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

Percentage Accurate: 94.6% → 96.5%

Time: 10.4s

Alternatives: 9

Speedup: 0.5×

• 22.7% 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: 94.6% 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: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq 10^{+236}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 1e+236)
     (* t_1 x)
     (* (/ (- (* y (- 1.0 z)) (* z t)) (- 1.0 z)) (/ 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 <= 1e+236) {
		tmp = t_1 * x;
	} else {
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (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 / (z + (-1.0d0)))
    if (t_1 <= 1d+236) then
        tmp = t_1 * x
    else
        tmp = (((y * (1.0d0 - z)) - (z * t)) / (1.0d0 - z)) * (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 / (z + -1.0));
	double tmp;
	if (t_1 <= 1e+236) {
		tmp = t_1 * x;
	} else {
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= 1e+236:
		tmp = t_1 * x
	else:
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (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 <= 1e+236)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(Float64(Float64(y * Float64(1.0 - z)) - Float64(z * t)) / Float64(1.0 - z)) * 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 <= 1e+236)
		tmp = t_1 * x;
	else
		tmp = (((y * (1.0 - z)) - (z * t)) / (1.0 - z)) * (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, 1e+236], N[(t$95$1 * x), $MachinePrecision], N[(N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.00000000000000005e236

   1. Initial program 96.9%

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

   if 1.00000000000000005e236 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 82.6%

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

      1. *-commutative N/A

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

      2. frac-sub N/A

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

      3. associate-*l/ N/A

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

      4. *-commutative N/A

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

      5. times-frac N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z}\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y \cdot \left(1 - z\right) - z \cdot t\right), \left(1 - z\right)\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\left(y \cdot \left(1 - z\right)\right), \left(z \cdot t\right)\right), \left(1 - z\right)\right), \left(\frac{x}{z}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \left(1 - z\right)\right), \left(z \cdot t\right)\right), \left(1 - z\right)\right), \left(\frac{x}{z}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, z\right)\right), \left(z \cdot t\right)\right), \left(1 - z\right)\right), \left(\frac{x}{z}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, z\right)\right), \mathsf{*.f64}\left(z, t\right)\right), \left(1 - z\right)\right), \left(\frac{x}{z}\right)\right) \]

      12. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, z\right)\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(1, z\right)\right), \left(\frac{x}{z}\right)\right) \]

      13. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(1, z\right)\right), \mathsf{*.f64}\left(z, t\right)\right), \mathsf{\_.f64}\left(1, z\right)\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 100.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+236}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(1 - z\right) - z \cdot t}{1 - z} \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4400000000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+129)
   (/ x (/ z y))
   (if (<= z -6.6e+36)
     (* x (/ t z))
     (if (<= z 4400000000000.0)
       (* x (- (/ y z) t))
       (if (<= z 1.45e+149) (/ x (/ z t)) (/ (* y x) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+129) {
		tmp = x / (z / y);
	} else if (z <= -6.6e+36) {
		tmp = x * (t / z);
	} else if (z <= 4400000000000.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.45e+149) {
		tmp = x / (z / t);
	} 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 (z <= (-5.5d+129)) then
        tmp = x / (z / y)
    else if (z <= (-6.6d+36)) then
        tmp = x * (t / z)
    else if (z <= 4400000000000.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 1.45d+149) then
        tmp = x / (z / t)
    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 (z <= -5.5e+129) {
		tmp = x / (z / y);
	} else if (z <= -6.6e+36) {
		tmp = x * (t / z);
	} else if (z <= 4400000000000.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 1.45e+149) {
		tmp = x / (z / t);
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+129:
		tmp = x / (z / y)
	elif z <= -6.6e+36:
		tmp = x * (t / z)
	elif z <= 4400000000000.0:
		tmp = x * ((y / z) - t)
	elif z <= 1.45e+149:
		tmp = x / (z / t)
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+129)
		tmp = Float64(x / Float64(z / y));
	elseif (z <= -6.6e+36)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 4400000000000.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 1.45e+149)
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+129)
		tmp = x / (z / y);
	elseif (z <= -6.6e+36)
		tmp = x * (t / z);
	elseif (z <= 4400000000000.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 1.45e+149)
		tmp = x / (z / t);
	else
		tmp = (y * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+129], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e+36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4400000000000.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+149], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.49999999999999984e129

