Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.5% → 95.1%

Time: 10.4s

Alternatives: 11

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- (/ y z) (/ t (- 1.0 z)))))

C

double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - 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 / (1.0d0 - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y / z) - (t / (1.0 - z)));
}

Python

def code(x, y, z, t):
	return x * ((y / z) - (t / (1.0 - z)))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y / z) - (t / (1.0 - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+256}:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z} \cdot \frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (+ (/ y z) (/ t (+ z -1.0))))))
   (*
    x_s
    (if (<= t_1 -5e+256)
      (* (/ (- (* y (- 1.0 z)) (* z t)) (- 1.0 z)) (/ x_m z))
      t_1))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * ((y / z) + (t / (z + -1.0)));
	double tmp;
	if (t_1 <= -5e+256) {
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * ((y / z) + (t / (z + (-1.0d0))))
    if (t_1 <= (-5d+256)) then
        tmp = (((y * (1.0d0 - z)) - (z * t)) / (1.0d0 - z)) * (x_m / 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);
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 + -1.0)));
	double tmp;
	if (t_1 <= -5e+256) {
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * ((y / z) + (t / (z + -1.0)))
	tmp = 0
	if t_1 <= -5e+256:
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (x_m / z)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(Float64(y / z) + Float64(t / Float64(z + -1.0))))
	tmp = 0.0
	if (t_1 <= -5e+256)
		tmp = Float64(Float64(Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t)) / Float64(1.0 - z)) * Float64(x_m / z));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * ((y / z) + (t / (z + -1.0)));
	tmp = 0.0;
	if (t_1 <= -5e+256)
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (x_m / 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]
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 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, -5e+256], N[(N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$1]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -5.00000000000000015e256

   1. Initial program 88.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-*.f64 N/A

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

      15. lower-/.f64 97.6

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

   4. Applied rewrites 97.6%

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

   if -5.00000000000000015e256 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))))

   1. Initial program 96.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq -5 \cdot 10^{+256}:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.3% accurate, 0.5× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (* x_s (if (<= t_1 (- INFINITY)) (* y (/ x_m z)) (* x_m t_1)))))

C

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

Java

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

Python

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

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x_m / z));
	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);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x_m / z);
	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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x$95$m / z), $MachinePrecision]), $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 (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 63.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 99.7

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

   5. Applied rewrites 99.7%

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

   7. Applied rewrites 99.8%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 97.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

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

Alternative 3: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y + t\right)}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x\_m \cdot y}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(-\mathsf{fma}\left(x\_m, z, x\_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (+ y t)) z)))
   (*
    x_s
    (if (<= z -2.45e-23)
      t_1
      (if (<= z 3.3e-143)
        (/ (* x_m y) z)
        (if (<= z 6.5e-9) (* t (- (fma x_m z x_m))) t_1))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y + t)) / z;
	double tmp;
	if (z <= -2.45e-23) {
		tmp = t_1;
	} else if (z <= 3.3e-143) {
		tmp = (x_m * y) / z;
	} else if (z <= 6.5e-9) {
		tmp = t * -fma(x_m, z, x_m);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y + t)) / z)
	tmp = 0.0
	if (z <= -2.45e-23)
		tmp = t_1;
	elseif (z <= 3.3e-143)
		tmp = Float64(Float64(x_m * y) / z);
	elseif (z <= 6.5e-9)
		tmp = Float64(t * Float64(-fma(x_m, z, x_m)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -2.45e-23], t$95$1, If[LessEqual[z, 3.3e-143], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.5e-9], N[(t * (-N[(x$95$m * z + x$95$m), $MachinePrecision])), $MachinePrecision], t$95$1]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4499999999999999e-23 or 6.5000000000000003e-9 < z

