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

Percentage Accurate: 94.9% → 97.4%

Time: 8.0s

Alternatives: 13

Speedup: 0.3×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+263}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+263)))
     (* (/ x z) y)
     (* x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+263)) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+263)) {
		tmp = (x / z) * y;
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+263):
		tmp = (x / z) * y
	else:
		tmp = x * t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+263))
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(x * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+263)))
		tmp = (x / z) * y;
	else
		tmp = x * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+263]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0 or 1.00000000000000002e263 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 73.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 71.5

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

   5. Applied rewrites 71.5%

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

   7. Applied rewrites 100.0%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.00000000000000002e263

   1. Initial program 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 10^{+263}\right):\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 0.44\right):\\ \;\;\;\;\frac{x}{\frac{z}{t + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+27) (not (<= z 0.44)))
   (/ x (/ z (+ t y)))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 0.44)) {
		tmp = x / (z / (t + y));
	} else {
		tmp = (x * (y - (t * z))) / 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 <= (-9.5d+27)) .or. (.not. (z <= 0.44d0))) then
        tmp = x / (z / (t + y))
    else
        tmp = (x * (y - (t * z))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 0.44)) {
		tmp = x / (z / (t + y));
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e+27) or not (z <= 0.44):
		tmp = x / (z / (t + y))
	else:
		tmp = (x * (y - (t * z))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e+27) || !(z <= 0.44))
		tmp = Float64(x / Float64(z / Float64(t + y)));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(t * z))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e+27) || ~((z <= 0.44)))
		tmp = x / (z / (t + y));
	else
		tmp = (x * (y - (t * z))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e+27], N[Not[LessEqual[z, 0.44]], $MachinePrecision]], N[(x / N[(z / N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999997e27 or 0.440000000000000002 < z

   1. Initial program 98.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. clear-num N/A

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

      8. flip-- N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in z around inf

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 97.4

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

   7. Applied rewrites 97.4%

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

   if -9.4999999999999997e27 < z < 0.440000000000000002

   1. Initial program 91.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. distribute-lft-out-- N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 92.9

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

   5. Applied rewrites 92.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 0.44\right):\\ \;\;\;\;\frac{x}{\frac{z}{t + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 440\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+27) (not (<= z 440.0)))
   (* x (/ (+ t y) z))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 440.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / 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 <= (-9.5d+27)) .or. (.not. (z <= 440.0d0))) then
        tmp = x * ((t + y) / z)
    else
        tmp = (x * (y - (t * z))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 440.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e+27) or not (z <= 440.0):
		tmp = x * ((t + y) / z)
	else:
		tmp = (x * (y - (t * z))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e+27) || !(z <= 440.0))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(t * z))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e+27) || ~((z <= 440.0)))
		tmp = x * ((t + y) / z);
	else
		tmp = (x * (y - (t * z))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e+27], N[Not[LessEqual[z, 440.0]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999997e27 or 440 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      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 -9.4999999999999997e27 < z < 440

   1. Initial program 91.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. distribute-lft-out-- N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 93.0

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

   5. Applied rewrites 93.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 440\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.6e+77)
   (* (/ y z) x)
   (if (<= z 1.28e+44)
     (* x (- (/ y z) t))
     (if (<= z 8.5e+186) (* x (/ t z)) (/ (* x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.6e+77) {
		tmp = (y / z) * x;
	} else if (z <= 1.28e+44) {
		tmp = x * ((y / z) - t);
	} else if (z <= 8.5e+186) {
		tmp = x * (t / z);
	} else {
		tmp = (x * y) / 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 <= (-7.6d+77)) then
        tmp = (y / z) * x
    else if (z <= 1.28d+44) then
        tmp = x * ((y / z) - t)
    else if (z <= 8.5d+186) then
        tmp = x * (t / z)
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.6e+77) {
		tmp = (y / z) * x;
	} else if (z <= 1.28e+44) {
		tmp = x * ((y / z) - t);
	} else if (z <= 8.5e+186) {
		tmp = x * (t / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.6e+77:
		tmp = (y / z) * x
	elif z <= 1.28e+44:
		tmp = x * ((y / z) - t)
	elif z <= 8.5e+186:
		tmp = x * (t / z)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.6e+77)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= 1.28e+44)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 8.5e+186)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.6e+77)
		tmp = (y / z) * x;
	elseif (z <= 1.28e+44)
		tmp = x * ((y / z) - t);
	elseif (z <= 8.5e+186)
		tmp = x * (t / z);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.6e+77], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.28e+44], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+186], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.6000000000000002e77

   1. Initial program 99.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 69.3

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

   5. Applied rewrites 69.3%

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

   if -7.6000000000000002e77 < z < 1.28000000000000006e44

   1. Initial program 92.3%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 92.2

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

   4. Applied rewrites 92.2%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 88.1

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 88.1%

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

   if 1.28000000000000006e44 < z < 8.4999999999999999e186

   1. Initial program 99.5%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. frac-add N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. distribute-neg-in N/A

