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

Percentage Accurate: 94.8% → 98.6%

Time: 13.0s

Alternatives: 15

Speedup: 0.6×

• 20.4% 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: 94.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z + -1}\\ t_2 := x \cdot \left(\frac{y}{z} + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 10^{+308}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \left(z + -1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1 + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (+ z -1.0))) (t_2 (* x (+ (/ y z) t_1))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+308)))
     (* (* x y) (+ (/ 1.0 z) (/ t (* y (+ z -1.0)))))
     (+ (* x t_1) (* x (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z + -1.0);
	double t_2 = x * ((y / z) + t_1);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+308)) {
		tmp = (x * y) * ((1.0 / z) + (t / (y * (z + -1.0))));
	} else {
		tmp = (x * t_1) + (x * (y / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z + -1.0);
	double t_2 = x * ((y / z) + t_1);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+308)) {
		tmp = (x * y) * ((1.0 / z) + (t / (y * (z + -1.0))));
	} else {
		tmp = (x * t_1) + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z + -1.0)
	t_2 = x * ((y / z) + t_1)
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+308):
		tmp = (x * y) * ((1.0 / z) + (t / (y * (z + -1.0))))
	else:
		tmp = (x * t_1) + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z + -1.0))
	t_2 = Float64(x * Float64(Float64(y / z) + t_1))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+308))
		tmp = Float64(Float64(x * y) * Float64(Float64(1.0 / z) + Float64(t / Float64(y * Float64(z + -1.0)))));
	else
		tmp = Float64(Float64(x * t_1) + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z + -1.0);
	t_2 = x * ((y / z) + t_1);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+308)))
		tmp = (x * y) * ((1.0 / z) + (t / (y * (z + -1.0))));
	else
		tmp = (x * t_1) + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 1e+308]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * N[(N[(1.0 / z), $MachinePrecision] + N[(t / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -inf.0 or 1e308 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))))

   1. Initial program 78.5%

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

   3. Taylor expanded in y around inf 92.7%

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

      1. associate-*r/ 92.7%

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

      2. associate-*r* 92.7%

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

      3. neg-mul-1 92.7%

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

      4. *-commutative 92.7%

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

      5. times-frac 92.7%

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

      6. distribute-frac-neg 92.7%

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

      7. distribute-neg-frac2 92.7%

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

      8. neg-sub0 92.7%

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

      9. associate--r- 92.7%

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

      10. metadata-eval 92.7%

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

   5. Simplified 92.7%

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

   6. Taylor expanded in x around 0 78.5%

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

      1. associate-*r* 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. remove-double-neg 99.8%

