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

Percentage Accurate: 94.1% → 97.0%

Time: 8.2s

Alternatives: 10

Speedup: 0.3×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

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: 94.1% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 5e+290) (* t_1 x) (/ (* x (+ y t)) z)))))

C

double code(double x, 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 / z);
	} else if (t_1 <= 5e+290) {
		tmp = t_1 * x;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Java

public static double code(double x, 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 / z);
	} else if (t_1 <= 5e+290) {
		tmp = t_1 * x;
	} else {
		tmp = (x * (y + t)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 5e+290:
		tmp = t_1 * x
	else:
		tmp = (x * (y + t)) / z
	return tmp

Julia

function code(x, 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 / z));
	elseif (t_1 <= 5e+290)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 5e+290)
		tmp = t_1 * x;
	else
		tmp = (x * (y + t)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+290], N[(t$95$1 * x), $MachinePrecision], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 62.5%

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

      1. clear-num 62.5%

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

      2. frac-sub 62.5%

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

      3. *-un-lft-identity 62.5%

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

   4. Applied egg-rr 62.5%

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

      1. div-sub 9.4%

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

      2. times-frac 9.4%

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

      3. *-inverses 62.5%

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

      4. *-lft-identity 62.5%

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

      5. remove-double-neg 62.5%

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

      6. distribute-frac-neg 62.5%

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

      7. *-rgt-identity 62.5%

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

      8. distribute-lft-neg-in 62.5%

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

      9. cancel-sign-sub 62.5%

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

      10. *-commutative 62.5%

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

      11. associate-/r* 62.5%

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

      12. *-inverses 62.5%

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

      13. *-rgt-identity 62.5%

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

      14. distribute-frac-neg 62.5%

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

      15. distribute-neg-frac2 62.5%

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

      16. neg-sub0 62.5%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 62.5%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/r/ 64.8%

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

   9. Simplified 64.8%

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

       1. associate-/r/ 99.9%

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

   11. Applied egg-rr 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 4.9999999999999998e290

   1. Initial program 98.8%

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

   if 4.9999999999999998e290 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 68.9%

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

   3. Taylor expanded in z around inf 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-219}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -5.8e+41)
     (* x (/ (+ y t) z))
     (if (<= z -1.3e-190)
       t_1
       (if (<= z 1.65e-219)
         (/ (* y x) z)
         (if (<= z 1.0) t_1 (* x (+ (/ y z) (/ t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -5.8e+41) {
		tmp = x * ((y + t) / z);
	} else if (z <= -1.3e-190) {
		tmp = t_1;
	} else if (z <= 1.65e-219) {
		tmp = (y * x) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	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 = x * ((y / z) - t)
    if (z <= (-5.8d+41)) then
        tmp = x * ((y + t) / z)
    else if (z <= (-1.3d-190)) then
        tmp = t_1
    else if (z <= 1.65d-219) then
        tmp = (y * x) / z
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = x * ((y / z) + (t / z))
    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);
	double tmp;
	if (z <= -5.8e+41) {
		tmp = x * ((y + t) / z);
	} else if (z <= -1.3e-190) {
		tmp = t_1;
	} else if (z <= 1.65e-219) {
		tmp = (y * x) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -5.8e+41:
		tmp = x * ((y + t) / z)
	elif z <= -1.3e-190:
		tmp = t_1
	elif z <= 1.65e-219:
		tmp = (y * x) / z
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = x * ((y / z) + (t / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -5.8e+41)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= -1.3e-190)
		tmp = t_1;
	elseif (z <= 1.65e-219)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -5.8e+41)
		tmp = x * ((y + t) / z);
	elseif (z <= -1.3e-190)
		tmp = t_1;
	elseif (z <= 1.65e-219)
		tmp = (y * x) / z;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = x * ((y / z) + (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+41], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-190], t$95$1, If[LessEqual[z, 1.65e-219], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.79999999999999977e41

