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

Percentage Accurate: 95.0% → 95.0%

Time: 8.1s

Alternatives: 13

Speedup: 1.0×

• 21.2% 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: 95.0% 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: 95.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* (- (/ y z) (/ t (- 1.0 z))) x))

C

double code(double x, double y, double z, double t) {
	return ((y / z) - (t / (1.0 - z))) * 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 = ((y / z) - (t / (1.0d0 - z))) * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((y / z) - (t / (1.0 - z))) * x;
}

Python

def code(x, y, z, t):
	return ((y / z) - (t / (1.0 - z))) * x

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))) * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((y / z) - (t / (1.0 - z))) * x;
end

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Final simplification 96.1%

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

Alternative 2: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{z} \cdot x\\ \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - \mathsf{fma}\left(\mathsf{fma}\left(t, z, t\right), z, t\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) z) x)))
   (if (<= z -17000000.0)
     t_1
     (if (<= z 1.0) (* (- (/ y z) (fma (fma t z t) z t)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) / z) * x;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y / z) - fma(fma(t, z, t), z, t)) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) / z) * x)
	tmp = 0.0
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(Float64(y / z) - fma(fma(t, z, t), z, t)) * x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -17000000.0], t$95$1, If[LessEqual[z, 1.0], N[(N[(N[(y / z), $MachinePrecision] - N[(N[(t * z + t), $MachinePrecision] * z + t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e7 or 1 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

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

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -1.7e7 < z < 1

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 93.2

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

   5. Applied rewrites 93.2%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - \mathsf{fma}\left(\mathsf{fma}\left(t, z, t\right), z, t\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{elif}\;y \leq 3.95 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (+ t y) x) z)))
   (if (<= y -3.1e-114)
     t_1
     (if (<= y 1.8e-156)
       (* (/ x (- z 1.0)) t)
       (if (<= y 3.95e+182) t_1 (* (/ x z) y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) * x) / z;
	double tmp;
	if (y <= -3.1e-114) {
		tmp = t_1;
	} else if (y <= 1.8e-156) {
		tmp = (x / (z - 1.0)) * t;
	} else if (y <= 3.95e+182) {
		tmp = t_1;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t + y) * x) / z
    if (y <= (-3.1d-114)) then
        tmp = t_1
    else if (y <= 1.8d-156) then
        tmp = (x / (z - 1.0d0)) * t
    else if (y <= 3.95d+182) then
        tmp = t_1
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) * x) / z;
	double tmp;
	if (y <= -3.1e-114) {
		tmp = t_1;
	} else if (y <= 1.8e-156) {
		tmp = (x / (z - 1.0)) * t;
	} else if (y <= 3.95e+182) {
		tmp = t_1;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) * x) / z
	tmp = 0
	if y <= -3.1e-114:
		tmp = t_1
	elif y <= 1.8e-156:
		tmp = (x / (z - 1.0)) * t
	elif y <= 3.95e+182:
		tmp = t_1
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) * x) / z)
	tmp = 0.0
	if (y <= -3.1e-114)
		tmp = t_1;
	elseif (y <= 1.8e-156)
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	elseif (y <= 3.95e+182)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) * x) / z;
	tmp = 0.0;
	if (y <= -3.1e-114)
		tmp = t_1;
	elseif (y <= 1.8e-156)
		tmp = (x / (z - 1.0)) * t;
	elseif (y <= 3.95e+182)
		tmp = t_1;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -3.1e-114], t$95$1, If[LessEqual[y, 1.8e-156], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3.95e+182], t$95$1, N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e-114 or 1.79999999999999999e-156 < y < 3.9500000000000001e182

   1. Initial program 95.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 70.7

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

   4. Applied rewrites 70.7%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 81.8

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

   7. Applied rewrites 81.8%

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

   if -3.1e-114 < y < 1.79999999999999999e-156

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 86.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 81.6%

