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

Percentage Accurate: 89.2% → 97.9%

Time: 11.7s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% 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

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 10^{-292}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z)))))
   (* x_s (if (<= t_1 1e-292) (/ (/ x_m (- t z)) (- y z)) 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 / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= 1e-292) {
		tmp = (x_m / (t - z)) / (y - z);
	} 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 / ((y - z) * (t - z))
    if (t_1 <= 1d-292) then
        tmp = (x_m / (t - z)) / (y - z)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 <= 1e-292) {
		tmp = (x_m / (t - z)) / (y - z);
	} 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 / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= 1e-292:
		tmp = (x_m / (t - z)) / (y - z)
	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(x_m / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= 1e-292)
		tmp = Float64(Float64(x_m / Float64(t - z)) / Float64(y - z));
	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 / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 1e-292)
		tmp = (x_m / (t - z)) / (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, 1e-292], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < 1.0000000000000001e-292

   1. Initial program 84.8%

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

      1. associate-/l/ N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 97.7

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

   4. Applied egg-rr 97.7%

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

   if 1.0000000000000001e-292 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 99.6%

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

Alternative 2: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z - t}}{z}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m (- y z)) t)
      (if (<= t_1 2e+306) (/ x_m t_1) (/ (/ x_m (- z t)) 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / (y - z)) / t;
	} else if (t_1 <= 2e+306) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / (z - t)) / 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / (y - z)) / t;
	} else if (t_1 <= 2e+306) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / (z - t)) / 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 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / (y - z)) / t
	elif t_1 <= 2e+306:
		tmp = x_m / t_1
	else:
		tmp = (x_m / (z - t)) / 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(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	elseif (t_1 <= 2e+306)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / Float64(z - t)) / 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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / (y - z)) / t;
	elseif (t_1 <= 2e+306)
		tmp = x_m / t_1;
	else
		tmp = (x_m / (z - t)) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 92.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000003e306

   1. Initial program 99.7%

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

   if 2.00000000000000003e306 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.0%

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

      1. clear-num N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

      4. flip-- N/A

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

      5. clear-num N/A

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

      6. /-lowering-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. --lowering--.f64 99.9

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

   4. Applied egg-rr 99.9%

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

      1. frac-2neg N/A

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

      2. div-inv N/A

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

      3. distribute-neg-frac2 N/A

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

      4. associate-*l/ N/A

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

      5. div-inv N/A

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

      6. /-lowering-/.f64 N/A

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

      7. distribute-frac-neg2 N/A

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

      8. clear-num N/A

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

      9. distribute-neg-frac2 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. sub-neg N/A

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

      19. +-commutative N/A

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

      20. distribute-neg-in N/A

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

      21. remove-double-neg N/A

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

      22. sub-neg N/A

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

      23. --lowering--.f64 99.9

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf

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

   9. Simplified 85.7%

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

Alternative 3: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x\_m}{y - z}}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+296}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m (- y z)) t)
      (if (<= t_1 1e+296) (/ x_m t_1) (/ (/ x_m z) (- z 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / (y - z)) / t;
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - y);
	}
	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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / (y - z)) / t;
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - 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):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / (y - z)) / t
	elif t_1 <= 1e+296:
		tmp = x_m / t_1
	else:
		tmp = (x_m / z) / (z - 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)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / Float64(y - z)) / t);
	elseif (t_1 <= 1e+296)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / z) / Float64(z - 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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / (y - z)) / t;
	elseif (t_1 <= 1e+296)
		tmp = x_m / t_1;
	else
		tmp = (x_m / z) / (z - 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+296], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 92.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 9.99999999999999981e295

   1. Initial program 99.7%

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

   if 9.99999999999999981e295 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 66.1

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

   5. Simplified 66.1%

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

      1. associate-/r* N/A

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

      2. sub-neg N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. /-lowering-/.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 87.5

