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

Percentage Accurate: 94.9% → 96.4%

Time: 8.2s

Alternatives: 12

Speedup: 0.5×

• 20.8% 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: 94.9% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+279}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(y, 1 - z, z \cdot \left(-t\right)\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+279)
     (* t_1 x)
     (/ (* x (fma y (- 1.0 z) (* z (- t)))) (* z (- 1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+279) {
		tmp = t_1 * x;
	} else {
		tmp = (x * fma(y, (1.0 - z), (z * -t))) / (z * (1.0 - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 2e+279)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(x * fma(y, Float64(1.0 - z), Float64(z * Float64(-t)))) / Float64(z * Float64(1.0 - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+279], N[(t$95$1 * x), $MachinePrecision], N[(N[(x * N[(y * N[(1.0 - z), $MachinePrecision] + N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2.00000000000000012e279

   1. Initial program 97.1%

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

   if 2.00000000000000012e279 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

      2. frac-sub 65.4%

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

      3. associate-*l/ 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. fma-def 99.9%

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

   3. Applied egg-rr 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+279}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(y, 1 - z, z \cdot \left(-t\right)\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \]

Alternative 2: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+296}:\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 4e+296) (* t_1 x) (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 4e+296) {
		tmp = t_1 * x;
	} 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 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 4d+296) then
        tmp = t_1 * x
    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 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 4e+296) {
		tmp = t_1 * x;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 4e+296:
		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(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 4e+296)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 4e+296)
		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[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+296], N[(t$95$1 * x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 3.99999999999999993e296

   1. Initial program 97.1%

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

   if 3.99999999999999993e296 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 58.9%

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

   2. Taylor expanded in y around inf 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 4 \cdot 10^{+296}:\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 3: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+171} \lor \neg \left(t \leq 2.5 \cdot 10^{+237}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -8.5e+118)
     t_1
     (if (<= t 3.4e+65)
       (* y (/ x z))
       (if (or (<= t 5e+171) (not (<= t 2.5e+237))) t_1 (* t (- x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -8.5e+118) {
		tmp = t_1;
	} else if (t <= 3.4e+65) {
		tmp = y * (x / z);
	} else if ((t <= 5e+171) || !(t <= 2.5e+237)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-8.5d+118)) then
        tmp = t_1
    else if (t <= 3.4d+65) then
        tmp = y * (x / z)
    else if ((t <= 5d+171) .or. (.not. (t <= 2.5d+237))) then
        tmp = t_1
    else
        tmp = t * -x
    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 tmp;
	if (t <= -8.5e+118) {
		tmp = t_1;
	} else if (t <= 3.4e+65) {
		tmp = y * (x / z);
	} else if ((t <= 5e+171) || !(t <= 2.5e+237)) {
		tmp = t_1;
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -8.5e+118:
		tmp = t_1
	elif t <= 3.4e+65:
		tmp = y * (x / z)
	elif (t <= 5e+171) or not (t <= 2.5e+237):
		tmp = t_1
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -8.5e+118)
		tmp = t_1;
	elseif (t <= 3.4e+65)
		tmp = Float64(y * Float64(x / z));
	elseif ((t <= 5e+171) || !(t <= 2.5e+237))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -8.5e+118)
		tmp = t_1;
	elseif (t <= 3.4e+65)
		tmp = y * (x / z);
	elseif ((t <= 5e+171) || ~((t <= 2.5e+237)))
		tmp = t_1;
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e+118], t$95$1, If[LessEqual[t, 3.4e+65], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5e+171], N[Not[LessEqual[t, 2.5e+237]], $MachinePrecision]], t$95$1, N[(t * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000033e118 or 3.3999999999999999e65 < t < 5.0000000000000004e171 or 2.5000000000000001e237 < t

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 61.8%

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

      1. sub-neg 61.8%

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

      2. remove-double-neg 61.8%

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

      3. neg-mul-1 61.8%

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

      4. distribute-neg-in 61.8%

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

      5. neg-mul-1 61.8%

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

      6. sub-neg 61.8%

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

      7. distribute-lft-neg-in 61.8%

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

      8. distribute-neg-frac 61.8%

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

      9. associate-/l* 52.1%

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

      10. associate-/r/ 67.0%

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

      11. distribute-lft-neg-in 67.0%

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

   4. Simplified 67.0%

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

   5. Taylor expanded in y around 0 60.1%

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

   if -8.50000000000000033e118 < t < 3.3999999999999999e65

   1. Initial program 93.4%

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

      1. frac-2neg 93.4%

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

      2. div-inv 93.4%

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

      3. fma-neg 93.4%

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

      4. distribute-neg-frac 93.4%

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

   3. Applied egg-rr 93.4%

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

      1. distribute-frac-neg 93.4%

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

      2. fma-neg 93.4%

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

      3. neg-mul-1 93.4%

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

      4. associate-/r* 93.4%

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

      5. metadata-eval 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around inf 71.8%