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. remove-double-neg 88.7%

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

      3. cancel-sign-sub-inv 88.7%

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

      4. metadata-eval 88.7%

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

      5. *-lft-identity 88.7%

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

      6. distribute-neg-out 88.7%

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

      7. neg-mul-1 88.7%

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

      8. sub-neg 88.7%

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

      9. distribute-lft-neg-in 88.7%

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

      10. *-commutative 88.7%

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

      11. distribute-neg-frac 88.7%

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

      12. associate-/l* 99.8%

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

      13. distribute-rgt-neg-in 99.8%

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

      14. distribute-neg-frac 99.8%

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

   5. Simplified 99.8%

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

   if -5.79999999999999977e41 < z < -1.2999999999999999e-190 or 1.6500000000000001e-219 < z < 1

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

      3. div-sub 92.9%

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

      4. associate-/l* 93.0%

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

      5. *-inverses 93.0%

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

      6. *-rgt-identity 93.0%

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

   5. Simplified 93.0%

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

   if -1.2999999999999999e-190 < z < 1.6500000000000001e-219

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 89.3%

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

   if 1 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. neg-mul-1 96.6%

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

   5. Simplified 96.6%

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

      1. sub-neg 96.6%

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

      2. distribute-frac-neg 96.6%

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

      3. remove-double-neg 96.6%

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

   7. Applied egg-rr 96.6%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-219}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* x (/ (+ y t) z))))
   (if (<= z -5.8e+41)
     t_2
     (if (<= z -3.6e-189)
       t_1
       (if (<= z 1.9e-218) (/ (* y x) z) (if (<= z 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -5.8e+41) {
		tmp = t_2;
	} else if (z <= -3.6e-189) {
		tmp = t_1;
	} else if (z <= 1.9e-218) {
		tmp = (y * x) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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)
    t_2 = x * ((y + t) / z)
    if (z <= (-5.8d+41)) then
        tmp = t_2
    else if (z <= (-3.6d-189)) then
        tmp = t_1
    else if (z <= 1.9d-218) then
        tmp = (y * x) / z
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    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);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -5.8e+41) {
		tmp = t_2;
	} else if (z <= -3.6e-189) {
		tmp = t_1;
	} else if (z <= 1.9e-218) {
		tmp = (y * x) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = x * ((y + t) / z)
	tmp = 0
	if z <= -5.8e+41:
		tmp = t_2
	elif z <= -3.6e-189:
		tmp = t_1
	elif z <= 1.9e-218:
		tmp = (y * x) / z
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -5.8e+41)
		tmp = t_2;
	elseif (z <= -3.6e-189)
		tmp = t_1;
	elseif (z <= 1.9e-218)
		tmp = Float64(Float64(y * x) / z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -5.8e+41)
		tmp = t_2;
	elseif (z <= -3.6e-189)
		tmp = t_1;
	elseif (z <= 1.9e-218)
		tmp = (y * x) / z;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+41], t$95$2, If[LessEqual[z, -3.6e-189], t$95$1, If[LessEqual[z, 1.9e-218], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.79999999999999977e41 or 1 < z

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. remove-double-neg 79.2%

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

      3. cancel-sign-sub-inv 79.2%

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

      4. metadata-eval 79.2%

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

      5. *-lft-identity 79.2%

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

      6. distribute-neg-out 79.2%

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

      7. neg-mul-1 79.2%

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

      8. sub-neg 79.2%

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

      9. distribute-lft-neg-in 79.2%

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

      10. *-commutative 79.2%

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

      11. distribute-neg-frac 79.2%

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

      12. associate-/l* 97.8%

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

      13. distribute-rgt-neg-in 97.8%

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

      14. distribute-neg-frac 97.8%

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

   5. Simplified 97.8%

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

   if -5.79999999999999977e41 < z < -3.60000000000000017e-189 or 1.8999999999999999e-218 < z < 1

