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

Percentage Accurate: 94.3% → 96.4%

Time: 9.9s

Alternatives: 13

Speedup: 0.5×

• 20.9% 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: 94.3% 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: 96.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (/ y z) (/ t (+ z -1.0))) (- INFINITY))
   (* y (/ x z))
   (* x (+ (/ y z) (* t (/ 1.0 (+ z -1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) + (t / (z + -1.0))) <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else {
		tmp = x * ((y / z) + (t * (1.0 / (z + -1.0))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y / z) + (t / (z + -1.0))) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else {
		tmp = x * ((y / z) + (t * (1.0 / (z + -1.0))));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t * N[(1.0 / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 71.7%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate--r- 99.9%

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

      6. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 99.9%

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

   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. Step-by-step derivation

      1. clear-num 97.0%

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

      2. associate-/r/ 97.2%

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

   4. Applied egg-rr 97.2%

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

4. Final simplification 97.3%

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

Alternative 2: 41.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -3.8 \cdot 10^{-282} \lor \neg \left(z \leq 4.5 \cdot 10^{-201}\right) \land z \leq 185000000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0)
         (not
          (or (<= z -3.8e-282)
              (and (not (<= z 4.5e-201)) (<= z 185000000.0)))))
   (* t (/ x z))
   (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !((z <= -3.8e-282) || (!(z <= 4.5e-201) && (z <= 185000000.0)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -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 ((z <= (-1.0d0)) .or. (.not. (z <= (-3.8d-282)) .or. (.not. (z <= 4.5d-201)) .and. (z <= 185000000.0d0))) then
        tmp = t * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !((z <= -3.8e-282) || (!(z <= 4.5e-201) && (z <= 185000000.0)))) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not ((z <= -3.8e-282) or (not (z <= 4.5e-201) and (z <= 185000000.0))):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !((z <= -3.8e-282) || (!(z <= 4.5e-201) && (z <= 185000000.0))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~(((z <= -3.8e-282) || (~((z <= 4.5e-201)) && (z <= 185000000.0)))))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[Or[LessEqual[z, -3.8e-282], And[N[Not[LessEqual[z, 4.5e-201]], $MachinePrecision], LessEqual[z, 185000000.0]]]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or -3.79999999999999992e-282 < z < 4.5000000000000002e-201 or 1.85e8 < z

   1. Initial program 95.0%

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

      1. clear-num 94.8%

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

      2. associate-/r/ 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 88.3%

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

      2. sub-neg 88.3%

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

      3. neg-mul-1 88.3%

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

      4. remove-double-neg 88.3%

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

   7. Simplified 88.3%

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

   8. Taylor expanded in y around 0 49.7%

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

      1. associate-/l* 51.7%

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

   10. Simplified 51.7%

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

   if -1 < z < -3.79999999999999992e-282 or 4.5000000000000002e-201 < z < 1.85e8

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in y around 0 33.6%

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

      1. neg-mul-1 33.6%

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

   6. Simplified 33.6%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -3.8 \cdot 10^{-282} \lor \neg \left(z \leq 4.5 \cdot 10^{-201}\right) \land z \leq 185000000\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := t \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* t (- x))))
   (if (<= z -1.0)
     t_1
     (if (<= z -5.6e-277)
       t_2
       (if (<= z 7.2e-194) (* t (/ x z)) (if (<= z 185000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = t * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -5.6e-277) {
		tmp = t_2;
	} else if (z <= 7.2e-194) {
		tmp = t * (x / z);
	} else if (z <= 185000000.0) {
		tmp = t_2;
	} 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 * (t / z)
    t_2 = t * -x
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= (-5.6d-277)) then
        tmp = t_2
    else if (z <= 7.2d-194) then
        tmp = t * (x / z)
    else if (z <= 185000000.0d0) then
        tmp = t_2
    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 * (t / z);
	double t_2 = t * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -5.6e-277) {
		tmp = t_2;
	} else if (z <= 7.2e-194) {
		tmp = t * (x / z);
	} else if (z <= 185000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = t * -x
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= -5.6e-277:
		tmp = t_2
	elif z <= 7.2e-194:
		tmp = t * (x / z)
	elif z <= 185000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(t * Float64(-x))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -5.6e-277)
		tmp = t_2;
	elseif (z <= 7.2e-194)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 185000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = t * -x;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -5.6e-277)
		tmp = t_2;
	elseif (z <= 7.2e-194)
		tmp = t * (x / z);
	elseif (z <= 185000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, -5.6e-277], t$95$2, If[LessEqual[z, 7.2e-194], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 185000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.85e8 < z