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

   if 3.9500000000000001e182 < y

   1. Initial program 87.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 71.8

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

   5. Applied rewrites 71.8%

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

   7. Applied rewrites 79.7%

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

Alternative 4: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{z} \cdot x\\ \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\left(y - t \cdot z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) z) x)))
   (if (<= z -17000000.0) t_1 (if (<= z 1.0) (/ (* (- y (* t z)) x) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) / z) * x;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y - (t * z)) * x) / 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) :: tmp
    t_1 = ((t + y) / z) * x
    if (z <= (-17000000.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = ((y - (t * z)) * x) / 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 = ((t + y) / z) * x;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y - (t * z)) * x) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) / z) * x
	tmp = 0
	if z <= -17000000.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = ((y - (t * z)) * x) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) / z) * x)
	tmp = 0.0
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(Float64(y - Float64(t * z)) * x) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) / z) * x;
	tmp = 0.0;
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = ((y - (t * z)) * x) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -17000000.0], t$95$1, If[LessEqual[z, 1.0], N[(N[(N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e7 or 1 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

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

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -1.7e7 < z < 1

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-out N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 92.8

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

   5. Applied rewrites 92.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\left(y - t \cdot z\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;\left(-t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e-36)
   (/ (* y x) z)
   (if (<= y 1.15e-278)
     (* (/ t z) x)
     (if (<= y 2.35e-172) (* (- t) x) (* (/ x z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-36) {
		tmp = (y * x) / z;
	} else if (y <= 1.15e-278) {
		tmp = (t / z) * x;
	} else if (y <= 2.35e-172) {
		tmp = -t * x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.2d-36)) then
        tmp = (y * x) / z
    else if (y <= 1.15d-278) then
        tmp = (t / z) * x
    else if (y <= 2.35d-172) then
        tmp = -t * x
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-36) {
		tmp = (y * x) / z;
	} else if (y <= 1.15e-278) {
		tmp = (t / z) * x;
	} else if (y <= 2.35e-172) {
		tmp = -t * x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e-36:
		tmp = (y * x) / z
	elif y <= 1.15e-278:
		tmp = (t / z) * x
	elif y <= 2.35e-172:
		tmp = -t * x
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e-36)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 1.15e-278)
		tmp = Float64(Float64(t / z) * x);
	elseif (y <= 2.35e-172)
		tmp = Float64(Float64(-t) * x);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.2e-36)
		tmp = (y * x) / z;
	elseif (y <= 1.15e-278)
		tmp = (t / z) * x;
	elseif (y <= 2.35e-172)
		tmp = -t * x;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.2e-36], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.15e-278], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.35e-172], N[((-t) * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.1999999999999997e-36

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 74.7%

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

   if -6.1999999999999997e-36 < y < 1.15000000000000001e-278

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. remove-double-neg N/A

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

      10. lft-mult-inverse N/A

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

      11. distribute-lft-neg-out N/A

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

      12. cancel-sub-sign N/A

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

      13. lft-mult-inverse N/A

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

      14. lower--.f64 79.8

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

   5. Applied rewrites 79.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 59.5%

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

   if 1.15000000000000001e-278 < y < 2.34999999999999988e-172

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-out N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