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

      3. div-sub 92.9%

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

      4. associate-/l* 93.0%

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

      5. *-inverses 93.0%

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

      6. *-rgt-identity 93.0%

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

   5. Simplified 93.0%

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

   if -3.60000000000000017e-189 < z < 1.8999999999999999e-218

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 89.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-218}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+153} \lor \neg \left(t \leq 3.7 \cdot 10^{+109} \lor \neg \left(t \leq 6 \cdot 10^{+160}\right) \land t \leq 1.2 \cdot 10^{+217}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e+153)
         (not (or (<= t 3.7e+109) (and (not (<= t 6e+160)) (<= t 1.2e+217)))))
   (* x (/ t z))
   (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+153) || !((t <= 3.7e+109) || (!(t <= 6e+160) && (t <= 1.2e+217)))) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	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) :: tmp
    if ((t <= (-8.5d+153)) .or. (.not. (t <= 3.7d+109) .or. (.not. (t <= 6d+160)) .and. (t <= 1.2d+217))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e+153) || !((t <= 3.7e+109) || (!(t <= 6e+160) && (t <= 1.2e+217)))) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e+153) or not ((t <= 3.7e+109) or (not (t <= 6e+160) and (t <= 1.2e+217))):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e+153) || !((t <= 3.7e+109) || (!(t <= 6e+160) && (t <= 1.2e+217))))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e+153) || ~(((t <= 3.7e+109) || (~((t <= 6e+160)) && (t <= 1.2e+217)))))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e+153], N[Not[Or[LessEqual[t, 3.7e+109], And[N[Not[LessEqual[t, 6e+160]], $MachinePrecision], LessEqual[t, 1.2e+217]]]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.49999999999999935e153 or 3.7000000000000002e109 < t < 5.9999999999999997e160 or 1.1999999999999999e217 < t

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-/l* 59.7%

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

      3. cancel-sign-sub-inv 59.7%

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

      4. metadata-eval 59.7%

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

      5. *-lft-identity 59.7%

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

      6. +-commutative 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in t around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. associate-*r/ 58.4%

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

   8. Simplified 58.4%

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

   if -8.49999999999999935e153 < t < 3.7000000000000002e109 or 5.9999999999999997e160 < t < 1.1999999999999999e217

   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 75.2%

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

      1. associate-*r/ 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+153} \lor \neg \left(t \leq 3.7 \cdot 10^{+109} \lor \neg \left(t \leq 6 \cdot 10^{+160}\right) \land t \leq 1.2 \cdot 10^{+217}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -5.4e-112)
     t_1
     (if (<= y 9.5e-114)
       (* x (/ t (+ z -1.0)))
       (if (<= y 1.4e+89) (* x (- (/ y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -5.4e-112) {
		tmp = t_1;
	} else if (y <= 9.5e-114) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 1.4e+89) {
		tmp = x * ((y / z) - t);
	} 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) :: tmp
    t_1 = y * (x / z)
    if (y <= (-5.4d-112)) then
        tmp = t_1
    else if (y <= 9.5d-114) then
        tmp = x * (t / (z + (-1.0d0)))
    else if (y <= 1.4d+89) then
        tmp = x * ((y / z) - t)
    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 = y * (x / z);
	double tmp;
	if (y <= -5.4e-112) {
		tmp = t_1;
	} else if (y <= 9.5e-114) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 1.4e+89) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -5.4e-112:
		tmp = t_1
	elif y <= 9.5e-114:
		tmp = x * (t / (z + -1.0))
	elif y <= 1.4e+89:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -5.4e-112)
		tmp = t_1;
	elseif (y <= 9.5e-114)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	elseif (y <= 1.4e+89)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -5.4e-112)
		tmp = t_1;
	elseif (y <= 9.5e-114)
		tmp = x * (t / (z + -1.0));
	elseif (y <= 1.4e+89)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e-112], t$95$1, If[LessEqual[y, 9.5e-114], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+89], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4000000000000001e-112 or 1.3999999999999999e89 < y

