+120:
		tmp = x_m / (y * (t - z))
	else:
		tmp = (x_m / z) * (1.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -1.35e+154)
		tmp = Float64(Float64(x_m / z) / z);
	elseif (z <= -1.5e-43)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (z <= 4e+120)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / z) * Float64(1.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e+154)
		tmp = (x_m / z) / z;
	elseif (z <= -1.5e-43)
		tmp = x_m / (z * (z - y));
	elseif (z <= 4e+120)
		tmp = x_m / (y * (t - z));
	else
		tmp = (x_m / z) * (1.0 / 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -1.35e+154], N[(N[(x$95$m / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.5e-43], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+120], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.35000000000000003e154

   1. Initial program 68.6%

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

   3. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. associate-/r* 96.9%

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

      3. distribute-neg-frac2 96.9%

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

      4. neg-sub0 96.9%

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

      5. sub-neg 96.9%

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

      6. +-commutative 96.9%

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

      7. associate--r+ 96.9%

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

      8. neg-sub0 96.9%

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

      9. remove-double-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf 92.1%

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

   if -1.35000000000000003e154 < z < -1.50000000000000002e-43

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-rgt-neg-in 70.4%

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

      3. neg-sub0 70.4%

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

      4. sub-neg 70.4%

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

      5. +-commutative 70.4%

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

      6. associate--r+ 70.4%

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

      7. neg-sub0 70.4%

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

      8. remove-double-neg 70.4%

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

   5. Simplified 70.4%

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

   if -1.50000000000000002e-43 < z < 3.9999999999999999e120

   1. Initial program 92.1%

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

      1. clear-num 91.1%

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

      2. associate-/r/ 91.9%

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

   4. Applied egg-rr 91.9%

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

      1. associate-*l/ 92.1%

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

      2. times-frac 93.4%

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

      3. *-commutative 93.4%

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

      4. clear-num 93.0%

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

      5. associate-*l/ 93.2%

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

      6. *-un-lft-identity 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in y around inf 76.9%

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

   if 3.9999999999999999e120 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-in 69.3%

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

      3. neg-sub0 69.3%

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

      4. sub-neg 69.3%

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

      5. +-commutative 69.3%

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

      6. associate--r+ 69.3%

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

      7. neg-sub0 69.3%

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

      8. remove-double-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around inf 69.2%

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

      1. associate-/r* 87.8%

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

      2. div-inv 87.9%

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

   8. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -12000000:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z}\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+120}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -12000000.0)
    (/ (/ x_m z) z)
    (if (<= z 2.06e+21)
      (/ (/ x_m y) t)
      (if (<= z 4.3e+120) (/ (/ x_m z) (- t)) (* (/ x_m z) (/ 1.0 z)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -12000000.0) {
		tmp = (x_m / z) / z;
	} else if (z <= 2.06e+21) {
		tmp = (x_m / y) / t;
	} else if (z <= 4.3e+120) {
		tmp = (x_m / z) / -t;
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-12000000.0d0)) then
        tmp = (x_m / z) / z
    else if (z <= 2.06d+21) then
        tmp = (x_m / y) / t
    else if (z <= 4.3d+120) then
        tmp = (x_m / z) / -t
    else
        tmp = (x_m / z) * (1.0d0 / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -12000000.0) {
		tmp = (x_m / z) / z;
	} else if (z <= 2.06e+21) {
		tmp = (x_m / y) / t;
	} else if (z <= 4.3e+120) {
		tmp = (x_m / z) / -t;
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -12000000.0:
		tmp = (x_m / z) / z
	elif z <= 2.06e+21:
		tmp = (x_m / y) / t
	elif z <= 4.3e+120:
		tmp = (x_m / z) / -t
	else:
		tmp = (x_m / z) * (1.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -12000000.0)
		tmp = Float64(Float64(x_m / z) / z);
	elseif (z <= 2.06e+21)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (z <= 4.3e+120)
		tmp = Float64(Float64(x_m / z) / Float64(-t));
	else
		tmp = Float64(Float64(x_m / z) * Float64(1.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -12000000.0)
		tmp = (x_m / z) / z;
	elseif (z <= 2.06e+21)
		tmp = (x_m / y) / t;
	elseif (z <= 4.3e+120)
		tmp = (x_m / z) / -t;
	else
		tmp = (x_m / z) * (1.0 / 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -12000000.0], N[(N[(x$95$m / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.06e+21], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.3e+120], N[(N[(x$95$m / z), $MachinePrecision] / (-t)), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e7