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

      21. metadata-eval N/A

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

      22. remove-double-neg N/A

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

      23. lower-+.f64 73.6

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

   4. Applied rewrites 73.6%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 99.5

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

   7. Applied rewrites 99.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 67.8%

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

   if 8.4999999999999999e186 < z

   1. Initial program 92.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 77.6

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

   5. Applied rewrites 77.6%

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

   7. Applied rewrites 81.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 0.44\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e+27) (not (<= z 0.44)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 0.44)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.5d+27)) .or. (.not. (z <= 0.44d0))) then
        tmp = x * ((t + y) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e+27) || !(z <= 0.44)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e+27) or not (z <= 0.44):
		tmp = x * ((t + y) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e+27) || !(z <= 0.44))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e+27) || ~((z <= 0.44)))
		tmp = x * ((t + y) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e+27], N[Not[LessEqual[z, 0.44]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999997e27 or 0.440000000000000002 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      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 -9.4999999999999997e27 < z < 0.440000000000000002

   1. Initial program 91.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 91.0

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 90.6

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

   7. Applied rewrites 90.6%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 90.6%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+27} \lor \neg \left(z \leq 0.44\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-22} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-22) (not (<= y 1.75e-78)))
   (/ (* x y) z)
   (* (/ x (- z 1.0)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-22) || !(y <= 1.75e-78)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / (z - 1.0)) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d-22)) .or. (.not. (y <= 1.75d-78))) then
        tmp = (x * y) / z
    else
        tmp = (x / (z - 1.0d0)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-22) || !(y <= 1.75e-78)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / (z - 1.0)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e-22) or not (y <= 1.75e-78):
		tmp = (x * y) / z
	else:
		tmp = (x / (z - 1.0)) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e-22) || !(y <= 1.75e-78))
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(Float64(x / Float64(z - 1.0)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e-22) || ~((y <= 1.75e-78)))
		tmp = (x * y) / z;
	else
		tmp = (x / (z - 1.0)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e-22], N[Not[LessEqual[y, 1.75e-78]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z - 1.0), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000023e-22 or 1.75e-78 < y

   1. Initial program 92.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 77.5

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

   5. Applied rewrites 77.5%

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

   7. Applied rewrites 81.4%

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

   if -3.80000000000000023e-22 < y < 1.75e-78

   1. Initial program 98.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. frac-add N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. distribute-neg-in N/A

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

      21. metadata-eval N/A

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

      22. remove-double-neg N/A

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

      23. lower-+.f64 87.1

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

   4. Applied rewrites 87.1%

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

   5. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 72.2

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

   7. Applied rewrites 72.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-22} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - 1} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-146} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-146) (not (<= y 1.75e-78)))
   (/ (* x y) z)
   (/ (* t x) (- z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-146) || !(y <= 1.75e-78)) {
		tmp = (x * y) / z;
	} else {
		tmp = (t * x) / (z - 1.0);
	}
	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 <= (-2d-146)) .or. (.not. (y <= 1.75d-78))) then
        tmp = (x * y) / z
    else
        tmp = (t * x) / (z - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-146) || !(y <= 1.75e-78)) {
		tmp = (x * y) / z;
	} else {
		tmp = (t * x) / (z - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-146) or not (y <= 1.75e-78):
		tmp = (x * y) / z
	else:
		tmp = (t * x) / (z - 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-146) || !(y <= 1.75e-78))
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(Float64(t * x) / Float64(z - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-146) || ~((y <= 1.75e-78)))
		tmp = (x * y) / z;
	else
		tmp = (t * x) / (z - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-146], N[Not[LessEqual[y, 1.75e-78]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000005e-146 or 1.75e-78 < y

   1. Initial program 93.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 73.7

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

   5. Applied rewrites 73.7%

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

   7. Applied rewrites 77.4%

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

   if -2.00000000000000005e-146 < y < 1.75e-78

   1. Initial program 98.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-146} \lor \neg \left(y \leq 1.75 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+98} \lor \neg \left(t \leq 5.8 \cdot 10^{+224}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e+98) (not (<= t 5.8e+224))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e+98) || !(t <= 5.8e+224)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.5d+98)) .or. (.not. (t <= 5.8d+224))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e+98) || !(t <= 5.8e+224)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e+98) or not (t <= 5.8e+224):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e+98) || !(t <= 5.8e+224))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.5e+98) || ~((t <= 5.8e+224)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e+98], N[Not[LessEqual[t, 5.8e+224]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5000000000000001e98 or 5.79999999999999978e224 < t

   1. Initial program 93.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. frac-add N/A

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

      7. lower-/.f64 N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. remove-double-neg N/A