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

      1. associate-*r/ 75.5%

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

   8. Simplified 75.5%

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

   if 5.0000000000000004e171 < t < 2.5000000000000001e237

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-/l* 90.5%

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

      3. associate-/r/ 90.3%

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

      4. distribute-rgt-neg-in 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+171} \lor \neg \left(t \leq 2.5 \cdot 10^{+237}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+172} \lor \neg \left(t \leq 7.5 \cdot 10^{+233}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -1.22e+110)
     t_1
     (if (<= t 1.75e+33)
       (* (/ y z) x)
       (if (or (<= t 4.5e+172) (not (<= t 7.5e+233))) t_1 (* t (- x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.22e+110) {
		tmp = t_1;
	} else if (t <= 1.75e+33) {
		tmp = (y / z) * x;
	} else if ((t <= 4.5e+172) || !(t <= 7.5e+233)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-1.22d+110)) then
        tmp = t_1
    else if (t <= 1.75d+33) then
        tmp = (y / z) * x
    else if ((t <= 4.5d+172) .or. (.not. (t <= 7.5d+233))) then
        tmp = t_1
    else
        tmp = t * -x
    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 tmp;
	if (t <= -1.22e+110) {
		tmp = t_1;
	} else if (t <= 1.75e+33) {
		tmp = (y / z) * x;
	} else if ((t <= 4.5e+172) || !(t <= 7.5e+233)) {
		tmp = t_1;
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -1.22e+110:
		tmp = t_1
	elif t <= 1.75e+33:
		tmp = (y / z) * x
	elif (t <= 4.5e+172) or not (t <= 7.5e+233):
		tmp = t_1
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -1.22e+110)
		tmp = t_1;
	elseif (t <= 1.75e+33)
		tmp = Float64(Float64(y / z) * x);
	elseif ((t <= 4.5e+172) || !(t <= 7.5e+233))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -1.22e+110)
		tmp = t_1;
	elseif (t <= 1.75e+33)
		tmp = (y / z) * x;
	elseif ((t <= 4.5e+172) || ~((t <= 7.5e+233)))
		tmp = t_1;
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+110], t$95$1, If[LessEqual[t, 1.75e+33], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[t, 4.5e+172], N[Not[LessEqual[t, 7.5e+233]], $MachinePrecision]], t$95$1, N[(t * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.22000000000000002e110 or 1.75000000000000005e33 < t < 4.5000000000000002e172 or 7.4999999999999997e233 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf 64.7%