   if 2.34999999999999988e-172 < y

   1. Initial program 93.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 73.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-278}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;\left(-t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;\left(-t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e-36)
   (/ (* y x) z)
   (if (<= y 3.3e-279)
     (* (/ x z) t)
     (if (<= y 2.35e-172) (* (- t) x) (* (/ x z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-36) {
		tmp = (y * x) / z;
	} else if (y <= 3.3e-279) {
		tmp = (x / z) * t;
	} else if (y <= 2.35e-172) {
		tmp = -t * x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.2d-36)) then
        tmp = (y * x) / z
    else if (y <= 3.3d-279) then
        tmp = (x / z) * t
    else if (y <= 2.35d-172) then
        tmp = -t * x
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-36) {
		tmp = (y * x) / z;
	} else if (y <= 3.3e-279) {
		tmp = (x / z) * t;
	} else if (y <= 2.35e-172) {
		tmp = -t * x;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e-36:
		tmp = (y * x) / z
	elif y <= 3.3e-279:
		tmp = (x / z) * t
	elif y <= 2.35e-172:
		tmp = -t * x
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e-36)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 3.3e-279)
		tmp = Float64(Float64(x / z) * t);
	elseif (y <= 2.35e-172)
		tmp = Float64(Float64(-t) * x);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.2e-36)
		tmp = (y * x) / z;
	elseif (y <= 3.3e-279)
		tmp = (x / z) * t;
	elseif (y <= 2.35e-172)
		tmp = -t * x;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.2e-36], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3.3e-279], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.35e-172], N[((-t) * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.1999999999999997e-36

   1. Initial program 95.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 70.8

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

   5. Applied rewrites 70.8%

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

   7. Applied rewrites 74.7%

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

   if -6.1999999999999997e-36 < y < 3.3e-279

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 76.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 56.4%

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

   if 3.3e-279 < y < 2.34999999999999988e-172

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-out N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

   if 2.34999999999999988e-172 < y

   1. Initial program 93.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 73.0%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;\left(-t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;\left(-t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) y)))
   (if (<= y -2.95e-117)
     t_1
     (if (<= y 3.3e-279)
       (* (/ x z) t)
       (if (<= y 2.35e-172) (* (- t) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * y;
	double tmp;
	if (y <= -2.95e-117) {
		tmp = t_1;
	} else if (y <= 3.3e-279) {
		tmp = (x / z) * t;
	} else if (y <= 2.35e-172) {
		tmp = -t * 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 / z) * y
    if (y <= (-2.95d-117)) then
        tmp = t_1
    else if (y <= 3.3d-279) then
        tmp = (x / z) * t
    else if (y <= 2.35d-172) then
        tmp = -t * 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 / z) * y;
	double tmp;
	if (y <= -2.95e-117) {
		tmp = t_1;
	} else if (y <= 3.3e-279) {
		tmp = (x / z) * t;
	} else if (y <= 2.35e-172) {
		tmp = -t * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * y
	tmp = 0
	if y <= -2.95e-117:
		tmp = t_1
	elif y <= 3.3e-279:
		tmp = (x / z) * t
	elif y <= 2.35e-172:
		tmp = -t * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * y)
	tmp = 0.0
	if (y <= -2.95e-117)
		tmp = t_1;
	elseif (y <= 3.3e-279)
		tmp = Float64(Float64(x / z) * t);
	elseif (y <= 2.35e-172)
		tmp = Float64(Float64(-t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * y;
	tmp = 0.0;
	if (y <= -2.95e-117)
		tmp = t_1;
	elseif (y <= 3.3e-279)
		tmp = (x / z) * t;
	elseif (y <= 2.35e-172)
		tmp = -t * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.95e-117], t$95$1, If[LessEqual[y, 3.3e-279], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.35e-172], N[((-t) * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9500000000000002e-117 or 2.34999999999999988e-172 < y

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 69.4

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

   5. Applied rewrites 69.4%

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

   7. Applied rewrites 70.8%

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

   if -2.9500000000000002e-117 < y < 3.3e-279

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 84.1%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 58.3%

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

   if 3.3e-279 < y < 2.34999999999999988e-172

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. associate-*r* N/A

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

      8. distribute-rgt-out N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 N/A

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

      13. lower-*.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.2%

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

Alternative 8: 94.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + y}{z} \cdot x\\ \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (+ t y) z) x)))
   (if (<= z -17000000.0) t_1 (if (<= z 1.0) (* (- (/ y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) / z) * x;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y / z) - t) * 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 = ((t + y) / z) * x
    if (z <= (-17000000.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = ((y / z) - t) * 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 = ((t + y) / z) * x;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y / z) - t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) / z) * x
	tmp = 0
	if z <= -17000000.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = ((y / z) - t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) / z) * x)
	tmp = 0.0
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(Float64(y / z) - t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) / z) * x;
	tmp = 0.0;
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = ((y / z) - t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -17000000.0], t$95$1, If[LessEqual[z, 1.0], N[(N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e7 or 1 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