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

   7. Applied egg-rr 87.5%

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

Alternative 4: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{elif}\;t\_1 \leq 10^{+296}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m (- t z)) y)
      (if (<= t_1 1e+296) (/ x_m t_1) (/ (/ x_m z) (- z 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / (t - z)) / y;
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - y);
	}
	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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / (t - z)) / y;
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - 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):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / (t - z)) / y
	elif t_1 <= 1e+296:
		tmp = x_m / t_1
	else:
		tmp = (x_m / z) / (z - 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)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (t_1 <= 1e+296)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / z) / Float64(z - 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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / (t - z)) / y;
	elseif (t_1 <= 1e+296)
		tmp = x_m / t_1;
	else
		tmp = (x_m / z) / (z - 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 1e+296], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.4%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-lowering-*.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 58.4

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

   4. Applied egg-rr 58.4%

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

   5. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 58.2

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

   7. Simplified 58.2%

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

      1. *-commutative N/A

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

      2. un-div-inv N/A

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

      3. associate-/r* N/A

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

      4. sub-neg N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. /-lowering-/.f64 N/A

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

      11. distribute-neg-frac2 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. sub-neg N/A

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

      17. /-lowering-/.f64 N/A

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

      18. --lowering--.f64 89.3

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

   9. Applied egg-rr 89.3%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 9.99999999999999981e295

   1. Initial program 99.7%

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

   if 9.99999999999999981e295 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 66.1

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

   5. Simplified 66.1%

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

      1. associate-/r* N/A

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

      2. sub-neg N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. /-lowering-/.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 87.5

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

   7. Applied egg-rr 87.5%

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

Alternative 5: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;t\_1 \leq 10^{+296}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{z}}{z - y}\\ \end{array} \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m y) (- t z))
      (if (<= t_1 1e+296) (/ x_m t_1) (/ (/ x_m z) (- z 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / y) / (t - z);
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - y);
	}
	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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / y) / (t - z);
	} else if (t_1 <= 1e+296) {
		tmp = x_m / t_1;
	} else {
		tmp = (x_m / z) / (z - 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):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / y) / (t - z)
	elif t_1 <= 1e+296:
		tmp = x_m / t_1
	else:
		tmp = (x_m / z) / (z - 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)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (t_1 <= 1e+296)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(x_m / z) / Float64(z - 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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / y) / (t - z);
	elseif (t_1 <= 1e+296)
		tmp = x_m / t_1;
	else
		tmp = (x_m / z) / (z - 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+296], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 89.3%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 9.99999999999999981e295

   1. Initial program 99.7%

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

   if 9.99999999999999981e295 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 66.1

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

   5. Simplified 66.1%

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

      1. associate-/r* N/A

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

      2. sub-neg N/A

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

      3. remove-double-neg N/A

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

      4. distribute-neg-in N/A

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

      5. +-commutative N/A

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

      6. sub-neg N/A

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

      7. /-lowering-/.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. sub-neg N/A

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

      10. +-commutative N/A

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

      11. distribute-neg-in N/A

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

      12. remove-double-neg N/A

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

      13. sub-neg N/A

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

      14. --lowering--.f64 87.5

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

   7. Applied egg-rr 87.5%

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

Alternative 6: 89.1% accurate, 0.6× speedup

Math

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

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 (* (- y z) (- t z))))
   (* x_s (if (<= t_1 (- INFINITY)) (/ (/ x_m y) t) (/ x_m 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / y) / t;
	} else {
		tmp = x_m / t_1;
	}
	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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / y) / t;
	} else {
		tmp = x_m / 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 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / y) / t
	else:
		tmp = x_m / 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(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / y) / t);
	else
		tmp = Float64(x_m / 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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / y) / t;
	else
		tmp = x_m / 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[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], N[(x$95$m / t$95$1), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.4%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 46.9