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

      1. sub-neg 64.7%

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

      2. remove-double-neg 64.7%

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

      3. neg-mul-1 64.7%

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

      4. distribute-neg-in 64.7%

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

      5. neg-mul-1 64.7%

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

      6. sub-neg 64.7%

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

      7. distribute-lft-neg-in 64.7%

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

      8. distribute-neg-frac 64.7%

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

      9. associate-/l* 55.0%

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

      10. associate-/r/ 67.4%

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

      11. distribute-lft-neg-in 67.4%

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

   4. Simplified 67.4%

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

   5. Taylor expanded in y around 0 60.0%

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

   if -1.22000000000000002e110 < t < 1.75000000000000005e33

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 72.2%

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

      1. associate-*l/ 77.8%

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

   4. Simplified 77.8%

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

   if 4.5000000000000002e172 < t < 7.4999999999999997e233

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-/l* 90.5%

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

      3. associate-/r/ 90.3%

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

      4. distribute-rgt-neg-in 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+172} \lor \neg \left(t \leq 7.5 \cdot 10^{+233}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 67.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+172} \lor \neg \left(t \leq 7.5 \cdot 10^{+233}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1.8e+108)
     t_1
     (if (<= t 5.8e+25)
       (* (/ y z) x)
       (if (or (<= t 2.8e+172) (not (<= t 7.5e+233))) t_1 (* t (- x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.8e+108) {
		tmp = t_1;
	} else if (t <= 5.8e+25) {
		tmp = (y / z) * x;
	} else if ((t <= 2.8e+172) || !(t <= 7.5e+233)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-1.8d+108)) then
        tmp = t_1
    else if (t <= 5.8d+25) then
        tmp = (y / z) * x
    else if ((t <= 2.8d+172) .or. (.not. (t <= 7.5d+233))) then
        tmp = t_1
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.8e+108) {
		tmp = t_1;
	} else if (t <= 5.8e+25) {
		tmp = (y / z) * x;
	} else if ((t <= 2.8e+172) || !(t <= 7.5e+233)) {
		tmp = t_1;
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1.8e+108:
		tmp = t_1
	elif t <= 5.8e+25:
		tmp = (y / z) * x
	elif (t <= 2.8e+172) or not (t <= 7.5e+233):
		tmp = t_1
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1.8e+108)
		tmp = t_1;
	elseif (t <= 5.8e+25)
		tmp = Float64(Float64(y / z) * x);
	elseif ((t <= 2.8e+172) || !(t <= 7.5e+233))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1.8e+108)
		tmp = t_1;
	elseif (t <= 5.8e+25)
		tmp = (y / z) * x;
	elseif ((t <= 2.8e+172) || ~((t <= 7.5e+233)))
		tmp = t_1;
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+108], t$95$1, If[LessEqual[t, 5.8e+25], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[t, 2.8e+172], N[Not[LessEqual[t, 7.5e+233]], $MachinePrecision]], t$95$1, N[(t * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8e108 or 5.7999999999999998e25 < t < 2.8e172 or 7.4999999999999997e233 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in z around inf 64.7%

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

      1. *-commutative 64.7%

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

      2. associate-/l* 67.5%

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

      3. neg-mul-1 67.5%

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

   4. Simplified 67.5%

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

   5. Taylor expanded in y around 0 60.1%

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

   if -1.8e108 < t < 5.7999999999999998e25

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 72.2%

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

      1. associate-*l/ 77.8%

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

   4. Simplified 77.8%

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

   if 2.8e172 < t < 7.4999999999999997e233

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-/l* 90.5%

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

      3. associate-/r/ 90.3%

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

      4. distribute-rgt-neg-in 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+172} \lor \neg \left(t \leq 7.5 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 6: 65.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+109}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+172} \lor \neg \left(t \leq 9 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9e+109)
   (/ (* t x) z)
   (if (<= t 3.3e+25)
     (* (/ y z) x)
     (if (or (<= t 1.55e+172) (not (<= t 9e+233)))
       (/ x (/ z t))
       (* t (- x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+109) {
		tmp = (t * x) / z;
	} else if (t <= 3.3e+25) {
		tmp = (y / z) * x;
	} else if ((t <= 1.55e+172) || !(t <= 9e+233)) {
		tmp = x / (z / t);
	} 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 (t <= (-9d+109)) then
        tmp = (t * x) / z
    else if (t <= 3.3d+25) then
        tmp = (y / z) * x
    else if ((t <= 1.55d+172) .or. (.not. (t <= 9d+233))) then
        tmp = x / (z / t)
    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 (t <= -9e+109) {
		tmp = (t * x) / z;
	} else if (t <= 3.3e+25) {
		tmp = (y / z) * x;
	} else if ((t <= 1.55e+172) || !(t <= 9e+233)) {
		tmp = x / (z / t);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9e+109:
		tmp = (t * x) / z
	elif t <= 3.3e+25:
		tmp = (y / z) * x
	elif (t <= 1.55e+172) or not (t <= 9e+233):
		tmp = x / (z / t)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e+109)
		tmp = Float64(Float64(t * x) / z);
	elseif (t <= 3.3e+25)
		tmp = Float64(Float64(y / z) * x);
	elseif ((t <= 1.55e+172) || !(t <= 9e+233))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9e+109)
		tmp = (t * x) / z;
	elseif (t <= 3.3e+25)
		tmp = (y / z) * x;
	elseif ((t <= 1.55e+172) || ~((t <= 9e+233)))
		tmp = x / (z / t);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9e+109], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 3.3e+25], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[t, 1.55e+172], N[Not[LessEqual[t, 9e+233]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.9999999999999992e109

   1. Initial program 93.0%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-/l* 62.6%

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

      3. associate-/r/ 79.4%

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

      4. distribute-rgt-neg-in 79.4%

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

   4. Simplified 79.4%

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

   5. Taylor expanded in z around inf 62.1%

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

   if -8.9999999999999992e109 < t < 3.3000000000000001e25

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 72.2%

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

      1. associate-*l/ 77.8%

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

   4. Simplified 77.8%

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

   if 3.3000000000000001e25 < t < 1.54999999999999994e172 or 8.99999999999999998e233 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 59.3%