   1. Initial program 88.3%

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

      1. clear-num 88.2%

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

      2. frac-sub 78.9%

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

      3. *-un-lft-identity 78.9%

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

   4. Applied egg-rr 78.9%

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

      1. div-sub 62.0%

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

      2. times-frac 67.1%

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

      3. *-inverses 84.7%

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

      4. *-lft-identity 84.7%

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

      5. remove-double-neg 84.7%

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

      6. distribute-frac-neg 84.7%

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

      7. *-rgt-identity 84.7%

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

      8. distribute-lft-neg-in 84.7%

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

      9. cancel-sign-sub 84.7%

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

      10. *-commutative 84.7%

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

      11. associate-/r* 88.2%

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

      12. *-inverses 88.2%

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

      13. *-rgt-identity 88.2%

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

      14. distribute-frac-neg 88.2%

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

      15. distribute-neg-frac2 88.2%

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

      16. neg-sub0 88.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 88.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in z around 0 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*r/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-/r/ 74.8%

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

   9. Simplified 74.8%

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

       1. associate-/r/ 83.7%

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

   11. Applied egg-rr 83.7%

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

   if -5.4000000000000001e-112 < y < 9.49999999999999958e-114

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-neg-frac2 75.0%

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

      3. neg-sub0 75.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{0 - \left(1 - z\right)}} \]

      4. associate--r- 75.0%

         \[\leadsto x \cdot \frac{t}{\color{blue}{\left(0 - 1\right) + z}} \]

      5. metadata-eval 75.0%

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

   5. Simplified 75.0%

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

   if 9.49999999999999958e-114 < y < 1.3999999999999999e89

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

      3. div-sub 86.9%

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

      4. associate-/l* 87.0%

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

      5. *-inverses 87.0%

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

      6. *-rgt-identity 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -2.8e-113)
     t_1
     (if (<= y 7.6e-114)
       (* t (/ x (+ z -1.0)))
       (if (<= y 1.7e+89) (* x (- (/ y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -2.8e-113) {
		tmp = t_1;
	} else if (y <= 7.6e-114) {
		tmp = t * (x / (z + -1.0));
	} else if (y <= 1.7e+89) {
		tmp = x * ((y / z) - t);
	} 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) :: tmp
    t_1 = y * (x / z)
    if (y <= (-2.8d-113)) then
        tmp = t_1
    else if (y <= 7.6d-114) then
        tmp = t * (x / (z + (-1.0d0)))
    else if (y <= 1.7d+89) then
        tmp = x * ((y / z) - t)
    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 = y * (x / z);
	double tmp;
	if (y <= -2.8e-113) {
		tmp = t_1;
	} else if (y <= 7.6e-114) {
		tmp = t * (x / (z + -1.0));
	} else if (y <= 1.7e+89) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -2.8e-113:
		tmp = t_1
	elif y <= 7.6e-114:
		tmp = t * (x / (z + -1.0))
	elif y <= 1.7e+89:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -2.8e-113)
		tmp = t_1;
	elseif (y <= 7.6e-114)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	elseif (y <= 1.7e+89)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -2.8e-113)
		tmp = t_1;
	elseif (y <= 7.6e-114)
		tmp = t * (x / (z + -1.0));
	elseif (y <= 1.7e+89)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-113], t$95$1, If[LessEqual[y, 7.6e-114], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+89], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e-113 or 1.7000000000000001e89 < y

   1. Initial program 88.3%

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

      1. clear-num 88.2%

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

      2. frac-sub 78.9%

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

      3. *-un-lft-identity 78.9%

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

   4. Applied egg-rr 78.9%

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

      1. div-sub 62.0%

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

      2. times-frac 67.1%

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

      3. *-inverses 84.7%

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

      4. *-lft-identity 84.7%

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

      5. remove-double-neg 84.7%

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

      6. distribute-frac-neg 84.7%

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

      7. *-rgt-identity 84.7%

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

      8. distribute-lft-neg-in 84.7%

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

      9. cancel-sign-sub 84.7%

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

      10. *-commutative 84.7%

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

      11. associate-/r* 88.2%

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

      12. *-inverses 88.2%

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

      13. *-rgt-identity 88.2%

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

      14. distribute-frac-neg 88.2%

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

      15. distribute-neg-frac2 88.2%

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

      16. neg-sub0 88.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 88.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in z around 0 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*r/ 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-/r/ 74.8%

