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

Percentage Accurate: 94.3% → 98.6%

Time: 10.8s

Alternatives: 13

Speedup: 0.3×

• 20.5% 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: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

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+304) (* t_1 x) (* y (/ x 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+304) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / 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+304) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / 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+304:
		tmp = t_1 * x
	else:
		tmp = y * (x / 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(Float64(y * x) / z);
	elseif (t_1 <= 5e+304)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / 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+304)
		tmp = t_1 * x;
	else
		tmp = y * (x / 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[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5e+304], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $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 58.9%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 4.9999999999999997e304

   1. Initial program 98.9%

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

   if 4.9999999999999997e304 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 46.8%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. associate-*r/ 46.8%

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

   5. Simplified 46.8%

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

      1. clear-num 46.8%

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

      2. un-div-inv 52.5%

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

   7. Applied egg-rr 52.5%

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

      1. associate-/r/ 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= y -1.15e-122)
     (* y (/ x z))
     (if (<= y -4.2e-197)
       t_1
       (if (<= y 2.7e-139)
         (* t (/ x (+ z -1.0)))
         (if (<= y 4.8e-18) t_1 (/ (* y x) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (y <= -1.15e-122) {
		tmp = y * (x / z);
	} else if (y <= -4.2e-197) {
		tmp = t_1;
	} else if (y <= 2.7e-139) {
		tmp = t * (x / (z + -1.0));
	} else if (y <= 4.8e-18) {
		tmp = t_1;
	} else {
		tmp = (y * x) / 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 (y <= (-1.15d-122)) then
        tmp = y * (x / z)
    else if (y <= (-4.2d-197)) then
        tmp = t_1
    else if (y <= 2.7d-139) then
        tmp = t * (x / (z + (-1.0d0)))
    else if (y <= 4.8d-18) then
        tmp = t_1
    else
        tmp = (y * x) / 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 (y <= -1.15e-122) {
		tmp = y * (x / z);
	} else if (y <= -4.2e-197) {
		tmp = t_1;
	} else if (y <= 2.7e-139) {
		tmp = t * (x / (z + -1.0));
	} else if (y <= 4.8e-18) {
		tmp = t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if y <= -1.15e-122:
		tmp = y * (x / z)
	elif y <= -4.2e-197:
		tmp = t_1
	elif y <= 2.7e-139:
		tmp = t * (x / (z + -1.0))
	elif y <= 4.8e-18:
		tmp = t_1
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (y <= -1.15e-122)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= -4.2e-197)
		tmp = t_1;
	elseif (y <= 2.7e-139)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	elseif (y <= 4.8e-18)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (y <= -1.15e-122)
		tmp = y * (x / z);
	elseif (y <= -4.2e-197)
		tmp = t_1;
	elseif (y <= 2.7e-139)
		tmp = t * (x / (z + -1.0));
	elseif (y <= 4.8e-18)
		tmp = t_1;
	else
		tmp = (y * x) / 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[y, -1.15e-122], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-197], t$95$1, If[LessEqual[y, 2.7e-139], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-18], t$95$1, N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.15000000000000003e-122

   1. Initial program 90.1%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. associate-*r/ 68.8%

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

   5. Simplified 68.8%

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

      1. clear-num 68.6%

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

      2. un-div-inv 69.5%

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

   7. Applied egg-rr 69.5%

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

      1. associate-/r/ 75.4%

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

   9. Simplified 75.4%

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

   if -1.15000000000000003e-122 < y < -4.2e-197 or 2.6999999999999998e-139 < y < 4.79999999999999988e-18

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0 80.8%

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

   if -4.2e-197 < y < 2.6999999999999998e-139

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. associate-/l* 81.7%

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

      3. distribute-rgt-neg-in 81.7%

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

      4. distribute-neg-frac2 81.7%

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

      5. neg-sub0 81.7%

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

      6. associate--r- 81.7%

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

      7. metadata-eval 81.7%

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

   5. Simplified 81.7%

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

   if 4.79999999999999988e-18 < y

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 82.2%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e+14) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e+14) || !(z <= 1.0)) {
		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 <= (-2.8d+14)) .or. (.not. (z <= 1.0d0))) 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 <= -2.8e+14) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e+14) or not (z <= 1.0):
		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 <= -2.8e+14) || !(z <= 1.0))
		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 <= -2.8e+14) || ~((z <= 1.0)))
		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, -2.8e+14], N[Not[LessEqual[z, 1.0]], $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 < -2.8e14 or 1 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 98.1%