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

      7. neg-mul-1 99.8%

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

      8. lft-mult-inverse 99.8%

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

      9. distribute-rgt-neg-out 99.8%

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

      10. distribute-rgt-in 99.8%

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

      11. +-commutative 99.8%

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

      12. distribute-lft-neg-in 99.8%

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

      13. distribute-neg-frac2 99.8%

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

      14. metadata-eval 99.8%

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

      15. sub-neg 99.8%

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

      16. associate-/r* 99.8%

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

   8. Simplified 99.8%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < 1e308

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. distribute-rgt-in 97.3%

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

      3. distribute-neg-frac 97.3%

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

   4. Applied egg-rr 97.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq -\infty \lor \neg \left(x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq 10^{+308}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(\frac{1}{z} + \frac{t}{y \cdot \left(z + -1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1} + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z + -1}\\ t_2 := x \cdot \left(\frac{y}{z} + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty \lor \neg \left(t\_2 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_1 + x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (+ z -1.0))) (t_2 (* x (+ (/ y z) t_1))))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+302)))
     (/ (* x (- y (* z t))) z)
     (+ (* x t_1) (* x (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z + -1.0);
	double t_2 = x * ((y / z) + t_1);
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+302)) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = (x * t_1) + (x * (y / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z + -1.0);
	double t_2 = x * ((y / z) + t_1);
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+302)) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = (x * t_1) + (x * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z + -1.0)
	t_2 = x * ((y / z) + t_1)
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+302):
		tmp = (x * (y - (z * t))) / z
	else:
		tmp = (x * t_1) + (x * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z + -1.0))
	t_2 = Float64(x * Float64(Float64(y / z) + t_1))
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+302))
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	else
		tmp = Float64(Float64(x * t_1) + Float64(x * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z + -1.0);
	t_2 = x * ((y / z) + t_1);
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+302)))
		tmp = (x * (y - (z * t))) / z;
	else
		tmp = (x * t_1) + (x * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+302]], $MachinePrecision]], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * t$95$1), $MachinePrecision] + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -inf.0 or 5e302 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))))

   1. Initial program 78.5%

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

   3. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

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

      3. unsub-neg 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in x around 0 97.0%

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

      1. *-commutative 97.0%

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

   8. Simplified 97.0%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < 5e302

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. distribute-rgt-in 97.3%

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

      3. distribute-neg-frac 97.3%

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

   4. Applied egg-rr 97.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq -\infty \lor \neg \left(x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1} + x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (/ y z) (/ t (+ z -1.0))))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+302)))
     (/ (* x (- y (* z t))) z)
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) + (t / (z + -1.0)));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+302)) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) + (t / (z + -1.0)));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+302)) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) + (t / (z + -1.0)))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+302):
		tmp = (x * (y - (z * t))) / 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(z + -1.0))))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+302))
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) + (t / (z + -1.0)));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+302)))
		tmp = (x * (y - (z * t))) / 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[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+302]], $MachinePrecision]], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < -inf.0 or 5e302 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))))

   1. Initial program 78.5%

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

   3. Taylor expanded in z around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

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

      3. unsub-neg 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in x around 0 97.0%

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

      1. *-commutative 97.0%

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

   8. Simplified 97.0%

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

   if -inf.0 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))) < 5e302

   1. Initial program 97.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq -\infty \lor \neg \left(x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right) \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z + -1}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-286}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))))
   (if (<= z -320000000.0)
     (* x (/ (+ y t) z))
     (if (<= z -8.4e-286)
       t_1
       (if (<= z 6e-191)
         (/ (* x y) z)
         (if (<= z 1.0) t_1 (* x (+ (/ y z) (/ t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -320000000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= -8.4e-286) {
		tmp = t_1;
	} else if (z <= 6e-191) {
		tmp = (x * y) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - t)
    if (z <= (-320000000.0d0)) then
        tmp = x * ((y + t) / z)
    else if (z <= (-8.4d-286)) then
        tmp = t_1
    else if (z <= 6d-191) then
        tmp = (x * y) / z
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = x * ((y / z) + (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double tmp;
	if (z <= -320000000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= -8.4e-286) {
		tmp = t_1;
	} else if (z <= 6e-191) {
		tmp = (x * y) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	tmp = 0
	if z <= -320000000.0:
		tmp = x * ((y + t) / z)
	elif z <= -8.4e-286:
		tmp = t_1
	elif z <= 6e-191:
		tmp = (x * y) / z
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = x * ((y / z) + (t / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	tmp = 0.0
	if (z <= -320000000.0)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= -8.4e-286)
		tmp = t_1;
	elseif (z <= 6e-191)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	tmp = 0.0;
	if (z <= -320000000.0)
		tmp = x * ((y + t) / z);
	elseif (z <= -8.4e-286)
		tmp = t_1;
	elseif (z <= 6e-191)
		tmp = (x * y) / z;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = x * ((y / z) + (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -320000000.0], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.4e-286], t$95$1, If[LessEqual[z, 6e-191], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2e8