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

      1. *-commutative 59.3%

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

      2. associate-/l* 68.2%

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

      3. neg-mul-1 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in y around 0 58.5%

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

   if 1.54999999999999994e172 < t < 8.99999999999999998e233

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-/l* 90.5%

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

      3. associate-/r/ 90.3%

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

      4. distribute-rgt-neg-in 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. distribute-rgt-neg-in 77.3%

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

   7. Simplified 77.3%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+109}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+172} \lor \neg \left(t \leq 9 \cdot 10^{+233}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 7: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+211}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e+43)
   (/ x (/ z t))
   (if (<= z 1.0)
     (* x (- (/ y z) t))
     (if (<= z 4.5e+211) (* (/ y z) x) (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+43) {
		tmp = x / (z / t);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4.5e+211) {
		tmp = (y / z) * x;
	} else {
		tmp = (t * 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 (z <= (-2.6d+43)) then
        tmp = x / (z / t)
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 4.5d+211) then
        tmp = (y / z) * x
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e+43) {
		tmp = x / (z / t);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 4.5e+211) {
		tmp = (y / z) * x;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e+43:
		tmp = x / (z / t)
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	elif z <= 4.5e+211:
		tmp = (y / z) * x
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e+43)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 4.5e+211)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e+43)
		tmp = x / (z / t);
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 4.5e+211)
		tmp = (y / z) * x;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e+43], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+211], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.60000000000000021e43

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-/l* 96.3%

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

      3. neg-mul-1 96.3%

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

   4. Simplified 96.3%

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

   5. Taylor expanded in y around 0 74.7%

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

   if -2.60000000000000021e43 < z < 1

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 89.3%

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

      1. associate-*l/ 88.6%

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

      2. associate-*r* 88.6%

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

      3. neg-mul-1 88.6%

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

      4. distribute-rgt-out 89.4%

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

      5. unsub-neg 89.4%

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

   4. Simplified 89.4%

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

   if 1 < z < 4.5e211

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 57.8%

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

      1. associate-*l/ 65.7%

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

   4. Simplified 65.7%

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

   if 4.5e211 < z

   1. Initial program 92.4%

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

   2. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. associate-/l* 54.9%

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

      3. associate-/r/ 77.2%

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

      4. distribute-rgt-neg-in 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in z around inf 81.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+211}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]

Alternative 8: 94.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (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 <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(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 <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < z

   1. Initial program 97.0%

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

   2. Taylor expanded in z around inf 87.4%

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

      1. sub-neg 87.4%

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

      2. remove-double-neg 87.4%

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

      3. neg-mul-1 87.4%

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

      4. distribute-neg-in 87.4%

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

      5. neg-mul-1 87.4%

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

      6. sub-neg 87.4%

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

      7. distribute-lft-neg-in 87.4%

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

      8. distribute-neg-frac 87.4%

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

      9. associate-/l* 83.1%

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

      10. associate-/r/ 95.7%

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

      11. distribute-lft-neg-in 95.7%

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

   4. Simplified 95.7%

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

   if -1 < z < 1

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

      1. associate-*l/ 90.7%

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

      2. associate-*r* 90.7%

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

      3. neg-mul-1 90.7%

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

      4. distribute-rgt-out 91.5%

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

      5. unsub-neg 91.5%

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

   4. Simplified 91.5%

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

4. Final simplification 93.7%

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

Alternative 9: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1)
   (/ x (/ z (+ y t)))
   (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 <= -1.1) {
		tmp = x / (z / (y + t));
	} 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 <= (-1.1d0)) then
        tmp = x / (z / (y + t))
    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 <= -1.1) {
		tmp = x / (z / (y + t));
	} 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 <= -1.1:
		tmp = x / (z / (y + t))
	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 <= -1.1)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	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 <= -1.1)
		tmp = x / (z / (y + t));
	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, -1.1], N[(x / N[(z / N[(y + t), $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 < -1.1000000000000001