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

      2. sub-neg 98.1%

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

      3. neg-mul-1 98.1%

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

      4. remove-double-neg 98.1%

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

      5. neg-mul-1 98.1%

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

      6. neg-mul-1 98.1%

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

      7. distribute-lft-in 98.1%

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

      8. neg-mul-1 98.1%

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

      9. sub-neg 98.1%

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

      10. *-commutative 98.1%

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

      11. associate-*l/ 98.1%

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

      12. *-commutative 98.1%

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

      13. associate-*r/ 98.1%

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

   5. Simplified 98.1%

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

   if -2.8e14 < z < 1

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 87.7%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+81} \lor \neg \left(t \leq 3.8 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.75e+81) (not (<= t 3.8e+54)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.75e+81) || !(t <= 3.8e+54)) {
		tmp = x * (t / (z + -1.0));
	} 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 <= (-1.75d+81)) .or. (.not. (t <= 3.8d+54))) then
        tmp = x * (t / (z + (-1.0d0)))
    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 <= -1.75e+81) || !(t <= 3.8e+54)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.75e+81) or not (t <= 3.8e+54):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.75e+81) || !(t <= 3.8e+54))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	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 <= -1.75e+81) || ~((t <= 3.8e+54)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.75e+81], N[Not[LessEqual[t, 3.8e+54]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e81 or 3.8000000000000002e54 < t

   1. Initial program 93.4%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.4%

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

   4. Applied egg-rr 93.4%

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

   5. Taylor expanded in y around 0 73.8%

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

      1. neg-mul-1 73.8%

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

      2. distribute-frac-neg2 73.8%

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

      3. sub-neg 73.8%

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

      4. distribute-neg-in 73.8%

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

      5. metadata-eval 73.8%

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

      6. remove-double-neg 73.8%

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

   7. Simplified 73.8%

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

   if -1.75e81 < t < 3.8000000000000002e54

   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 inf 83.2%

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

      1. associate-*r/ 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+81} \lor \neg \left(t \leq 3.8 \cdot 10^{+54}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+81} \lor \neg \left(t \leq 1.26 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e+81) (not (<= t 1.26e+53)))
   (* t (/ x (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e+81) || !(t <= 1.26e+53)) {
		tmp = t * (x / (z + -1.0));
	} 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 <= (-1.55d+81)) .or. (.not. (t <= 1.26d+53))) then
        tmp = t * (x / (z + (-1.0d0)))
    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 <= -1.55e+81) || !(t <= 1.26e+53)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e+81) or not (t <= 1.26e+53):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e+81) || !(t <= 1.26e+53))
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	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 <= -1.55e+81) || ~((t <= 1.26e+53)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e+81], N[Not[LessEqual[t, 1.26e+53]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55e81 or 1.25999999999999999e53 < t

   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 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. associate-/l* 64.3%

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

      3. distribute-rgt-neg-in 64.3%

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

      4. distribute-neg-frac2 64.3%

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

      5. neg-sub0 64.3%

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

      6. associate--r- 64.3%

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

      7. metadata-eval 64.3%

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

   5. Simplified 64.3%

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

   if -1.55e81 < t < 1.25999999999999999e53

   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 inf 83.2%

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

      1. associate-*r/ 83.1%

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

   5. Simplified 83.1%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.3%

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

   7. Applied egg-rr 83.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+81} \lor \neg \left(t \leq 1.26 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+14)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 1.0) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+14) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 1.0) {
		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 <= (-2.8d+14)) then
        tmp = x * ((y / z) + (t / z))
    else if (z <= 1.0d0) 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 <= -2.8e+14) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+14:
		tmp = x * ((y / z) + (t / z))
	elif z <= 1.0:
		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 <= -2.8e+14)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 1.0)
		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 <= -2.8e+14)
		tmp = x * ((y / z) + (t / z));
	elseif (z <= 1.0)
		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, -2.8e+14], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], 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 < -2.8e14