   1. Initial program 97.7%

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

      1. clear-num 97.4%

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

      2. associate-/r/ 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 96.5%

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

      2. sub-neg 96.5%

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

      3. neg-mul-1 96.5%

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

      4. remove-double-neg 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in y around 0 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/l* 63.7%

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

   10. Simplified 63.7%

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

   if -1 < z < -5.59999999999999953e-277 or 7.2e-194 < z < 1.85e8

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in y around 0 33.6%

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

      1. neg-mul-1 33.6%

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

   6. Simplified 33.6%

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

   if -5.59999999999999953e-277 < z < 7.2e-194

   1. Initial program 82.9%

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

      1. clear-num 82.9%

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

      2. associate-/r/ 82.9%

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

   4. Applied egg-rr 82.9%

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

   5. Taylor expanded in z around inf 58.5%

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

      1. associate-/l* 51.4%

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

      2. sub-neg 51.4%

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

      3. neg-mul-1 51.4%

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

      4. remove-double-neg 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in y around 0 11.0%

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

      1. associate-/l* 20.9%

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

   10. Simplified 20.9%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-277}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 185000000:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

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

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 {
		tmp = t_1 * x;
	}
	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 {
		tmp = t_1 * x;
	}
	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)
	else:
		tmp = t_1 * x
	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));
	else
		tmp = Float64(t_1 * x);
	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);
	else
		tmp = t_1 * x;
	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], N[(t$95$1 * x), $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 71.7%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-neg-frac2 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. neg-sub0 99.9%

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

      5. associate--r- 99.9%

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

      6. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 99.9%

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

   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 97.3%

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

Alternative 5: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \frac{y - z \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05)
   (* x (* (+ y t) (/ 1.0 z)))
   (if (<= z 0.22) (* x (/ (- y (* z t)) z)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 0.22) {
		tmp = x * ((y - (z * t)) / z);
	} else {
		tmp = x * ((y + 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 (z <= (-1.05d0)) then
        tmp = x * ((y + t) * (1.0d0 / z))
    else if (z <= 0.22d0) then
        tmp = x * ((y - (z * t)) / z)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 0.22) {
		tmp = x * ((y - (z * t)) / z);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05:
		tmp = x * ((y + t) * (1.0 / z))
	elif z <= 0.22:
		tmp = x * ((y - (z * t)) / z)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(x * Float64(Float64(y + t) * Float64(1.0 / z)));
	elseif (z <= 0.22)
		tmp = Float64(x * Float64(Float64(y - Float64(z * t)) / z));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = x * ((y + t) * (1.0 / z));
	elseif (z <= 0.22)
		tmp = x * ((y - (z * t)) / z);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05], N[(x * N[(N[(y + t), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.22], N[(x * N[(N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 88.5%

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

      1. associate-/l* 95.7%

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

      2. sub-neg 95.7%

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

      3. neg-mul-1 95.7%

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

      4. remove-double-neg 95.7%

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

   7. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.8%

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

   9. Applied egg-rr 95.8%

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

   if -1.05000000000000004 < z < 0.220000000000000001

   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 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   5. Simplified 92.7%

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

   if 0.220000000000000001 < 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 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.4%

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

      13. distribute-rgt-neg-in 97.4%

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

      14. distribute-neg-frac 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \frac{y - z \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \frac{y - z \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (+ (/ y z) (* t (/ 1.0 z))))
   (if (<= z 0.22) (* x (/ (- y (* z t)) z)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y / z) + (t * (1.0 / z)));
	} else if (z <= 0.22) {
		tmp = x * ((y - (z * t)) / z);
	} else {
		tmp = x * ((y + 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 (z <= (-1.0d0)) then
        tmp = x * ((y / z) + (t * (1.0d0 / z)))
    else if (z <= 0.22d0) then
        tmp = x * ((y - (z * t)) / z)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y / z) + (t * (1.0 / z)));
	} else if (z <= 0.22) {
		tmp = x * ((y - (z * t)) / z);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * ((y / z) + (t * (1.0 / z)))
	elif z <= 0.22:
		tmp = x * ((y - (z * t)) / z)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t * Float64(1.0 / z))));
	elseif (z <= 0.22)
		tmp = Float64(x * Float64(Float64(y - Float64(z * t)) / z));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * ((y / z) + (t * (1.0 / z)));
	elseif (z <= 0.22)
		tmp = x * ((y - (z * t)) / z);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.22], N[(x * N[(N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 95.8%

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

   if -1 < z < 0.220000000000000001

   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 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. unsub-neg 92.7%

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

   5. Simplified 92.7%

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

   if 0.220000000000000001 < 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 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.4%

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

      13. distribute-rgt-neg-in 97.4%

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

      14. distribute-neg-frac 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + t \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \frac{y - z \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.22\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.22)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.22)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - 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 <= (-1.0d0)) .or. (.not. (z <= 0.22d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.22)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.22):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.22))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.22)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.22]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.220000000000000001 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. *-commutative 87.6%