   1. Initial program 97.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 88.6%

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

   if -2.4499999999999999e-23 < z < 3.3000000000000001e-143

   1. Initial program 90.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.0

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

   5. Applied rewrites 77.0%

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

   if 3.3000000000000001e-143 < z < 6.5000000000000003e-9

   1. Initial program 95.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-/.f64 N/A

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

      7. frac-add N/A

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

      8. *-rgt-identity N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 95.5%

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

   5. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 62.1%

       \[\leadsto t \cdot \left(-\mathsf{fma}\left(x, z, x\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y + t\right)}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -0.000365:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\_m \cdot \mathsf{fma}\left(t, -1, \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (+ y t)) z)))
   (*
    x_s
    (if (<= z -0.000365)
      t_1
      (if (<= z 1.0) (* x_m (fma t -1.0 (/ y z))) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y + t)) / z;
	double tmp;
	if (z <= -0.000365) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x_m * fma(t, -1.0, (y / z));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y + t)) / z)
	tmp = 0.0
	if (z <= -0.000365)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(x_m * fma(t, -1.0, Float64(y / z)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

Wolfram

x\_m = N[Abs[x], $MachinePrecision]
x\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -0.000365], t$95$1, If[LessEqual[z, 1.0], N[(x$95$m * N[(t * -1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6499999999999998e-4 or 1 < z

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 89.7%

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

   if -3.6499999999999998e-4 < z < 1

   1. Initial program 91.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. div-inv N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 91.7

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

   4. Applied rewrites 91.7%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 90.9%

      \[\leadsto x \cdot \mathsf{fma}\left(t, \color{blue}{-1}, \frac{y}{z}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot \left(y + t\right)}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \frac{x\_m}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m (+ y t)) z)))
   (*
    x_s
    (if (<= y -8.4e-160)
      t_1
      (if (<= y 6.8e-93) (* t (/ x_m (+ z -1.0))) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * (y + t)) / z;
	double tmp;
	if (y <= -8.4e-160) {
		tmp = t_1;
	} else if (y <= 6.8e-93) {
		tmp = t * (x_m / (z + -1.0));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m * (y + t)) / z
    if (y <= (-8.4d-160)) then
        tmp = t_1
    else if (y <= 6.8d-93) then
        tmp = t * (x_m / (z + (-1.0d0)))
    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);
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 <= -8.4e-160) {
		tmp = t_1;
	} else if (y <= 6.8e-93) {
		tmp = t * (x_m / (z + -1.0));
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * (y + t)) / z
	tmp = 0
	if y <= -8.4e-160:
		tmp = t_1
	elif y <= 6.8e-93:
		tmp = t * (x_m / (z + -1.0))
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * Float64(y + t)) / z)
	tmp = 0.0
	if (y <= -8.4e-160)
		tmp = t_1;
	elseif (y <= 6.8e-93)
		tmp = Float64(t * Float64(x_m / Float64(z + -1.0)));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * (y + t)) / z;
	tmp = 0.0;
	if (y <= -8.4e-160)
		tmp = t_1;
	elseif (y <= 6.8e-93)
		tmp = t * (x_m / (z + -1.0));
	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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -8.4e-160], t$95$1, If[LessEqual[y, 6.8e-93], N[(t * N[(x$95$m / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4000000000000002e-160 or 6.80000000000000002e-93 < y

   1. Initial program 93.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 83.2%

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

   if -8.4000000000000002e-160 < y < 6.80000000000000002e-93

   1. Initial program 98.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-/.f64 N/A

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

      7. frac-add N/A

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

      8. *-rgt-identity N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 88.4

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

   7. Applied rewrites 88.4%

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

Alternative 6: 67.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \frac{t}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+102}:\\ \;\;\;\;x\_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (/ t z))))
   (* x_s (if (<= t -2.2e+71) t_1 (if (<= t 1.9e+102) (* x_m (/ y z)) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (t / z);
	double tmp;
	if (t <= -2.2e+71) {
		tmp = t_1;
	} else if (t <= 1.9e+102) {
		tmp = x_m * (y / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * (t / z)
    if (t <= (-2.2d+71)) then
        tmp = t_1
    else if (t <= 1.9d+102) then
        tmp = x_m * (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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * (t / z);
	double tmp;
	if (t <= -2.2e+71) {
		tmp = t_1;
	} else if (t <= 1.9e+102) {
		tmp = x_m * (y / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * (t / z)
	tmp = 0
	if t <= -2.2e+71:
		tmp = t_1
	elif t <= 1.9e+102:
		tmp = x_m * (y / z)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(t / z))
	tmp = 0.0
	if (t <= -2.2e+71)
		tmp = t_1;
	elseif (t <= 1.9e+102)
		tmp = Float64(x_m * 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);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * (t / z);
	tmp = 0.0;
	if (t <= -2.2e+71)
		tmp = t_1;
	elseif (t <= 1.9e+102)
		tmp = x_m * (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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * N[(t / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -2.2e+71], t$95$1, If[LessEqual[t, 1.9e+102], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999995e71 or 1.89999999999999989e102 < t