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 95.5%

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

      3. neg-mul-1 95.5%

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

   4. Simplified 95.5%

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

   if -1.1000000000000001 < z < 1

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 92.1%

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

      1. associate-*l/ 90.7%

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

      2. associate-*r* 90.7%

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

      3. neg-mul-1 90.7%

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

      4. distribute-rgt-out 91.5%

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

      5. unsub-neg 91.5%

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

   4. Simplified 91.5%

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

   if 1 < z

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 89.4%

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

      1. sub-neg 89.4%

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

      2. remove-double-neg 89.4%

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

      3. neg-mul-1 89.4%

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

      4. distribute-neg-in 89.4%

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

      5. neg-mul-1 89.4%

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

      6. sub-neg 89.4%

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

      7. distribute-lft-neg-in 89.4%

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

      8. distribute-neg-frac 89.4%

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

      9. associate-/l* 82.2%

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

      10. associate-/r/ 95.8%

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

      11. distribute-lft-neg-in 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 10: 41.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 8.5e+23))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 8.5e+23)) {
		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 <= 8.5d+23))) 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 <= 8.5e+23)) {
		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 <= 8.5e+23):
		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 <= 8.5e+23))
		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 <= 8.5e+23)))
		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[LessEqual[z, 8.5e+23]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 8.5000000000000001e23 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-/l* 54.0%

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

      3. associate-/r/ 64.3%

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

      4. distribute-rgt-neg-in 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. *-lft-identity 61.4%

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

      2. times-frac 54.9%

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

      3. /-rgt-identity 54.9%

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

   7. Simplified 54.9%

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

   if -1 < z < 8.5000000000000001e23

   1. Initial program 92.4%

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

   2. Taylor expanded in y around 0 41.0%

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

      1. mul-1-neg 41.0%

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

      2. associate-/l* 40.9%

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

      3. associate-/r/ 41.0%

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

      4. distribute-rgt-neg-in 41.0%

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

   4. Simplified 41.0%

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

   5. Taylor expanded in z around 0 39.6%

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

      1. mul-1-neg 39.6%

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

      2. *-commutative 39.6%

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

      3. distribute-rgt-neg-in 39.6%

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

   7. Simplified 39.6%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.5 \cdot 10^{+23}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 11: 63.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.9e+123)
   (* t (/ x z))
   (if (<= t 5e+133) (* y (/ x z)) (* t (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.9e+123) {
		tmp = t * (x / z);
	} else if (t <= 5e+133) {
		tmp = y * (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 (t <= (-2.9d+123)) then
        tmp = t * (x / z)
    else if (t <= 5d+133) then
        tmp = y * (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 (t <= -2.9e+123) {
		tmp = t * (x / z);
	} else if (t <= 5e+133) {
		tmp = y * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.9e+123:
		tmp = t * (x / z)
	elif t <= 5e+133:
		tmp = y * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.9e+123)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= 5e+133)
		tmp = Float64(y * 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 (t <= -2.9e+123)
		tmp = t * (x / z);
	elseif (t <= 5e+133)
		tmp = y * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.9e+123], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+133], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000001e123

   1. Initial program 95.0%

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

   2. Taylor expanded in y around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. associate-/l* 62.2%

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

      3. associate-/r/ 80.3%

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

      4. distribute-rgt-neg-in 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around inf 61.7%

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

      1. *-lft-identity 61.7%

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

      2. times-frac 45.6%

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

      3. /-rgt-identity 45.6%

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

   7. Simplified 45.6%

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

   if -2.9000000000000001e123 < t < 4.99999999999999961e133

   1. Initial program 93.9%

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

      1. frac-2neg 93.9%

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

      2. div-inv 93.8%

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

      3. fma-neg 93.8%

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

      4. distribute-neg-frac 93.8%

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

   3. Applied egg-rr 93.8%

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

      1. distribute-frac-neg 93.8%

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

      2. fma-neg 93.8%

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

      3. neg-mul-1 93.8%

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

      4. associate-/r* 93.8%

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

      5. metadata-eval 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around inf 69.0%

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

      1. associate-*r/ 72.9%

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

   8. Simplified 72.9%

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

   if 4.99999999999999961e133 < t

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. associate-/l* 70.8%

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

      3. associate-/r/ 81.9%

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

      4. distribute-rgt-neg-in 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in z around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-rgt-neg-in 51.5%

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

   7. Simplified 51.5%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+123}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 12: 22.8% 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 94.7%

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

2. Taylor expanded in y around 0 51.6%

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

   1. mul-1-neg 51.6%

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

   2. associate-/l* 47.6%

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

   3. associate-/r/ 52.9%

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

   4. distribute-rgt-neg-in 52.9%

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

4. Simplified 52.9%

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

5. Taylor expanded in z around 0 26.9%

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

   1. mul-1-neg 26.9%

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

   2. *-commutative 26.9%

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

   3. distribute-rgt-neg-in 26.9%

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

7. Simplified 26.9%

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

8. Final simplification 26.9%

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

Developer target: 95.3% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (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)))))