   1. Initial program 82.3%

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

   3. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/r* 85.4%

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

      3. distribute-neg-frac2 85.4%

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

      4. neg-sub0 85.4%

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

      5. sub-neg 85.4%

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

      6. +-commutative 85.4%

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

      7. associate--r+ 85.4%

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

      8. neg-sub0 85.4%

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

      9. remove-double-neg 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around inf 78.0%

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

   if -1.2e7 < z < 2.06e21

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in t around inf 60.3%

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

   if 2.06e21 < z < 4.3000000000000002e120

   1. Initial program 74.5%

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

   3. Taylor expanded in y around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. associate-/r* 39.9%

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

      3. distribute-neg-frac2 39.9%

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

      4. sub-neg 39.9%

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

      5. +-commutative 39.9%

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

      6. distribute-neg-in 39.9%

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

      7. remove-double-neg 39.9%

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

      8. unsub-neg 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in z around 0 34.3%

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

      1. neg-mul-1 34.3%

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

   8. Simplified 34.3%

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

   if 4.3000000000000002e120 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-in 69.3%

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

      3. neg-sub0 69.3%

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

      4. sub-neg 69.3%

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

      5. +-commutative 69.3%

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

      6. associate--r+ 69.3%

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

      7. neg-sub0 69.3%

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

      8. remove-double-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around inf 69.2%

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

      1. associate-/r* 87.8%

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

      2. div-inv 87.9%

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

   8. Applied egg-rr 87.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 11: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{z}}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3700000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+120}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m z) z)))
   (*
    x_s
    (if (<= z -3700000.0)
      t_1
      (if (<= z 3.25e+19)
        (/ (/ x_m y) t)
        (if (<= z 4e+120) (/ (/ x_m z) (- t)) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / z;
	double tmp;
	if (z <= -3700000.0) {
		tmp = t_1;
	} else if (z <= 3.25e+19) {
		tmp = (x_m / y) / t;
	} else if (z <= 4e+120) {
		tmp = (x_m / z) / -t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / z) / z
    if (z <= (-3700000.0d0)) then
        tmp = t_1
    else if (z <= 3.25d+19) then
        tmp = (x_m / y) / t
    else if (z <= 4d+120) then
        tmp = (x_m / z) / -t
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / z) / z;
	double tmp;
	if (z <= -3700000.0) {
		tmp = t_1;
	} else if (z <= 3.25e+19) {
		tmp = (x_m / y) / t;
	} else if (z <= 4e+120) {
		tmp = (x_m / z) / -t;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / z) / z
	tmp = 0
	if z <= -3700000.0:
		tmp = t_1
	elif z <= 3.25e+19:
		tmp = (x_m / y) / t
	elif z <= 4e+120:
		tmp = (x_m / z) / -t
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / z) / z)
	tmp = 0.0
	if (z <= -3700000.0)
		tmp = t_1;
	elseif (z <= 3.25e+19)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (z <= 4e+120)
		tmp = Float64(Float64(x_m / z) / Float64(-t));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / z) / z;
	tmp = 0.0;
	if (z <= -3700000.0)
		tmp = t_1;
	elseif (z <= 3.25e+19)
		tmp = (x_m / y) / t;
	elseif (z <= 4e+120)
		tmp = (x_m / z) / -t;
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / z), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3700000.0], t$95$1, If[LessEqual[z, 3.25e+19], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4e+120], N[(N[(x$95$m / z), $MachinePrecision] / (-t)), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -3.7e6 or 3.9999999999999999e120 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-/r* 88.0%