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

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 97.1

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

   5. Applied rewrites 97.1%

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

   if -1.7e7 < z < 1

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0

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

      1. div-add N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. mul-1-neg N/A

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

      5. *-inverses N/A

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

      6. cancel-sub-sign N/A

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

      7. *-rgt-identity N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (+ t y) x) z)))
   (if (<= z -7.5e-19) t_1 (if (<= z 1.0) (* (- (/ y z) t) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((t + y) * x) / z;
	double tmp;
	if (z <= -7.5e-19) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y / z) - t) * 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 = ((t + y) * x) / z
    if (z <= (-7.5d-19)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = ((y / z) - t) * 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 = ((t + y) * x) / z;
	double tmp;
	if (z <= -7.5e-19) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = ((y / z) - t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((t + y) * x) / z
	tmp = 0
	if z <= -7.5e-19:
		tmp = t_1
	elif z <= 1.0:
		tmp = ((y / z) - t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(t + y) * x) / z)
	tmp = 0.0
	if (z <= -7.5e-19)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = Float64(Float64(Float64(y / z) - t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((t + y) * x) / z;
	tmp = 0.0;
	if (z <= -7.5e-19)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = ((y / z) - t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(t + y), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -7.5e-19], t$95$1, If[LessEqual[z, 1.0], N[(N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999957e-19 or 1 < z

   1. Initial program 98.4%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. frac-sub N/A

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

      7. associate-*l/ N/A

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

      8. lower-/.f64 N/A

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

      9. lower-*.f64 N/A

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

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

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 47.8

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

   4. Applied rewrites 47.8%

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

   5. Taylor expanded in z around -inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 87.8

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

   7. Applied rewrites 87.8%

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

   if -7.49999999999999957e-19 < z < 1

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0

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

      1. div-add N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. mul-1-neg N/A

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

      5. *-inverses N/A

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

      6. cancel-sub-sign N/A

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

      7. *-rgt-identity N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(\frac{y}{z} - t\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(t + y\right) \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.64 \cdot 10^{-23}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.64e-23)
   (/ (* y x) z)
   (if (<= y 2.1e-156) (* (/ x (- z 1.0)) t) (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.64e-23) {
		tmp = (y * x) / z;
	} else if (y <= 2.1e-156) {
		tmp = (x / (z - 1.0)) * t;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.64d-23)) then
        tmp = (y * x) / z
    else if (y <= 2.1d-156) then
        tmp = (x / (z - 1.0d0)) * t
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.64e-23) {
		tmp = (y * x) / z;
	} else if (y <= 2.1e-156) {
		tmp = (x / (z - 1.0)) * t;
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.64e-23:
		tmp = (y * x) / z
	elif y <= 2.1e-156:
		tmp = (x / (z - 1.0)) * t
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.64e-23)
		tmp = Float64(Float64(y * x) / z);
	elseif (y <= 2.1e-156)
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	else
		tmp = Float64(Float64(x / z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.64e-23)
		tmp = (y * x) / z;
	elseif (y <= 2.1e-156)
		tmp = (x / (z - 1.0)) * t;
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.64e-23], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.1e-156], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.64000000000000006e-23

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 72.9

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

   5. Applied rewrites 72.9%

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

   7. Applied rewrites 77.1%

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

   if -1.64000000000000006e-23 < y < 2.10000000000000012e-156

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 86.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 75.8%

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

   if 2.10000000000000012e-156 < y

   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 inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 70.4