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

      2. remove-double-neg 87.6%

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

      3. cancel-sign-sub-inv 87.6%

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

      4. metadata-eval 87.6%

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

      5. *-lft-identity 87.6%

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

      6. distribute-neg-out 87.6%

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

      7. neg-mul-1 87.6%

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

      8. sub-neg 87.6%

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

      9. distribute-lft-neg-in 87.6%

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

      10. *-commutative 87.6%

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

      11. distribute-neg-frac 87.6%

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

      12. associate-/l* 96.5%

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

      13. distribute-rgt-neg-in 96.5%

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

      14. distribute-neg-frac 96.5%

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

   5. Simplified 96.5%

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

   if -1 < z < 0.220000000000000001

   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 0 92.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.22\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.88)
   (/ x (/ z (+ y t)))
   (if (<= z 0.22) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.88) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.22) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + 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 (z <= (-0.88d0)) then
        tmp = x / (z / (y + t))
    else if (z <= 0.22d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.88) {
		tmp = x / (z / (y + t));
	} else if (z <= 0.22) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.88:
		tmp = x / (z / (y + t))
	elif z <= 0.22:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.88)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	elseif (z <= 0.22)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.88)
		tmp = x / (z / (y + t));
	elseif (z <= 0.22)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.88], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.22], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.880000000000000004

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 88.5%

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

      1. associate-/l* 95.7%

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

      2. sub-neg 95.7%

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

      3. neg-mul-1 95.7%

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

      4. remove-double-neg 95.7%

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

   7. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. un-div-inv 95.7%

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

   9. Applied egg-rr 95.7%

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

   if -0.880000000000000004 < z < 0.220000000000000001

   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 0 92.7%

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

   if 0.220000000000000001 < 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 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.4%

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

      13. distribute-rgt-neg-in 97.4%

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

      14. distribute-neg-frac 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0)
   (* x (* (+ y t) (/ 1.0 z)))
   (if (<= z 0.22) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 0.22) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + 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 (z <= (-1.0d0)) then
        tmp = x * ((y + t) * (1.0d0 / z))
    else if (z <= 0.22d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * ((y + t) * (1.0 / z));
	} else if (z <= 0.22) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * ((y + t) * (1.0 / z))
	elif z <= 0.22:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * Float64(Float64(y + t) * Float64(1.0 / z)));
	elseif (z <= 0.22)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * ((y + t) * (1.0 / z));
	elseif (z <= 0.22)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * N[(N[(y + t), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.22], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 98.1%

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

      1. clear-num 98.1%

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

      2. associate-/r/ 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 88.5%

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

      1. associate-/l* 95.7%

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

      2. sub-neg 95.7%

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

      3. neg-mul-1 95.7%

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

      4. remove-double-neg 95.7%

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

   7. Simplified 95.7%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.8%

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

   9. Applied egg-rr 95.8%

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

   if -1 < z < 0.220000000000000001

   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 0 92.7%

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

   if 0.220000000000000001 < 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 86.7%

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

      1. *-commutative 86.7%

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

      2. remove-double-neg 86.7%

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

      3. cancel-sign-sub-inv 86.7%

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

      4. metadata-eval 86.7%

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

      5. *-lft-identity 86.7%

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

      6. distribute-neg-out 86.7%

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

      7. neg-mul-1 86.7%

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

      8. sub-neg 86.7%

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

      9. distribute-lft-neg-in 86.7%

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

      10. *-commutative 86.7%

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

      11. distribute-neg-frac 86.7%

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

      12. associate-/l* 97.4%

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

      13. distribute-rgt-neg-in 97.4%

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

      14. distribute-neg-frac 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \left(\left(y + t\right) \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 0.22:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+86} \lor \neg \left(t \leq 4.8 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.05e+86) (not (<= t 4.8e+99))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.05e+86) || !(t <= 4.8e+99)) {
		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 <= (-2.05d+86)) .or. (.not. (t <= 4.8d+99))) 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 <= -2.05e+86) || !(t <= 4.8e+99)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.05e+86) or not (t <= 4.8e+99):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.05e+86) || !(t <= 4.8e+99))
		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 <= -2.05e+86) || ~((t <= 4.8e+99)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.05e+86], N[Not[LessEqual[t, 4.8e+99]], $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 < -2.05e86 or 4.8000000000000002e99 < t

   1. Initial program 94.1%

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

      1. clear-num 94.0%

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

      2. associate-/r/ 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in z around inf 56.2%

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

      1. associate-/l* 65.8%

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

      2. sub-neg 65.8%

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

      3. neg-mul-1 65.8%

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

      4. remove-double-neg 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in y around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. associate-/l* 58.6%