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

      14. lower-+.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-*.f64 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. distribute-neg-in N/A

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

      21. metadata-eval N/A

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

      22. remove-double-neg N/A

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

      23. lower-+.f64 60.0

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

   4. Applied rewrites 60.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 61.0

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

   7. Applied rewrites 61.0%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 54.6%

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

   if -1.5000000000000001e98 < t < 5.79999999999999978e224

   1. Initial program 94.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 78.1

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

   5. Applied rewrites 78.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+98} \lor \neg \left(t \leq 5.8 \cdot 10^{+224}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-28} \lor \neg \left(z \leq 0.205\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e-28) (not (<= z 0.205)))
   (* t (/ x z))
   (* (- t) (fma x z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e-28) || !(z <= 0.205)) {
		tmp = t * (x / z);
	} else {
		tmp = -t * fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e-28) || !(z <= 0.205))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(-t) * fma(x, z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e-28], N[Not[LessEqual[z, 0.205]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(x * z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000005e-28 or 0.204999999999999988 < z

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 47.6

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

   5. Applied rewrites 47.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.8%

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

   if -1.90000000000000005e-28 < z < 0.204999999999999988

   1. Initial program 90.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 32.9

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

   5. Applied rewrites 32.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 32.9%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-28} \lor \neg \left(z \leq 0.205\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-141}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-174}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e-141)
   (/ (* x y) z)
   (if (<= y 2e-174) (* t (/ x z)) (* (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-141) {
		tmp = (x * y) / z;
	} else if (y <= 2e-174) {
		tmp = t * (x / z);
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d-141)) then
        tmp = (x * y) / z
    else if (y <= 2d-174) then
        tmp = t * (x / z)
    else
        tmp = (x / z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-141) {
		tmp = (x * y) / z;
	} else if (y <= 2e-174) {
		tmp = t * (x / z);
	} else {
		tmp = (x / z) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e-141:
		tmp = (x * y) / z
	elif y <= 2e-174:
		tmp = t * (x / z)
	else:
		tmp = (x / z) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e-141)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 2e-174)
		tmp = Float64(t * Float64(x / z));
	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 <= -1.25e-141)
		tmp = (x * y) / z;
	elseif (y <= 2e-174)
		tmp = t * (x / z);
	else
		tmp = (x / z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e-141], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2e-174], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e-141

   1. Initial program 92.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 70.2

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

   5. Applied rewrites 70.2%

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

   7. Applied rewrites 76.8%

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

   if -1.25e-141 < y < 2e-174

   1. Initial program 98.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.3%

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

   if 2e-174 < 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 74.8

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

   5. Applied rewrites 74.8%

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

   7. Applied rewrites 75.8%

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

Alternative 11: 41.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 0.205:\\ \;\;\;\;\left(-t\right) \cdot \mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e-28)
   (* t (/ x z))
   (if (<= z 0.205) (* (- t) (fma x z x)) (/ (* t x) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e-28) {
		tmp = t * (x / z);
	} else if (z <= 0.205) {
		tmp = -t * fma(x, z, x);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e-28)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 0.205)
		tmp = Float64(Float64(-t) * fma(x, z, x));
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e-28], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.205], N[((-t) * N[(x * z + x), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000005e-28

   1. Initial program 99.6%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 43.1

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

   5. Applied rewrites 43.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 47.9%

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

   if -1.90000000000000005e-28 < z < 0.204999999999999988

   1. Initial program 90.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 32.9

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

   5. Applied rewrites 32.9%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 32.9%

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

   if 0.204999999999999988 < z

   1. Initial program 97.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 49.4%

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

   10. Applied rewrites 49.4%

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

Alternative 12: 62.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+243}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.7e+243) (* (/ x z) y) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e+243) {
		tmp = (x / z) * y;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.7d+243) then
        tmp = (x / z) * y
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.7e+243) {
		tmp = (x / z) * y;
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 2.7e+243:
		tmp = (x / z) * y
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.7e+243)
		tmp = Float64(Float64(x / z) * y);
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 2.7e+243)
		tmp = (x / z) * y;
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.7e+243], N[(N[(x / z), $MachinePrecision] * y), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.7000000000000001e243

   1. Initial program 94.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 67.9

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

   5. Applied rewrites 67.9%

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

   7. Applied rewrites 69.9%

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

   if 2.7000000000000001e243 < t

   1. Initial program 99.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 73.1

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

   7. Applied rewrites 73.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 71.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+243}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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 * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 94.5

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

4. Applied rewrites 94.5%

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

5. Taylor expanded in z around 0

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

   1. lower-/.f64 N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. associate-*r* N/A

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

   5. lower-fma.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 65.9

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

7. Applied rewrites 65.9%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 23.0%

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

11. Final simplification 23.0%

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

Developer Target 1: 95.2% 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 2024324 
(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)))))