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 98.2%

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

      1. associate-*r/ 98.2%

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

      2. neg-mul-1 98.2%

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

   5. Simplified 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-frac-neg 98.2%

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

      3. remove-double-neg 98.2%

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

   7. Applied egg-rr 98.2%

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

   if -2.8e14 < z < 1

   1. Initial program 88.5%

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

   3. Taylor expanded in z around 0 87.7%

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

   if 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 85.9%

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

      1. associate-/l* 98.0%

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

      2. sub-neg 98.0%

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

      3. neg-mul-1 98.0%

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

      4. remove-double-neg 98.0%

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

      5. neg-mul-1 98.0%

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

      6. neg-mul-1 98.0%

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

      7. distribute-lft-in 98.0%

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

      8. neg-mul-1 98.0%

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

      9. sub-neg 98.0%

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

      10. *-commutative 98.0%

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

      11. associate-*l/ 98.0%

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

      12. *-commutative 98.0%

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

      13. associate-*r/ 98.0%

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

   5. Simplified 98.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+81} \lor \neg \left(t \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.75e+81) (not (<= t 1.25e+183))) (* x (/ t z)) (/ (* y x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.75e+81) || !(t <= 1.25e+183)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / 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 <= (-1.75d+81)) .or. (.not. (t <= 1.25d+183))) then
        tmp = x * (t / z)
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.75e+81) || !(t <= 1.25e+183)) {
		tmp = x * (t / z);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.75e+81) or not (t <= 1.25e+183):
		tmp = x * (t / z)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.75e+81) || !(t <= 1.25e+183))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.75e+81) || ~((t <= 1.25e+183)))
		tmp = x * (t / z);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.75e+81], N[Not[LessEqual[t, 1.25e+183]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.75e81 or 1.25000000000000002e183 < t

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. neg-mul-1 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 58.2%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   if -1.75e81 < t < 1.25000000000000002e183

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 77.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+81} \lor \neg \left(t \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+81} \lor \neg \left(t \leq 3.3 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e+81) (not (<= t 3.3e+183))) (* x (/ t z)) (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e+81) || !(t <= 3.3e+183)) {
		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 <= (-1.55d+81)) .or. (.not. (t <= 3.3d+183))) 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 <= -1.55e+81) || !(t <= 3.3e+183)) {
		tmp = x * (t / z);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e+81) or not (t <= 3.3e+183):
		tmp = x * (t / z)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e+81) || !(t <= 3.3e+183))
		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 <= -1.55e+81) || ~((t <= 3.3e+183)))
		tmp = x * (t / z);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e+81], N[Not[LessEqual[t, 3.3e+183]], $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 < -1.55e81 or 3.3000000000000001e183 < t

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. neg-mul-1 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 58.2%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   if -1.55e81 < t < 3.3000000000000001e183

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 77.8%

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

      1. associate-*r/ 76.2%

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

   5. Simplified 76.2%

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

      1. clear-num 76.1%

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

      2. un-div-inv 76.9%

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

   7. Applied egg-rr 76.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+81} \lor \neg \left(t \leq 3.3 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+81} \lor \neg \left(t \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e+81) (not (<= t 1.25e+183))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+81) || !(t <= 1.25e+183)) {
		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 <= (-1.6d+81)) .or. (.not. (t <= 1.25d+183))) 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 <= -1.6e+81) || !(t <= 1.25e+183)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e+81) or not (t <= 1.25e+183):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e+81) || !(t <= 1.25e+183))
		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 <= -1.6e+81) || ~((t <= 1.25e+183)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e+81], N[Not[LessEqual[t, 1.25e+183]], $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 < -1.6e81 or 1.25000000000000002e183 < t