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

   9. Simplified 74.8%

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

       1. associate-/r/ 83.7%

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

   11. Applied egg-rr 83.7%

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

   if -2.8e-113 < y < 7.5999999999999997e-114

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-neg-frac2 73.2%

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

      5. neg-sub0 73.2%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 73.2%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 73.2%

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

   5. Simplified 73.2%

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

   if 7.5999999999999997e-114 < y < 1.7000000000000001e89

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. unsub-neg 86.9%

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

      3. div-sub 86.9%

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

      4. associate-/l* 87.0%

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

      5. *-inverses 87.0%

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

      6. *-rgt-identity 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-105} \lor \neg \left(y \leq 5.4 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e-105) (not (<= y 5.4e-55)))
   (* y (/ x z))
   (* t (/ x (+ z -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-105) || !(y <= 5.4e-55)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / (z + -1.0));
	}
	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) :: tmp
    if ((y <= (-3.6d-105)) .or. (.not. (y <= 5.4d-55))) then
        tmp = y * (x / z)
    else
        tmp = t * (x / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-105) || !(y <= 5.4e-55)) {
		tmp = y * (x / z);
	} else {
		tmp = t * (x / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e-105) or not (y <= 5.4e-55):
		tmp = y * (x / z)
	else:
		tmp = t * (x / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e-105) || !(y <= 5.4e-55))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.6e-105) || ~((y <= 5.4e-55)))
		tmp = y * (x / z);
	else
		tmp = t * (x / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e-105], N[Not[LessEqual[y, 5.4e-55]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999964e-105 or 5.40000000000000008e-55 < y

   1. Initial program 90.5%

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

      1. clear-num 90.5%

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

      2. frac-sub 80.6%

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

      3. *-un-lft-identity 80.6%

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

   4. Applied egg-rr 80.6%

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

      1. div-sub 66.4%

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

      2. times-frac 71.1%

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

      3. *-inverses 86.5%

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

      4. *-lft-identity 86.5%

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

      5. remove-double-neg 86.5%

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

      6. distribute-frac-neg 86.5%

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

      7. *-rgt-identity 86.5%

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

      8. distribute-lft-neg-in 86.5%

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

      9. cancel-sign-sub 86.5%

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

      10. *-commutative 86.5%

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

      11. associate-/r* 90.5%

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

      12. *-inverses 90.5%

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

      13. *-rgt-identity 90.5%

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

      14. distribute-frac-neg 90.5%

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

      15. distribute-neg-frac2 90.5%

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

      16. neg-sub0 90.5%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 90.5%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in z around 0 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*r/ 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/r/ 75.8%

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

   9. Simplified 75.8%

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

       1. associate-/r/ 82.4%

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

   11. Applied egg-rr 82.4%

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

   if -3.59999999999999964e-105 < y < 5.40000000000000008e-55

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. distribute-neg-frac2 70.5%

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

      5. neg-sub0 70.5%

         \[\leadsto t \cdot \frac{x}{\color{blue}{0 - \left(1 - z\right)}} \]

      6. associate--r- 70.5%

         \[\leadsto t \cdot \frac{x}{\color{blue}{\left(0 - 1\right) + z}} \]

      7. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-105} \lor \neg \left(y \leq 5.4 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-116} \lor \neg \left(y \leq 7.6 \cdot 10^{-114}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-116) (not (<= y 7.6e-114))) (* y (/ x z)) (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-116) || !(y <= 7.6e-114)) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	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) :: tmp
    if ((y <= (-4.2d-116)) .or. (.not. (y <= 7.6d-114))) then
        tmp = y * (x / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-116) || !(y <= 7.6e-114)) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-116) or not (y <= 7.6e-114):
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-116) || !(y <= 7.6e-114))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e-116) || ~((y <= 7.6e-114)))
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e-116], N[Not[LessEqual[y, 7.6e-114]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999998e-116 or 7.5999999999999997e-114 < y