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

   5. Simplified 46.9%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 81.8

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

   7. Applied egg-rr 81.8%

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

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

   1. Initial program 92.1%

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

Alternative 7: 89.2% accurate, 0.6× speedup

Math

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

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 (* (- y z) (- t z))))
   (* x_s (if (<= t_1 (- INFINITY)) (/ (/ x_m t) y) (/ x_m 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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / t) / y;
	} else {
		tmp = x_m / t_1;
	}
	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 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / t) / y;
	} else {
		tmp = x_m / 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 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / t) / y
	else:
		tmp = x_m / 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(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / t) / y);
	else
		tmp = Float64(x_m / 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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / t) / y;
	else
		tmp = x_m / 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[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / t$95$1), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.4%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 46.9

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

   5. Simplified 46.9%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 71.8

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

   7. Applied egg-rr 71.8%

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

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

   1. Initial program 92.1%

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

Alternative 8: 92.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{z}}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 -1.35e+154)
      t_1
      (if (<= z 2.9e+150) (/ x_m (* (- y z) (- t z))) 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 <= -1.35e+154) {
		tmp = t_1;
	} else if (z <= 2.9e+150) {
		tmp = x_m / ((y - z) * (t - z));
	} 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 <= (-1.35d+154)) then
        tmp = t_1
    else if (z <= 2.9d+150) then
        tmp = x_m / ((y - z) * (t - z))
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 <= -1.35e+154) {
		tmp = t_1;
	} else if (z <= 2.9e+150) {
		tmp = x_m / ((y - z) * (t - z));
	} 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 <= -1.35e+154:
		tmp = t_1
	elif z <= 2.9e+150:
		tmp = x_m / ((y - z) * (t - z))
	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 <= -1.35e+154)
		tmp = t_1;
	elseif (z <= 2.9e+150)
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
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 <= -1.35e+154)
		tmp = t_1;
	elseif (z <= 2.9e+150)
		tmp = x_m / ((y - z) * (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -1.35e+154], t$95$1, If[LessEqual[z, 2.9e+150], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000003e154 or 2.90000000000000011e150 < z

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 73.7

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

   5. Simplified 73.7%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 90.6

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

   7. Applied egg-rr 90.6%

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

   if -1.35000000000000003e154 < z < 2.90000000000000011e150

   1. Initial program 94.0%

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

Alternative 9: 78.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= y -2.4e-70)
    (/ x_m (* y (- t z)))
    (if (<= y 5e-156) (/ x_m (* z (- z t))) (/ 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 (y <= -2.4e-70) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 5e-156) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
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 <= (-2.4d-70)) then
        tmp = x_m / (y * (t - z))
    else if (y <= 5d-156) then
        tmp = x_m / (z * (z - t))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 <= -2.4e-70) {
		tmp = x_m / (y * (t - z));
	} else if (y <= 5e-156) {
		tmp = x_m / (z * (z - t));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z, t] = sort([x_m, y, z, t])
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.4e-70:
		tmp = x_m / (y * (t - z))
	elif y <= 5e-156:
		tmp = x_m / (z * (z - t))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
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 <= -2.4e-70)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	elseif (y <= 5e-156)
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	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 (y <= -2.4e-70)
		tmp = x_m / (y * (t - z));
	elseif (y <= 5e-156)
		tmp = x_m / (z * (z - t));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -2.4e-70], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-156], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000001e-70