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 67.0%

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

      1. associate-*r/ 67.0%

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

      2. neg-mul-1 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around 0 58.2%

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

      1. associate-*l/ 60.7%

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

      2. *-commutative 60.7%

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

   8. Simplified 60.7%

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

   if -1.6e81 < t < 1.25000000000000002e183

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 77.8%

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

      1. associate-*r/ 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+81} \lor \neg \left(t \leq 1.25 \cdot 10^{+183}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e-15) (not (<= z 1.0))) (* x (/ t z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-15) || !(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 <= (-5d-15)) .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 <= -5e-15) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e-15) 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 <= -5e-15) || !(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 <= -5e-15) || ~((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, -5e-15], 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 < -4.99999999999999999e-15 or 1 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 98.0%

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

      1. associate-*r/ 98.0%

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

      2. neg-mul-1 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0 54.9%

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

      1. associate-*l/ 56.4%

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

      2. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   if -4.99999999999999999e-15 < z < 1

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 87.2%

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

   4. Taylor expanded in y around 0 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   6. Simplified 31.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-15) (not (<= z 1.0))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-15) || !(z <= 1.0)) {
		tmp = t * (x / 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 <= (-7.2d-15)) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / 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 <= -7.2e-15) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-15) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-15) || !(z <= 1.0))
		tmp = Float64(t * Float64(x / 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 <= -7.2e-15) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-15], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000002e-15 or 1 < z

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 98.0%

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

      1. associate-*r/ 98.0%

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

      2. neg-mul-1 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 48.8%

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

   8. Simplified 48.8%

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

   if -7.2000000000000002e-15 < z < 1

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 0 87.2%

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

   4. Taylor expanded in y around 0 31.5%

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

      1. associate-*r* 31.5%

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

      2. neg-mul-1 31.5%

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

   6. Simplified 31.5%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+67}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+67) (* t x) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+67) {
		tmp = t * x;
	} 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 (y <= (-1.12d+67)) then
        tmp = t * x
    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 (y <= -1.12e+67) {
		tmp = t * x;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+67:
		tmp = t * x
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+67)
		tmp = Float64(t * x);
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.12e+67)
		tmp = t * x;
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+67], N[(t * x), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e67

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 66.4%

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

   4. Taylor expanded in y around 0 2.5%

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

      1. associate-*r* 2.5%

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

      2. neg-mul-1 2.5%

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

   6. Simplified 2.5%

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

      1. add-sqr-sqrt 1.5%

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

      2. sqrt-unprod 5.3%

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

      3. sqr-neg 5.3%

         \[\leadsto \sqrt{\color{blue}{t \cdot t}} \cdot x \]

      4. sqrt-unprod 3.9%

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

      5. add-sqr-sqrt 13.7%

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

      6. pow1 13.7%

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

      7. *-commutative 13.7%

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

   8. Applied egg-rr 13.7%

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

      1. unpow1 13.7%

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

      2. *-commutative 13.7%

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

   10. Simplified 13.7%

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

   if -1.12e67 < y

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 63.6%

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

   4. Taylor expanded in y around 0 25.3%

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

      1. associate-*r* 25.3%

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

      2. neg-mul-1 25.3%

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

   6. Simplified 25.3%

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

4. Final simplification 23.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+67}:\\ \;\;\;\;t \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 9.7% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ t \cdot x \end{array} \]

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 * 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 93.1%

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

3. Taylor expanded in z around 0 64.0%

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

4. Taylor expanded in y around 0 22.0%

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

   1. associate-*r* 22.0%

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

   2. neg-mul-1 22.0%

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

6. Simplified 22.0%

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

   1. add-sqr-sqrt 11.8%

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

   2. sqrt-unprod 14.2%

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

   3. sqr-neg 14.2%

      \[\leadsto \sqrt{\color{blue}{t \cdot t}} \cdot x \]

   4. sqrt-unprod 4.5%

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

   5. add-sqr-sqrt 9.0%

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

   6. pow1 9.0%

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

   7. *-commutative 9.0%

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

8. Applied egg-rr 9.0%

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

   1. unpow1 9.0%

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

   2. *-commutative 9.0%

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

10. Simplified 9.0%

    \[\leadsto \color{blue}{t \cdot x} \]
11. Add Preprocessing

Developer Target 1: 94.4% 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 2024116 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

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