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. associate-/l* 95.9%

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

      2. neg-mul-1 95.9%

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

      3. sub-neg 95.9%

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

      4. remove-double-neg 95.9%

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

      5. neg-mul-1 95.9%

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

      6. neg-mul-1 95.9%

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

      7. distribute-lft-in 95.9%

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

      8. neg-mul-1 95.9%

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

      9. sub-neg 95.9%

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

      10. *-commutative 95.9%

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

      11. associate-*l/ 95.9%

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

      12. *-commutative 95.9%

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

      13. associate-*r/ 95.9%

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

      14. sub-neg 95.9%

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

      15. neg-mul-1 95.9%

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

      16. distribute-lft-in 95.9%

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

      17. neg-mul-1 95.9%

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

      18. remove-double-neg 95.9%

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

      19. neg-mul-1 95.9%

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

      20. remove-double-neg 95.9%

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

      21. +-commutative 95.9%

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

   5. Simplified 95.9%

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

   if -3.2e8 < z < -8.39999999999999954e-286 or 6.0000000000000001e-191 < z < 1

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 91.6%

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

   if -8.39999999999999954e-286 < z < 6.0000000000000001e-191

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 93.6%

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

   if 1 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 96.1%

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

      1. associate-*r/ 96.1%

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

      2. neg-mul-1 96.1%

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

   5. Simplified 96.1%

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

      1. sub-neg 96.1%

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

      2. add-sqr-sqrt 48.1%

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

      3. sqrt-unprod 58.7%

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

      4. sqr-neg 58.7%

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

      5. sqrt-unprod 24.4%

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

      6. add-sqr-sqrt 51.0%

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

      7. distribute-frac-neg 51.0%

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

      8. add-sqr-sqrt 26.6%

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

      9. sqrt-unprod 53.3%

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

      10. sqr-neg 53.3%

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

      11. sqrt-unprod 47.8%

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

      12. add-sqr-sqrt 96.1%

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

   7. Applied egg-rr 96.1%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t\right)\\ t_2 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-285}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) t))) (t_2 (* x (/ (+ y t) z))))
   (if (<= z -320000000.0)
     t_2
     (if (<= z -7.5e-285)
       t_1
       (if (<= z 8.7e-191) (/ (* x y) z) (if (<= z 1.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -320000000.0) {
		tmp = t_2;
	} else if (z <= -7.5e-285) {
		tmp = t_1;
	} else if (z <= 8.7e-191) {
		tmp = (x * y) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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)
    t_2 = x * ((y + t) / z)
    if (z <= (-320000000.0d0)) then
        tmp = t_2
    else if (z <= (-7.5d-285)) then
        tmp = t_1
    else if (z <= 8.7d-191) then
        tmp = (x * y) / z
    else if (z <= 1.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - t);
	double t_2 = x * ((y + t) / z);
	double tmp;
	if (z <= -320000000.0) {
		tmp = t_2;
	} else if (z <= -7.5e-285) {
		tmp = t_1;
	} else if (z <= 8.7e-191) {
		tmp = (x * y) / z;
	} else if (z <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - t)
	t_2 = x * ((y + t) / z)
	tmp = 0
	if z <= -320000000.0:
		tmp = t_2
	elif z <= -7.5e-285:
		tmp = t_1
	elif z <= 8.7e-191:
		tmp = (x * y) / z
	elif z <= 1.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - t))
	t_2 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -320000000.0)
		tmp = t_2;
	elseif (z <= -7.5e-285)
		tmp = t_1;
	elseif (z <= 8.7e-191)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - t);
	t_2 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -320000000.0)
		tmp = t_2;
	elseif (z <= -7.5e-285)
		tmp = t_1;
	elseif (z <= 8.7e-191)
		tmp = (x * y) / z;
	elseif (z <= 1.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -320000000.0], t$95$2, If[LessEqual[z, -7.5e-285], t$95$1, If[LessEqual[z, 8.7e-191], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e8 or 1 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 90.2%