   1. Initial program 81.6%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 72.1

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

   5. Simplified 72.1%

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

   if -2.4000000000000001e-70 < y < 5.00000000000000007e-156

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 84.0

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

   5. Simplified 84.0%

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

   if 5.00000000000000007e-156 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 58.7%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{y \cdot \left(t - z\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 (* y (- t z)))))
   (*
    x_s
    (if (<= y -1.38e-70) t_1 (if (<= y 2.5e-26) (/ x_m (* z (- 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 / (y * (t - z));
	double tmp;
	if (y <= -1.38e-70) {
		tmp = t_1;
	} else if (y <= 2.5e-26) {
		tmp = x_m / (z * (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 / (y * (t - z))
    if (y <= (-1.38d-70)) then
        tmp = t_1
    else if (y <= 2.5d-26) then
        tmp = x_m / (z * (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 / (y * (t - z));
	double tmp;
	if (y <= -1.38e-70) {
		tmp = t_1;
	} else if (y <= 2.5e-26) {
		tmp = x_m / (z * (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 / (y * (t - z))
	tmp = 0
	if y <= -1.38e-70:
		tmp = t_1
	elif y <= 2.5e-26:
		tmp = x_m / (z * (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(x_m / Float64(y * Float64(t - z)))
	tmp = 0.0
	if (y <= -1.38e-70)
		tmp = t_1;
	elseif (y <= 2.5e-26)
		tmp = Float64(x_m / Float64(z * Float64(z - 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 / (y * (t - z));
	tmp = 0.0;
	if (y <= -1.38e-70)
		tmp = t_1;
	elseif (y <= 2.5e-26)
		tmp = x_m / (z * (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[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.38e-70], t$95$1, If[LessEqual[y, 2.5e-26], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3800000000000001e-70 or 2.5000000000000001e-26 < y

   1. Initial program 84.9%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 77.7

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

   5. Simplified 77.7%

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

   if -1.3800000000000001e-70 < y < 2.5000000000000001e-26

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 81.1

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

   5. Simplified 81.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-130}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
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 -1.2e-130)
    (/ x_m (* z (- z y)))
    (if (<= z 1.2e-72) (/ x_m (* y t)) (/ x_m (* z (- 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 (z <= -1.2e-130) {
		tmp = x_m / (z * (z - y));
	} else if (z <= 1.2e-72) {
		tmp = x_m / (y * t);
	} else {
		tmp = x_m / (z * (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 (z <= (-1.2d-130)) then
        tmp = x_m / (z * (z - y))
    else if (z <= 1.2d-72) then
        tmp = x_m / (y * t)
    else
        tmp = x_m / (z * (z - t))
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 <= -1.2e-130) {
		tmp = x_m / (z * (z - y));
	} else if (z <= 1.2e-72) {
		tmp = x_m / (y * t);
	} else {
		tmp = x_m / (z * (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 z <= -1.2e-130:
		tmp = x_m / (z * (z - y))
	elif z <= 1.2e-72:
		tmp = x_m / (y * t)
	else:
		tmp = x_m / (z * (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 (z <= -1.2e-130)
		tmp = Float64(x_m / Float64(z * Float64(z - y)));
	elseif (z <= 1.2e-72)
		tmp = Float64(x_m / Float64(y * t));
	else
		tmp = Float64(x_m / Float64(z * Float64(z - t)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
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 <= -1.2e-130)
		tmp = x_m / (z * (z - y));
	elseif (z <= 1.2e-72)
		tmp = x_m / (y * t);
	else
		tmp = x_m / (z * (z - t));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -1.2e-130], N[(x$95$m / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-72], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999998e-130

   1. Initial program 82.5%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. --lowering--.f64 70.1

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

   5. Simplified 70.1%

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

   if -1.19999999999999998e-130 < z < 1.2e-72

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 72.3

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

   5. Simplified 72.3%

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

   if 1.2e-72 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 71.0

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

   5. Simplified 71.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot \left(z - t\right)}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-74}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 t)))))
   (* x_s (if (<= z -2.6e-61) t_1 (if (<= z 2.65e-74) (/ x_m (* y 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 - t));
	double tmp;
	if (z <= -2.6e-61) {
		tmp = t_1;
	} else if (z <= 2.65e-74) {
		tmp = x_m / (y * 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 - t))
    if (z <= (-2.6d-61)) then
        tmp = t_1
    else if (z <= 2.65d-74) then
        tmp = x_m / (y * t)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 - t));
	double tmp;
	if (z <= -2.6e-61) {
		tmp = t_1;
	} else if (z <= 2.65e-74) {
		tmp = x_m / (y * t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[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 - t))
	tmp = 0
	if z <= -2.6e-61:
		tmp = t_1
	elif z <= 2.65e-74:
		tmp = x_m / (y * 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(x_m / Float64(z * Float64(z - t)))
	tmp = 0.0
	if (z <= -2.6e-61)
		tmp = t_1;
	elseif (z <= 2.65e-74)
		tmp = Float64(x_m / Float64(y * t));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
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 - t));
	tmp = 0.0;
	if (z <= -2.6e-61)
		tmp = t_1;
	elseif (z <= 2.65e-74)
		tmp = x_m / (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.6e-61], t$95$1, If[LessEqual[z, 2.65e-74], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e-61 or 2.64999999999999994e-74 < z