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

   5. Applied rewrites 70.4%

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

   7. Applied rewrites 74.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.64 \cdot 10^{-23}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) t)))
   (if (<= t -2.4e+161) t_1 (if (<= t 1.25e+90) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double tmp;
	if (t <= -2.4e+161) {
		tmp = t_1;
	} else if (t <= 1.25e+90) {
		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 / z) * t
    if (t <= (-2.4d+161)) then
        tmp = t_1
    else if (t <= 1.25d+90) 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 / z) * t;
	double tmp;
	if (t <= -2.4e+161) {
		tmp = t_1;
	} else if (t <= 1.25e+90) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * t
	tmp = 0
	if t <= -2.4e+161:
		tmp = t_1
	elif t <= 1.25e+90:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t <= -2.4e+161)
		tmp = t_1;
	elseif (t <= 1.25e+90)
		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 / z) * t;
	tmp = 0.0;
	if (t <= -2.4e+161)
		tmp = t_1;
	elseif (t <= 1.25e+90)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.4e+161], t$95$1, If[LessEqual[t, 1.25e+90], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e161 or 1.2500000000000001e90 < t

   1. Initial program 94.5%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 74.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 49.3%

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

   if -2.3999999999999999e161 < t < 1.2500000000000001e90

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 74.3

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

   5. Applied rewrites 74.3%

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

Alternative 12: 42.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot t\\ \mathbf{if}\;z \leq -17000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 650000:\\ \;\;\;\;\left(\left(-1 - z\right) \cdot x\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) t)))
   (if (<= z -17000000.0)
     t_1
     (if (<= z 650000.0) (* (* (- -1.0 z) x) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * t;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 650000.0) {
		tmp = ((-1.0 - z) * x) * 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 / z) * t
    if (z <= (-17000000.0d0)) then
        tmp = t_1
    else if (z <= 650000.0d0) then
        tmp = (((-1.0d0) - z) * x) * 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 / z) * t;
	double tmp;
	if (z <= -17000000.0) {
		tmp = t_1;
	} else if (z <= 650000.0) {
		tmp = ((-1.0 - z) * x) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * t
	tmp = 0
	if z <= -17000000.0:
		tmp = t_1
	elif z <= 650000.0:
		tmp = ((-1.0 - z) * x) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 650000.0)
		tmp = Float64(Float64(Float64(-1.0 - z) * x) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * t;
	tmp = 0.0;
	if (z <= -17000000.0)
		tmp = t_1;
	elseif (z <= 650000.0)
		tmp = ((-1.0 - z) * x) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -17000000.0], t$95$1, If[LessEqual[z, 650000.0], N[(N[(N[(-1.0 - z), $MachinePrecision] * x), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e7 or 6.5e5 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 53.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 52.3%

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

   if -1.7e7 < z < 6.5e5

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. *-lft-identity N/A

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

      3. metadata-eval N/A

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

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

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. distribute-neg-in N/A

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

      8. +-commutative N/A

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

      9. lower-*.f64 N/A

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

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 35.3%

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

   9. Taylor expanded in z around 0

      \[\leadsto \left(-1 \cdot x + -1 \cdot \left(x \cdot z\right)\right) \cdot t \]
   10. Step-by-step derivation

   11. Applied rewrites 35.1%

       \[\leadsto \left(\left(-1 - z\right) \cdot x\right) \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 23.2% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -t * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in z around 0

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

   1. lower-/.f64 N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. *-commutative N/A

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

   6. associate-*r* N/A

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

   7. associate-*r* N/A

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

   8. distribute-rgt-out N/A

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

   9. lower-*.f64 N/A

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

   10. mul-1-neg N/A

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

   11. unsub-neg N/A

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

   12. lower--.f64 N/A

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

   13. lower-*.f64 60.9

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

5. Applied rewrites 60.9%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 22.4%

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

Developer Target 1: 95.5% 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 2024298 
(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)))))