   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 inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 81.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 81.3%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      4. /-lowering-/.f64 81.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 81.4%

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

   if -5.49999999999999984e129 < z < -6.5999999999999997e36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 74.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 74.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 74.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 74.1%

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

   if -6.5999999999999997e36 < z < 4.4e12

   1. Initial program 93.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.8%

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

   if 4.4e12 < z < 1.4500000000000001e149

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 67.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 67.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 67.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 67.4%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      4. /-lowering-/.f64 67.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   10. Applied egg-rr 67.5%

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

   if 1.4500000000000001e149 < z

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      2. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 4400000000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+149}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+291}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 2e+291) (* 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 <= 2e+291) {
		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 / (z + (-1.0d0)))
    if (t_1 <= 2d+291) 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 / (z + -1.0));
	double tmp;
	if (t_1 <= 2e+291) {
		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 <= 2e+291:
		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 <= 2e+291)
		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 <= 2e+291)
		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, 2e+291], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.9999999999999999e291

   1. Initial program 97.0%

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

   if 1.9999999999999999e291 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 76.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 76.9%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. div-inv N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{y}\right) \]

      6. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), y\right) \]

   7. Applied egg-rr 100.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.05e+28) t_1 (if (<= z 8e-5) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.05e+28) {
		tmp = t_1;
	} else if (z <= 8e-5) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-1.05d+28)) then
        tmp = t_1
    else if (z <= 8d-5) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.05e+28) {
		tmp = t_1;
	} else if (z <= 8e-5) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -1.05e+28:
		tmp = t_1
	elif z <= 8e-5:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1.05e+28)
		tmp = t_1;
	elseif (z <= 8e-5)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1.05e+28)
		tmp = t_1;
	elseif (z <= 8e-5)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+28], t$95$1, If[LessEqual[z, 8e-5], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999995e28 or 8.00000000000000065e-5 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

      2. cancel-sign-sub-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-lowering-+.f64 96.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), z\right)\right) \]

   5. Simplified 96.2%

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

   if -1.04999999999999995e28 < z < 8.00000000000000065e-5

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 92.0%

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

Alternative 5: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -1.35e+122) t_1 (if (<= t 1.2e+123) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.35e+122) {
		tmp = t_1;
	} else if (t <= 1.2e+123) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z + (-1.0d0)))
    if (t <= (-1.35d+122)) then
        tmp = t_1
    else if (t <= 1.2d+123) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.35e+122) {
		tmp = t_1;
	} else if (t <= 1.2e+123) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -1.35e+122:
		tmp = t_1
	elif t <= 1.2e+123:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.35e+122)
		tmp = t_1;
	elseif (t <= 1.2e+123)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.35e+122)
		tmp = t_1;
	elseif (t <= 1.2e+123)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+122], t$95$1, If[LessEqual[t, 1.2e+123], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3499999999999999e122 or 1.19999999999999994e123 < t

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 79.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 79.7%

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

   if -1.3499999999999999e122 < t < 1.19999999999999994e123

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 81.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 81.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.4e+134)
   (* x (/ t z))
   (if (<= t 8e+111) (* (/ y z) x) (/ x (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+134) {
		tmp = x * (t / z);
	} else if (t <= 8e+111) {
		tmp = (y / z) * x;
	} else {
		tmp = x / (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 (t <= (-2.4d+134)) then
        tmp = x * (t / z)
    else if (t <= 8d+111) then
        tmp = (y / z) * x
    else
        tmp = x / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+134) {
		tmp = x * (t / z);
	} else if (t <= 8e+111) {
		tmp = (y / z) * x;
	} else {
		tmp = x / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.4e+134:
		tmp = x * (t / z)
	elif t <= 8e+111:
		tmp = (y / z) * x
	else:
		tmp = x / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.4e+134)
		tmp = Float64(x * Float64(t / z));
	elseif (t <= 8e+111)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.4e+134)
		tmp = x * (t / z);
	elseif (t <= 8e+111)
		tmp = (y / z) * x;
	else
		tmp = x / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.4e+134], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+111], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.40000000000000005e134