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

      1. associate-/l* 96.0%

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

      2. neg-mul-1 96.0%

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

      3. sub-neg 96.0%

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

      4. remove-double-neg 96.0%

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

      5. neg-mul-1 96.0%

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

      6. neg-mul-1 96.0%

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

      7. distribute-lft-in 96.0%

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

      8. neg-mul-1 96.0%

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

      9. sub-neg 96.0%

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

      10. *-commutative 96.0%

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

      11. associate-*l/ 96.0%

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

      12. *-commutative 96.0%

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

      13. associate-*r/ 96.0%

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

      14. sub-neg 96.0%

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

      15. neg-mul-1 96.0%

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

      16. distribute-lft-in 96.0%

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

      17. neg-mul-1 96.0%

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

      18. remove-double-neg 96.0%

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

      19. neg-mul-1 96.0%

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

      20. remove-double-neg 96.0%

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

      21. +-commutative 96.0%

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

   5. Simplified 96.0%

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

   if -3.2e8 < z < -7.4999999999999999e-285 or 8.69999999999999979e-191 < z < 1

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 91.6%

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

   if -7.4999999999999999e-285 < z < 8.69999999999999979e-191

   1. Initial program 75.1%

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

   3. Taylor expanded in y around inf 93.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-285}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{-191}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z + -1}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (+ z -1.0)))))
   (if (<= t -1.25e+70)
     t_1
     (if (<= t 1.05e+20)
       (/ (* x y) z)
       (if (<= t 6e+162)
         (* x (- (/ y z) t))
         (if (<= t 1.5e+286) (* x (/ t z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -1.25e+70) {
		tmp = t_1;
	} else if (t <= 1.05e+20) {
		tmp = (x * y) / z;
	} else if (t <= 6e+162) {
		tmp = x * ((y / z) - t);
	} else if (t <= 1.5e+286) {
		tmp = x * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z + (-1.0d0)))
    if (t <= (-1.25d+70)) then
        tmp = t_1
    else if (t <= 1.05d+20) then
        tmp = (x * y) / z
    else if (t <= 6d+162) then
        tmp = x * ((y / z) - t)
    else if (t <= 1.5d+286) then
        tmp = x * (t / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z + -1.0));
	double tmp;
	if (t <= -1.25e+70) {
		tmp = t_1;
	} else if (t <= 1.05e+20) {
		tmp = (x * y) / z;
	} else if (t <= 6e+162) {
		tmp = x * ((y / z) - t);
	} else if (t <= 1.5e+286) {
		tmp = x * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z + -1.0))
	tmp = 0
	if t <= -1.25e+70:
		tmp = t_1
	elif t <= 1.05e+20:
		tmp = (x * y) / z
	elif t <= 6e+162:
		tmp = x * ((y / z) - t)
	elif t <= 1.5e+286:
		tmp = x * (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.25e+70)
		tmp = t_1;
	elseif (t <= 1.05e+20)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= 6e+162)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (t <= 1.5e+286)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.25e+70)
		tmp = t_1;
	elseif (t <= 1.05e+20)
		tmp = (x * y) / z;
	elseif (t <= 6e+162)
		tmp = x * ((y / z) - t);
	elseif (t <= 1.5e+286)
		tmp = x * (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+70], t$95$1, If[LessEqual[t, 1.05e+20], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 6e+162], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+286], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2500000000000001e70 or 1.4999999999999999e286 < t

   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 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-/l* 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

      4. distribute-neg-frac2 82.4%

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

      5. neg-sub0 82.4%

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

      6. associate--r- 82.4%

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

      7. metadata-eval 82.4%

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

   5. Simplified 82.4%

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

   if -1.2500000000000001e70 < t < 1.05e20

   1. Initial program 91.3%

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

   3. Taylor expanded in y around inf 85.0%

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

   if 1.05e20 < t < 5.9999999999999996e162

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 66.3%

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

   if 5.9999999999999996e162 < t < 1.4999999999999999e286

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. distribute-neg-frac2 72.1%