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

      3. distribute-neg-frac2 88.0%

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

      4. neg-sub0 88.0%

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

      5. sub-neg 88.0%

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

      6. +-commutative 88.0%

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

      7. associate--r+ 88.0%

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

      8. neg-sub0 88.0%

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

      9. remove-double-neg 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around inf 81.6%

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

   if -3.7e6 < z < 3.25e19

   1. Initial program 94.6%

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

   3. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in t around inf 60.3%

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

   if 3.25e19 < z < 3.9999999999999999e120

   1. Initial program 74.5%

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

   3. Taylor expanded in y around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. associate-/r* 39.9%

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

      3. distribute-neg-frac2 39.9%

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

      4. sub-neg 39.9%

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

      5. +-commutative 39.9%

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

      6. distribute-neg-in 39.9%

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

      7. remove-double-neg 39.9%

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

      8. unsub-neg 39.9%

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

   5. Simplified 39.9%

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

   6. Taylor expanded in z around 0 34.3%

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

      1. neg-mul-1 34.3%

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

   8. Simplified 34.3%

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

Alternative 12: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-209}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 0.0019:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.12e-209)
    (/ x_m (* y (- t z)))
    (if (<= t 0.0019) (/ x_m (* z (- z y))) (/ x_m (* (- y z) t))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.12e-209) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 0.0019) {
		tmp = x_m / (z * (z - y));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.12d-209)) then
        tmp = x_m / (y * (t - z))
    else if (t <= 0.0019d0) then
        tmp = x_m / (z * (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);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.12e-209) {
		tmp = x_m / (y * (t - z));
	} else if (t <= 0.0019) {
		tmp = x_m / (z * (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)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.12e-209:
		tmp = x_m / (y * (t - z))
	elif t <= 0.0019:
		tmp = x_m / (z * (z - y))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.12e-209)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (t <= 0.0019)
		tmp = Float64(x_m / Float64(z * Float64(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);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.12e-209)
		tmp = x_m / (y * (t - z));
	elseif (t <= 0.0019)
		tmp = x_m / (z * (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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.12e-209], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0019], N[(x$95$m / N[(z * N[(z - y), $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 t < -1.12e-209

   1. Initial program 87.4%

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

      1. clear-num 87.3%

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

      2. associate-/r/ 87.3%

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

   4. Applied egg-rr 87.3%

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

      1. associate-*l/ 87.4%

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

      2. times-frac 95.8%

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

      3. *-commutative 95.8%

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

      4. clear-num 95.6%

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

      5. associate-*l/ 96.2%

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

      6. *-un-lft-identity 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around inf 53.0%

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

   if -1.12e-209 < t < 0.0019

   1. Initial program 87.2%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-in 77.8%

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

      3. neg-sub0 77.8%

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

      4. sub-neg 77.8%

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

      5. +-commutative 77.8%

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

      6. associate--r+ 77.8%

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

      7. neg-sub0 77.8%

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

      8. remove-double-neg 77.8%

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

   5. Simplified 77.8%

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

   if 0.0019 < t

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf 75.8%

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

Alternative 13: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+120}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= z -48000000000000.0)
    (/ (/ x_m z) z)
    (if (<= z 5.5e+120) (/ x_m (* y (- t z))) (* (/ x_m z) (/ 1.0 z))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -48000000000000.0) {
		tmp = (x_m / z) / z;
	} else if (z <= 5.5e+120) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-48000000000000.0d0)) then
        tmp = (x_m / z) / z
    else if (z <= 5.5d+120) then
        tmp = x_m / (y * (t - z))
    else
        tmp = (x_m / z) * (1.0d0 / z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (z <= -48000000000000.0) {
		tmp = (x_m / z) / z;
	} else if (z <= 5.5e+120) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / z) * (1.0 / z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if z <= -48000000000000.0:
		tmp = (x_m / z) / z
	elif z <= 5.5e+120:
		tmp = x_m / (y * (t - z))
	else:
		tmp = (x_m / z) * (1.0 / z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (z <= -48000000000000.0)
		tmp = Float64(Float64(x_m / z) / z);
	elseif (z <= 5.5e+120)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / z) * Float64(1.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (z <= -48000000000000.0)
		tmp = (x_m / z) / z;
	elseif (z <= 5.5e+120)
		tmp = x_m / (y * (t - z));
	else
		tmp = (x_m / z) * (1.0 / 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[z, -48000000000000.0], N[(N[(x$95$m / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.5e+120], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e13