   1. Initial program 97.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. metadata-eval N/A

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

      11. lower-+.f64 82.9

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

   5. Applied rewrites 82.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 56.6%

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

   if -2.19999999999999995e71 < t < 1.89999999999999989e102

   1. Initial program 93.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 78.0

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

   5. Applied rewrites 78.0%

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

Alternative 7: 64.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot y}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m y) z)))
   (* x_s (if (<= y -8e-118) t_1 (if (<= y 6e-151) (* t (/ x_m z)) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * y) / z;
	double tmp;
	if (y <= -8e-118) {
		tmp = t_1;
	} else if (y <= 6e-151) {
		tmp = t * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m * y) / z
    if (y <= (-8d-118)) then
        tmp = t_1
    else if (y <= 6d-151) then
        tmp = t * (x_m / 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * y) / z;
	double tmp;
	if (y <= -8e-118) {
		tmp = t_1;
	} else if (y <= 6e-151) {
		tmp = t * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * y) / z
	tmp = 0
	if y <= -8e-118:
		tmp = t_1
	elif y <= 6e-151:
		tmp = t * (x_m / z)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * y) / z)
	tmp = 0.0
	if (y <= -8e-118)
		tmp = t_1;
	elseif (y <= 6e-151)
		tmp = Float64(t * Float64(x_m / z));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * y) / z;
	tmp = 0.0;
	if (y <= -8e-118)
		tmp = t_1;
	elseif (y <= 6e-151)
		tmp = t * (x_m / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -8e-118], t$95$1, If[LessEqual[y, 6e-151], N[(t * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999988e-118 or 6e-151 < y

   1. Initial program 93.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -7.99999999999999988e-118 < y < 6e-151

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-/.f64 N/A

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

      7. frac-add N/A

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

      8. *-rgt-identity N/A

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

      9. lower-/.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. lower-+.f64 89.9

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

   7. Applied rewrites 89.9%

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

   8. Taylor expanded in z around inf

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

   10. Applied rewrites 63.4%

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

Alternative 8: 64.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m \cdot y}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{x\_m \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (* x_m y) z)))
   (* x_s (if (<= y -9.2e-118) t_1 (if (<= y 5.5e-151) (/ (* x_m t) z) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * y) / z;
	double tmp;
	if (y <= -9.2e-118) {
		tmp = t_1;
	} else if (y <= 5.5e-151) {
		tmp = (x_m * t) / z;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m * y) / z
    if (y <= (-9.2d-118)) then
        tmp = t_1
    else if (y <= 5.5d-151) then
        tmp = (x_m * 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m * y) / z;
	double tmp;
	if (y <= -9.2e-118) {
		tmp = t_1;
	} else if (y <= 5.5e-151) {
		tmp = (x_m * t) / z;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m * y) / z
	tmp = 0
	if y <= -9.2e-118:
		tmp = t_1
	elif y <= 5.5e-151:
		tmp = (x_m * t) / z
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m * y) / z)
	tmp = 0.0
	if (y <= -9.2e-118)
		tmp = t_1;
	elseif (y <= 5.5e-151)
		tmp = Float64(Float64(x_m * 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);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m * y) / z;
	tmp = 0.0;
	if (y <= -9.2e-118)
		tmp = t_1;
	elseif (y <= 5.5e-151)
		tmp = (x_m * 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -9.2e-118], t$95$1, If[LessEqual[y, 5.5e-151], N[(N[(x$95$m * t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.20000000000000084e-118 or 5.4999999999999998e-151 < y

   1. Initial program 93.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   if -9.20000000000000084e-118 < y < 5.4999999999999998e-151