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

      3. neg-sub0 72.1%

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

      4. associate--r- 72.1%

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

      5. metadata-eval 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in z around inf 65.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+162}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -4.2 \cdot 10^{-285}\right) \land \left(z \leq 1.35 \cdot 10^{-245} \lor \neg \left(z \leq 1.25\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0)
         (and (not (<= z -4.2e-285)) (or (<= z 1.35e-245) (not (<= z 1.25)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || (!(z <= -4.2e-285) && ((z <= 1.35e-245) || !(z <= 1.25)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= (-4.2d-285))) .and. (z <= 1.35d-245) .or. (.not. (z <= 1.25d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || (!(z <= -4.2e-285) && ((z <= 1.35e-245) || !(z <= 1.25)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or (not (z <= -4.2e-285) and ((z <= 1.35e-245) or not (z <= 1.25))):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || (!(z <= -4.2e-285) && ((z <= 1.35e-245) || !(z <= 1.25))))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || (~((z <= -4.2e-285)) && ((z <= 1.35e-245) || ~((z <= 1.25)))))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], And[N[Not[LessEqual[z, -4.2e-285]], $MachinePrecision], Or[LessEqual[z, 1.35e-245], N[Not[LessEqual[z, 1.25]], $MachinePrecision]]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or -4.19999999999999968e-285 < z < 1.34999999999999995e-245 or 1.25 < z

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-neg-frac2 55.1%

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

      3. neg-sub0 55.1%

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

      4. associate--r- 55.1%

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

      5. metadata-eval 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in z around inf 54.0%

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

      1. associate-/l* 51.8%

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

   8. Simplified 51.8%

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

   if -1 < z < -4.19999999999999968e-285 or 1.34999999999999995e-245 < z < 1.25

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-neg-frac2 37.0%

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

      3. neg-sub0 37.0%

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

      4. associate--r- 37.0%

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

      5. metadata-eval 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in z around 0 35.9%

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

      1. mul-1-neg 35.9%

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

   8. Simplified 35.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq -4.2 \cdot 10^{-285}\right) \land \left(z \leq 1.35 \cdot 10^{-245} \lor \neg \left(z \leq 1.25\right)\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := t \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* t (- x))))
   (if (<= z -1.0)
     t_1
     (if (<= z -7.2e-285)
       t_2
       (if (<= z 1.5e-248) (* t (/ x z)) (if (<= z 1.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = t * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -7.2e-285) {
		tmp = t_2;
	} else if (z <= 1.5e-248) {
		tmp = t * (x / z);
	} else if (z <= 1.0) {
		tmp = t_2;
	} 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 * (t / z)
    t_2 = t * -x
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= (-7.2d-285)) then
        tmp = t_2
    else if (z <= 1.5d-248) then
        tmp = t * (x / z)
    else if (z <= 1.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = t * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= -7.2e-285) {
		tmp = t_2;
	} else if (z <= 1.5e-248) {
		tmp = t * (x / z);
	} else if (z <= 1.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = t * -x
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= -7.2e-285:
		tmp = t_2
	elif z <= 1.5e-248:
		tmp = t * (x / z)
	elif z <= 1.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(t * Float64(-x))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -7.2e-285)
		tmp = t_2;
	elseif (z <= 1.5e-248)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = t * -x;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= -7.2e-285)
		tmp = t_2;
	elseif (z <= 1.5e-248)
		tmp = t * (x / z);
	elseif (z <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, -7.2e-285], t$95$2, If[LessEqual[z, 1.5e-248], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. distribute-neg-frac2 61.4%

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

      3. neg-sub0 61.4%

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

      4. associate--r- 61.4%

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

      5. metadata-eval 61.4%

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

   5. Simplified 61.4%

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

   6. Taylor expanded in z around inf 61.4%

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

   if -1 < z < -7.20000000000000008e-285 or 1.50000000000000007e-248 < z < 1

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. distribute-neg-frac2 37.0%

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

      3. neg-sub0 37.0%

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

      4. associate--r- 37.0%

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

      5. metadata-eval 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in z around 0 35.9%