   1. Initial program 91.2%

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

      1. clear-num 91.2%

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

      2. frac-sub 81.1%

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

      3. *-un-lft-identity 81.1%

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

   4. Applied egg-rr 81.1%

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

      1. div-sub 68.0%

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

      2. times-frac 72.8%

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

      3. *-inverses 87.5%

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

      4. *-lft-identity 87.5%

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

      5. remove-double-neg 87.5%

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

      6. distribute-frac-neg 87.5%

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

      7. *-rgt-identity 87.5%

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

      8. distribute-lft-neg-in 87.5%

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

      9. cancel-sign-sub 87.5%

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

      10. *-commutative 87.5%

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

      11. associate-/r* 91.2%

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

      12. *-inverses 91.2%

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

      13. *-rgt-identity 91.2%

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

      14. distribute-frac-neg 91.2%

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

      15. distribute-neg-frac2 91.2%

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

      16. neg-sub0 91.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{0 - \left(1 - z\right)}}\right) \]

      17. associate--r- 91.2%

          \[\leadsto x \cdot \left(\frac{1}{\frac{z}{y}} + \frac{t}{\color{blue}{\left(0 - 1\right) + z}}\right) \]

      18. metadata-eval 91.2%

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

   6. Simplified 91.2%

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

   7. Taylor expanded in z around 0 74.9%

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

      1. *-commutative 74.9%

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

      2. associate-*r/ 80.2%

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

      3. *-commutative 80.2%

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

      4. associate-/r/ 73.6%

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

   9. Simplified 73.6%

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

       1. associate-/r/ 80.2%

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

   11. Applied egg-rr 80.2%

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

   if -4.1999999999999998e-116 < y < 7.5999999999999997e-114

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/l* 54.6%

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

      3. cancel-sign-sub-inv 54.6%

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

      4. metadata-eval 54.6%

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

      5. *-lft-identity 54.6%

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

      6. +-commutative 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in t around inf 47.7%

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

      1. *-commutative 47.7%

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

      2. associate-*r/ 51.7%

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

   8. Simplified 51.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-116} \lor \neg \left(y \leq 7.6 \cdot 10^{-114}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e+41) (not (<= z 1.0))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+41) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	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) :: tmp
    if ((z <= (-1.3d+41)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+41) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e+41) or not (z <= 1.0):
		tmp = x * (t / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e+41) || !(z <= 1.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.3e+41) || ~((z <= 1.0)))
		tmp = x * (t / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e+41], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e41 or 1 < z

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. *-commutative 79.3%

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

      2. associate-/l* 91.4%

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

      3. cancel-sign-sub-inv 91.4%

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

      4. metadata-eval 91.4%

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

      5. *-lft-identity 91.4%

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

      6. +-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in t around inf 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-*r/ 55.9%

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

   8. Simplified 55.9%

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

   if -1.3e41 < z < 1

   1. Initial program 89.6%

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

   3. Taylor expanded in z around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

      3. div-sub 88.2%

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

      4. associate-/l* 88.3%

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

      5. *-inverses 88.3%

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

      6. *-rgt-identity 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in y around 0 27.2%

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

      1. associate-*r* 27.2%

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

      2. mul-1-neg 27.2%

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

   8. Simplified 27.2%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+41} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 22.5% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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 * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

3. Taylor expanded in z around 0 66.3%

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

   1. mul-1-neg 66.3%

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

   2. unsub-neg 66.3%

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

   3. div-sub 66.3%

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

   4. associate-/l* 66.4%

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

   5. *-inverses 66.4%

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

   6. *-rgt-identity 66.4%

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

5. Simplified 66.4%

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

6. Taylor expanded in y around 0 20.2%

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

   1. associate-*r* 20.2%

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

   2. mul-1-neg 20.2%

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

8. Simplified 20.2%

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

9. Final simplification 20.2%

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

Developer target: 94.6% accurate, 0.2× 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 2024091 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

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