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. remove-double-neg N/A

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

      14. unsub-neg N/A

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

      15. --lowering--.f64 70.3

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

   5. Simplified 70.3%

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

   if -2.6000000000000001e-61 < z < 2.64999999999999994e-74

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 70.1

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

   5. Simplified 70.1%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 90.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -2.6e+141) (/ (/ x_m y) (- t z)) (/ x_m (* (- y z) (- t 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 <= -2.6e+141) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = x_m / ((y - z) * (t - 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 <= (-2.6d+141)) then
        tmp = (x_m / y) / (t - z)
    else
        tmp = x_m / ((y - z) * (t - 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 <= -2.6e+141) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = x_m / ((y - z) * (t - 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 <= -2.6e+141:
		tmp = (x_m / y) / (t - z)
	else:
		tmp = x_m / ((y - z) * (t - 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 <= -2.6e+141)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * Float64(t - 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 <= -2.6e+141)
		tmp = (x_m / y) / (t - z);
	else
		tmp = x_m / ((y - z) * (t - z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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, -2.6e+141], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.5999999999999999e141

   1. Initial program 78.8%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. --lowering--.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 99.7%

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

   if -2.5999999999999999e141 < y

   1. Initial program 90.3%

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

Alternative 14: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z, t] = \mathsf{sort}([x_m, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x\_m}{z \cdot z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

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 -3.5e-45) t_1 (if (<= z 2.8e-51) (/ x_m (* y 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 <= -3.5e-45) {
		tmp = t_1;
	} else if (z <= 2.8e-51) {
		tmp = x_m / (y * 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 <= (-3.5d-45)) then
        tmp = t_1
    else if (z <= 2.8d-51) then
        tmp = x_m / (y * t)
    else
        tmp = t_1
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
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 <= -3.5e-45) {
		tmp = t_1;
	} else if (z <= 2.8e-51) {
		tmp = x_m / (y * t);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[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 <= -3.5e-45:
		tmp = t_1
	elif z <= 2.8e-51:
		tmp = x_m / (y * 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(x_m / Float64(z * z))
	tmp = 0.0
	if (z <= -3.5e-45)
		tmp = t_1;
	elseif (z <= 2.8e-51)
		tmp = Float64(x_m / Float64(y * t));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
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 <= -3.5e-45)
		tmp = t_1;
	elseif (z <= 2.8e-51)
		tmp = x_m / (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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[(z * z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -3.5e-45], t$95$1, If[LessEqual[z, 2.8e-51], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e-45 or 2.8e-51 < z

   1. Initial program 82.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 57.9

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

   5. Simplified 57.9%

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

   if -3.5e-45 < z < 2.8e-51

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 68.4

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

   5. Simplified 68.4%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.2% accurate, 1.0× speedup

Math

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

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 z) (- t 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) {
	return x_s * (x_m / ((y - z) * (t - z)));
}

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 - z) * (t - z)))
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 - z) * (t - z)));
}

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 - z) * (t - z)))

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(Float64(y - z) * Float64(t - z))))
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 - z) * (t - z)));
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.4%

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

Alternative 16: 39.9% accurate, 1.4× speedup

Math

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

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 88.4%

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

3. Taylor expanded in z around 0

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

   1. /-lowering-/.f64 N/A

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

   2. *-lowering-*.f64 41.2

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

5. Simplified 41.2%

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

6. Final simplification 41.2%

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

Developer Target 1: 88.0% 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 2024199 
(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))))