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

      1. mul-1-neg 35.9%

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

   8. Simplified 35.9%

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

   if -7.20000000000000008e-285 < z < 1.50000000000000007e-248

   1. Initial program 71.1%

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

   3. Taylor expanded in y around 0 7.8%

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

      1. mul-1-neg 7.8%

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

      2. distribute-neg-frac2 7.8%

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

      3. neg-sub0 7.8%

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

      4. associate--r- 7.8%

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

      5. metadata-eval 7.8%

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

   5. Simplified 7.8%

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

   6. Taylor expanded in z around inf 33.8%

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

      1. associate-/l* 39.7%

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

   8. Simplified 39.7%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -320000000.0)
   (* x (/ (+ y t) z))
   (if (<= z 1.0) (/ (* x (- y (* z t))) z) (* x (+ (/ y z) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -320000000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 1.0) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-320000000.0d0)) then
        tmp = x * ((y + t) / z)
    else if (z <= 1.0d0) then
        tmp = (x * (y - (z * t))) / z
    else
        tmp = x * ((y / z) + (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -320000000.0) {
		tmp = x * ((y + t) / z);
	} else if (z <= 1.0) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = x * ((y / z) + (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -320000000.0:
		tmp = x * ((y + t) / z)
	elif z <= 1.0:
		tmp = (x * (y - (z * t))) / z
	else:
		tmp = x * ((y / z) + (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -320000000.0)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= 1.0)
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	else
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -320000000.0)
		tmp = x * ((y + t) / z);
	elseif (z <= 1.0)
		tmp = (x * (y - (z * t))) / z;
	else
		tmp = x * ((y / z) + (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -320000000.0], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e8

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. associate-/l* 95.9%

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

      2. neg-mul-1 95.9%

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

      3. sub-neg 95.9%

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

      4. remove-double-neg 95.9%

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

      5. neg-mul-1 95.9%

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

      6. neg-mul-1 95.9%

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

      7. distribute-lft-in 95.9%

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

      8. neg-mul-1 95.9%

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

      9. sub-neg 95.9%

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

      10. *-commutative 95.9%

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

      11. associate-*l/ 95.9%

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

      12. *-commutative 95.9%

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

      13. associate-*r/ 95.9%

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

      14. sub-neg 95.9%

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

      15. neg-mul-1 95.9%

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

      16. distribute-lft-in 95.9%

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

      17. neg-mul-1 95.9%

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

      18. remove-double-neg 95.9%

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

      19. neg-mul-1 95.9%

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

      20. remove-double-neg 95.9%

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

      21. +-commutative 95.9%

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

   5. Simplified 95.9%

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

   if -3.2e8 < z < 1

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in x around 0 94.0%

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

      1. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   if 1 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 96.1%

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

      1. associate-*r/ 96.1%

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

      2. neg-mul-1 96.1%

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

   5. Simplified 96.1%

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

      1. sub-neg 96.1%

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

      2. add-sqr-sqrt 48.1%

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

      3. sqrt-unprod 58.7%

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

      4. sqr-neg 58.7%

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

      5. sqrt-unprod 24.4%

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

      6. add-sqr-sqrt 51.0%

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

      7. distribute-frac-neg 51.0%

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

      8. add-sqr-sqrt 26.6%

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

      9. sqrt-unprod 53.3%

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

      10. sqr-neg 53.3%

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

      11. sqrt-unprod 47.8%

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

      12. add-sqr-sqrt 96.1%

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

   7. Applied egg-rr 96.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000000:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+70} \lor \neg \left(t \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e+70) (not (<= t 4.8e+43)))
   (* x (/ t (+ z -1.0)))
   (/ (* x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e+70) || !(t <= 4.8e+43)) {
		tmp = x * (t / (z + -1.0));
	} 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 ((t <= (-4.1d+70)) .or. (.not. (t <= 4.8d+43))) then
        tmp = x * (t / (z + (-1.0d0)))
    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 ((t <= -4.1e+70) || !(t <= 4.8e+43)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e+70) or not (t <= 4.8e+43):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e+70) || !(t <= 4.8e+43))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e+70) || ~((t <= 4.8e+43)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e+70], N[Not[LessEqual[t, 4.8e+43]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.1000000000000002e70 or 4.80000000000000046e43 < t