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

   10. Simplified 58.6%

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

   if -2.05e86 < t < 4.8000000000000002e99

   1. Initial program 96.5%

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

   3. Taylor expanded in y around inf 81.7%

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

      1. associate-*r/ 85.2%

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

   5. Simplified 85.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+86} \lor \neg \left(t \leq 4.8 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+86} \lor \neg \left(t \leq 4.7 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.2e+86) (not (<= t 4.7e+99))) (* x (/ t z)) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+86) || !(t <= 4.7e+99)) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	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 <= (-1.2d+86)) .or. (.not. (t <= 4.7d+99))) then
        tmp = x * (t / z)
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+86) || !(t <= 4.7e+99)) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.2e+86) or not (t <= 4.7e+99):
		tmp = x * (t / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.2e+86) || !(t <= 4.7e+99))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.2e+86) || ~((t <= 4.7e+99)))
		tmp = x * (t / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.2e+86], N[Not[LessEqual[t, 4.7e+99]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e86 or 4.69999999999999982e99 < t

   1. Initial program 94.1%

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

      1. clear-num 94.0%

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

      2. associate-/r/ 94.1%

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

   4. Applied egg-rr 94.1%

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

   5. Taylor expanded in z around inf 56.2%

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

      1. associate-/l* 65.8%

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

      2. sub-neg 65.8%

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

      3. neg-mul-1 65.8%

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

      4. remove-double-neg 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in y around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. associate-/l* 58.6%

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

   10. Simplified 58.6%

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

   if -1.2e86 < t < 4.69999999999999982e99

   1. Initial program 96.5%

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

      1. clear-num 96.3%

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

      2. associate-/r/ 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 79.9%

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

      2. sub-neg 79.9%

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

      3. neg-mul-1 79.9%

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

      4. remove-double-neg 79.9%

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

   7. Simplified 79.9%

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

      1. clear-num 79.6%

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

      2. un-div-inv 79.9%

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

   9. Applied egg-rr 79.9%

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

   10. Taylor expanded in y around inf 85.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+86} \lor \neg \left(t \leq 4.7 \cdot 10^{+99}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e+86)
   (* t (/ x (+ z -1.0)))
   (if (<= t 1.65e+100) (/ x (/ z y)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e+86) {
		tmp = t * (x / (z + -1.0));
	} else if (t <= 1.65e+100) {
		tmp = x / (z / y);
	} 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 (t <= (-1.6d+86)) then
        tmp = t * (x / (z + (-1.0d0)))
    else if (t <= 1.65d+100) then
        tmp = x / (z / y)
    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 (t <= -1.6e+86) {
		tmp = t * (x / (z + -1.0));
	} else if (t <= 1.65e+100) {
		tmp = x / (z / y);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e+86:
		tmp = t * (x / (z + -1.0))
	elif t <= 1.65e+100:
		tmp = x / (z / y)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e+86)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	elseif (t <= 1.65e+100)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e+86)
		tmp = t * (x / (z + -1.0));
	elseif (t <= 1.65e+100)
		tmp = x / (z / y);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e+86], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.65e+100], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e86

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-/l* 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. distribute-neg-frac2 71.2%

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

      5. neg-sub0 71.2%

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

      6. associate--r- 71.2%

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

      7. metadata-eval 71.2%

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

   5. Simplified 71.2%

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

   if -1.6e86 < t < 1.6500000000000001e100

   1. Initial program 96.5%

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

      1. clear-num 96.3%

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

      2. associate-/r/ 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around inf 82.1%

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

      1. associate-/l* 79.9%

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

      2. sub-neg 79.9%

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

      3. neg-mul-1 79.9%

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

      4. remove-double-neg 79.9%

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

   7. Simplified 79.9%

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

      1. clear-num 79.6%

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

      2. un-div-inv 79.9%

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

   9. Applied egg-rr 79.9%

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

   10. Taylor expanded in y around inf 85.3%

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

   if 1.6500000000000001e100 < t

   1. Initial program 95.5%

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

      1. clear-num 95.5%

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

      2. associate-/r/ 95.5%

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

   4. Applied egg-rr 95.5%

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

   5. Taylor expanded in z around inf 60.8%

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

      1. associate-/l* 69.0%

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

      2. sub-neg 69.0%

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

      3. neg-mul-1 69.0%

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

      4. remove-double-neg 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

      2. associate-/l* 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 22.6% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

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 = t * -x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in z around 0 64.2%

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

4. Taylor expanded in y around 0 19.7%

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

   1. neg-mul-1 19.7%

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

6. Simplified 19.7%

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

7. Final simplification 19.7%

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

Developer target: 94.9% 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 2024078 
(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)))))