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 82.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 82.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 67.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 67.6%

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

   if -2.40000000000000005e134 < t < 7.99999999999999965e111

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 81.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 81.6%

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

   if 7.99999999999999965e111 < t

   1. Initial program 89.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 76.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 76.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 52.5%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 52.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      4. /-lowering-/.f64 52.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   10. Applied egg-rr 52.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -5.1e+135) t_1 (if (<= t 3e+97) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.1e+135) {
		tmp = t_1;
	} else if (t <= 3e+97) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-5.1d+135)) then
        tmp = t_1
    else if (t <= 3d+97) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -5.1e+135) {
		tmp = t_1;
	} else if (t <= 3e+97) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -5.1e+135:
		tmp = t_1
	elif t <= 3e+97:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -5.1e+135)
		tmp = t_1;
	elseif (t <= 3e+97)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -5.1e+135)
		tmp = t_1;
	elseif (t <= 3e+97)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e+135], t$95$1, If[LessEqual[t, 3e+97], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.09999999999999982e135 or 2.9999999999999998e97 < t

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 79.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 79.1%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 58.7%

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

   if -5.09999999999999982e135 < t < 2.9999999999999998e97

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 81.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 81.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+97}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 44.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -1.0) t_1 (if (<= z 1.0) (* t (- 0.0 x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = t * (0.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = t * (0.0d0 - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = t * (0.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = t * (0.0 - x)
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 1.0], N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 55.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 55.8%

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

   6. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 54.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   8. Simplified 54.6%

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

   if -1 < z < 1

   1. Initial program 92.8%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. *-commutative N/A

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

      5. associate-*r* N/A

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

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

      17. +-lowering-+.f64 31.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   5. Simplified 31.2%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{t \cdot x} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right) \]

      4. *-lowering-*.f64 30.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

   8. Simplified 30.3%

      \[\leadsto \color{blue}{0 - t \cdot x} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

      2. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(t \cdot x\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{neg.f64}\left(\left(x \cdot t\right)\right) \]

      4. *-lowering-*.f64 30.3%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, t\right)\right) \]

   10. Applied egg-rr 30.3%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 22.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(0 - x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 0.0 x)))

C

double code(double x, double y, double z, double t) {
	return t * (0.0 - 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 * (0.0d0 - x)
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (0.0 - x);
}

Python

def code(x, y, z, t):
	return t * (0.0 - x)

Julia

function code(x, y, z, t)
	return Float64(t * Float64(0.0 - x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (0.0 - x);
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. associate-*r* N/A

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

   4. *-commutative N/A

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

   5. associate-*r* N/A

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

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]

   7. mul-1-neg N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

   10. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

   11. mul-1-neg N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

   12. distribute-neg-in N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\left(\mathsf{neg}\left(-1 \cdot z\right)\right)}\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot z}\right)\right)\right)\right)\right) \]

   14. mul-1-neg N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

   15. remove-double-neg N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(-1 + z\right)\right)\right) \]

   16. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \color{blue}{-1}\right)\right)\right) \]

   17. +-lowering-+.f64 43.2%

       \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

5. Simplified 43.2%

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

6. Taylor expanded in z around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

   2. neg-sub0 N/A

      \[\leadsto 0 - \color{blue}{t \cdot x} \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right) \]

   4. *-lowering-*.f64 20.5%

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

8. Simplified 20.5%

   \[\leadsto \color{blue}{0 - t \cdot x} \]
9. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

   2. neg-lowering-neg.f64 N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(t \cdot x\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{neg.f64}\left(\left(x \cdot t\right)\right) \]

   4. *-lowering-*.f64 20.5%

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, t\right)\right) \]

10. Applied egg-rr 20.5%

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

11. Final simplification 20.5%

    \[\leadsto t \cdot \left(0 - x\right) \]
12. Add Preprocessing

Developer Target 1: 95.0% 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 2024191 
(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)))))