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

Alternative 9: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := y \cdot \frac{x\_m}{z}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{x\_m \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x_m z))))
   (* x_s (if (<= y -9.2e-118) t_1 (if (<= y 5.3e-151) (/ (* x_m t) z) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = y * (x_m / z);
	double tmp;
	if (y <= -9.2e-118) {
		tmp = t_1;
	} else if (y <= 5.3e-151) {
		tmp = (x_m * t) / z;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x_m / z)
    if (y <= (-9.2d-118)) then
        tmp = t_1
    else if (y <= 5.3d-151) then
        tmp = (x_m * 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = y * (x_m / z);
	double tmp;
	if (y <= -9.2e-118) {
		tmp = t_1;
	} else if (y <= 5.3e-151) {
		tmp = (x_m * t) / z;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = y * (x_m / z)
	tmp = 0
	if y <= -9.2e-118:
		tmp = t_1
	elif y <= 5.3e-151:
		tmp = (x_m * t) / z
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(y * Float64(x_m / z))
	tmp = 0.0
	if (y <= -9.2e-118)
		tmp = t_1;
	elseif (y <= 5.3e-151)
		tmp = Float64(Float64(x_m * 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);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = y * (x_m / z);
	tmp = 0.0;
	if (y <= -9.2e-118)
		tmp = t_1;
	elseif (y <= 5.3e-151)
		tmp = (x_m * 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -9.2e-118], t$95$1, If[LessEqual[y, 5.3e-151], N[(N[(x$95$m * t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.20000000000000084e-118 or 5.29999999999999978e-151 < y

   1. Initial program 93.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.7

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 71.7%

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

   if -9.20000000000000084e-118 < y < 5.29999999999999978e-151

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. remove-double-neg N/A

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

      3. neg-mul-1 N/A

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

      4. distribute-lft-out-- N/A

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

      5. neg-mul-1 N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. distribute-lft-neg-in N/A

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

      9. *-commutative N/A

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

      10. mul-1-neg N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 67.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.3%

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

Alternative 10: 62.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := x\_m \cdot \left(-t\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* x_m (- t))))
   (* x_s (if (<= t -6.2e+200) t_1 (if (<= t 3.7e+133) (* y (/ x_m z)) t_1)))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * -t;
	double tmp;
	if (t <= -6.2e+200) {
		tmp = t_1;
	} else if (t <= 3.7e+133) {
		tmp = y * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x_m * -t
    if (t <= (-6.2d+200)) then
        tmp = t_1
    else if (t <= 3.7d+133) then
        tmp = y * (x_m / 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);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m * -t;
	double tmp;
	if (t <= -6.2e+200) {
		tmp = t_1;
	} else if (t <= 3.7e+133) {
		tmp = y * (x_m / z);
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m * -t
	tmp = 0
	if t <= -6.2e+200:
		tmp = t_1
	elif t <= 3.7e+133:
		tmp = y * (x_m / z)
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m * Float64(-t))
	tmp = 0.0
	if (t <= -6.2e+200)
		tmp = t_1;
	elseif (t <= 3.7e+133)
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m * -t;
	tmp = 0.0;
	if (t <= -6.2e+200)
		tmp = t_1;
	elseif (t <= 3.7e+133)
		tmp = y * (x_m / 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]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m * (-t)), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t, -6.2e+200], t$95$1, If[LessEqual[t, 3.7e+133], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999988e200 or 3.70000000000000023e133 < t

   1. Initial program 98.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. metadata-eval N/A

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

      11. lower-+.f64 86.4

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

   5. Applied rewrites 86.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 47.6%

      \[\leadsto x \cdot \left(-t\right) \]

   if -6.19999999999999988e200 < t < 3.70000000000000023e133

   1. Initial program 93.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.9

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

   5. Applied rewrites 73.9%

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

   7. Applied rewrites 72.1%

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

Alternative 11: 23.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m * -t);
end

Wolfram

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

Derivation

1. Initial program 94.8%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. distribute-neg-frac2 N/A

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

   3. lower-/.f64 N/A

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

   4. sub-neg N/A

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

   5. mul-1-neg N/A

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

   6. +-commutative N/A

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

   7. distribute-neg-in N/A

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

   8. mul-1-neg N/A

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

   9. remove-double-neg N/A

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

   10. metadata-eval N/A

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

   11. lower-+.f64 48.3

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

5. Applied rewrites 48.3%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 23.4%

   \[\leadsto x \cdot \left(-t\right) \]
9. Add Preprocessing

Developer Target 1: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024222 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

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