   1. Initial program 81.5%

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

   3. Taylor expanded in t around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. associate-/r* 86.3%

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

      3. distribute-neg-frac2 86.3%

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

      4. neg-sub0 86.3%

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

      5. sub-neg 86.3%

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

      6. +-commutative 86.3%

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

      7. associate--r+ 86.3%

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

      8. neg-sub0 86.3%

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

      9. remove-double-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in z around inf 80.0%

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

   if -4.8e13 < z < 5.50000000000000003e120

   1. Initial program 92.1%

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

      1. clear-num 91.2%

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

      2. associate-/r/ 92.0%

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

   4. Applied egg-rr 92.0%

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

      1. associate-*l/ 92.1%

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

      2. times-frac 94.0%

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

      3. *-commutative 94.0%

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

      4. clear-num 93.6%

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

      5. associate-*l/ 93.8%

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

      6. *-un-lft-identity 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 73.4%

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

   if 5.50000000000000003e120 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-rgt-neg-in 69.3%

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

      3. neg-sub0 69.3%

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

      4. sub-neg 69.3%

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

      5. +-commutative 69.3%

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

      6. associate--r+ 69.3%

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

      7. neg-sub0 69.3%

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

      8. remove-double-neg 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in z around inf 69.2%

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

      1. associate-/r* 87.8%

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

      2. div-inv 87.9%

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

   8. Applied egg-rr 87.9%

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

Alternative 14: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3100000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3100000.0) (not (<= z 4e+120)))
    (/ (/ x_m z) z)
    (/ (/ x_m y) t))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3100000.0) || !(z <= 4e+120)) {
		tmp = (x_m / z) / z;
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3100000.0d0)) .or. (.not. (z <= 4d+120))) then
        tmp = (x_m / z) / 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);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3100000.0) || !(z <= 4e+120)) {
		tmp = (x_m / z) / z;
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -3100000.0) or not (z <= 4e+120):
		tmp = (x_m / z) / z
	else:
		tmp = (x_m / y) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -3100000.0) || !(z <= 4e+120))
		tmp = Float64(Float64(x_m / z) / z);
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -3100000.0) || ~((z <= 4e+120)))
		tmp = (x_m / z) / 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -3100000.0], N[Not[LessEqual[z, 4e+120]], $MachinePrecision]], N[(N[(x$95$m / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e6 or 3.9999999999999999e120 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-/r* 88.0%

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

      3. distribute-neg-frac2 88.0%

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

      4. neg-sub0 88.0%

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

      5. sub-neg 88.0%

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

      6. +-commutative 88.0%

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

      7. associate--r+ 88.0%

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

      8. neg-sub0 88.0%

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

      9. remove-double-neg 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around inf 81.6%

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

   if -3.1e6 < z < 3.9999999999999999e120

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 74.2%

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

      1. associate-/r* 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around inf 57.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3100000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -24000000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -24000000.0) (not (<= z 4e+120)))
    (/ x_m (* z z))
    (/ (/ x_m y) t))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -24000000.0) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-24000000.0d0)) .or. (.not. (z <= 4d+120))) then
        tmp = x_m / (z * 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);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -24000000.0) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -24000000.0) or not (z <= 4e+120):
		tmp = x_m / (z * z)
	else:
		tmp = (x_m / y) / t
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -24000000.0) || !(z <= 4e+120))
		tmp = Float64(x_m / Float64(z * z));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -24000000.0) || ~((z <= 4e+120)))
		tmp = x_m / (z * 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -24000000.0], N[Not[LessEqual[z, 4e+120]], $MachinePrecision]], N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e7 or 3.9999999999999999e120 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

      3. neg-sub0 71.0%

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

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

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

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around inf 68.4%

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

   if -2.4e7 < z < 3.9999999999999999e120

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 74.2%

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

      1. associate-/r* 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around inf 57.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -24000000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -400000.0) (not (<= z 4e+120)))
    (/ x_m (* z z))
    (/ (/ x_m t) y))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-400000.0d0)) .or. (.not. (z <= 4d+120))) then
        tmp = x_m / (z * 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);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -400000.0) or not (z <= 4e+120):
		tmp = x_m / (z * z)
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -400000.0) || !(z <= 4e+120))
		tmp = Float64(x_m / Float64(z * 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);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -400000.0) || ~((z <= 4e+120)))
		tmp = x_m / (z * 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -400000.0], N[Not[LessEqual[z, 4e+120]], $MachinePrecision]], N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -4e5 or 3.9999999999999999e120 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

      3. neg-sub0 71.0%

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

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

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

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in z around inf 68.4%

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

   if -4e5 < z < 3.9999999999999999e120

   1. Initial program 92.0%

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

      1. clear-num 91.0%

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

      2. associate-/r/ 91.9%

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

   4. Applied egg-rr 91.9%

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

      1. associate-*l/ 92.0%

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

      2. times-frac 93.9%

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

      3. *-commutative 93.9%

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

      4. clear-num 93.5%

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

      5. associate-*l/ 93.7%

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

      6. *-un-lft-identity 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in z around 0 52.0%

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

      1. associate-/r* 54.4%

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

   9. Simplified 54.4%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-43} \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.7e-43) (not (<= z 4e+120)))
    (/ x_m (* z z))
    (/ x_m (* y t)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z && z < t);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-43) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.7d-43)) .or. (.not. (z <= 4d+120))) then
        tmp = x_m / (z * 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);
assert x_m < y && y < z && z < t;
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-43) || !(z <= 4e+120)) {
		tmp = x_m / (z * z);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.7e-43) or not (z <= 4e+120):
		tmp = x_m / (z * z)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z, t = sort([x_m, y, z, t])
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-43) || !(z <= 4e+120))
		tmp = Float64(x_m / Float64(z * 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);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-43) || ~((z <= 4e+120)))
		tmp = x_m / (z * 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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.7e-43], N[Not[LessEqual[z, 4e+120]], $MachinePrecision]], N[(x$95$m / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-43 or 3.9999999999999999e120 < z

   1. Initial program 78.9%

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

   3. Taylor expanded in t around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. neg-sub0 69.6%

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

      4. sub-neg 69.6%

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

      5. +-commutative 69.6%

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

      6. associate--r+ 69.6%

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

      7. neg-sub0 69.6%

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

      8. remove-double-neg 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in z around inf 64.8%

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

   if -1.7e-43 < z < 3.9999999999999999e120

   1. Initial program 92.1%

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

   3. Taylor expanded in z around 0 54.4%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-43} \lor \neg \left(z \leq 4 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.2% accurate, 1.8× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
(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);
assert(x_m < y && y < z && z < t);
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)
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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);
assert x_m < y && y < z && z < t;
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)
[x_m, y, z, t] = sort([x_m, y, z, t])
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)
x_m, y, z, t = sort([x_m, y, z, t])
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);
x_m, y, z, t = num2cell(sort([x_m, y, z, t])){:}
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]
NOTE: x_m, y, z, and t should be sorted in increasing order before calling this function.
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 85.8%

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

3. Taylor expanded in z around 0 35.1%

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

4. Final simplification 35.1%

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

Developer Target 1: 87.4% 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 2024172 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

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