   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 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-neg-frac2 79.2%

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

      3. neg-sub0 79.2%

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

      4. associate--r- 79.2%

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

      5. metadata-eval 79.2%

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

   5. Simplified 79.2%

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

   if -4.1000000000000002e70 < t < 4.80000000000000046e43

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 84.3%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+70} \lor \neg \left(t \leq 4.8 \cdot 10^{+43}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+70} \lor \neg \left(t \leq 2.4 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e+70) (not (<= t 2.4e+43)))
   (* t (/ x (+ z -1.0)))
   (/ (* x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+70) || !(t <= 2.4e+43)) {
		tmp = t * (x / (z + -1.0));
	} 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 ((t <= (-1.65d+70)) .or. (.not. (t <= 2.4d+43))) then
        tmp = t * (x / (z + (-1.0d0)))
    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 ((t <= -1.65e+70) || !(t <= 2.4e+43)) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e+70) or not (t <= 2.4e+43):
		tmp = t * (x / (z + -1.0))
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e+70) || !(t <= 2.4e+43))
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e+70) || ~((t <= 2.4e+43)))
		tmp = t * (x / (z + -1.0));
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e+70], N[Not[LessEqual[t, 2.4e+43]], $MachinePrecision]], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000008e70 or 2.40000000000000023e43 < t

   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 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. distribute-neg-frac2 70.5%

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

      5. neg-sub0 70.5%

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

      6. associate--r- 70.5%

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

      7. metadata-eval 70.5%

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

   5. Simplified 70.5%

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

   if -1.65000000000000008e70 < t < 2.40000000000000023e43

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 84.3%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+70} \lor \neg \left(t \leq 2.4 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+71} \lor \neg \left(t \leq 4.2 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+71) (not (<= t 4.2e+145))) (* x (/ t z)) (/ (* x y) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+71) || !(t <= 4.2e+145)) {
		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 ((t <= (-5d+71)) .or. (.not. (t <= 4.2d+145))) 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 ((t <= -5e+71) || !(t <= 4.2e+145)) {
		tmp = x * (t / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+71) or not (t <= 4.2e+145):
		tmp = x * (t / z)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e+71) || !(t <= 4.2e+145))
		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 ((t <= -5e+71) || ~((t <= 4.2e+145)))
		tmp = x * (t / z);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e+71], N[Not[LessEqual[t, 4.2e+145]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999972e71 or 4.19999999999999979e145 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-neg-frac2 82.0%

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

      3. neg-sub0 82.0%

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

      4. associate--r- 82.0%

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

      5. metadata-eval 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -4.99999999999999972e71 < t < 4.19999999999999979e145

   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 78.8%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+71} \lor \neg \left(t \leq 4.2 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+72} \lor \neg \left(t \leq 2.2 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.38e+72) (not (<= t 2.2e+144))) (* x (/ t z)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.38e+72) || !(t <= 2.2e+144)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.38d+72)) .or. (.not. (t <= 2.2d+144))) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.38e+72) || !(t <= 2.2e+144)) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.38e+72) or not (t <= 2.2e+144):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.38e+72) || !(t <= 2.2e+144))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.38e+72) || ~((t <= 2.2e+144)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.38e+72], N[Not[LessEqual[t, 2.2e+144]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.37999999999999995e72 or 2.19999999999999988e144 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-neg-frac2 82.0%

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

      3. neg-sub0 82.0%

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

      4. associate--r- 82.0%

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

      5. metadata-eval 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around inf 62.6%

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

   if -1.37999999999999995e72 < t < 2.19999999999999988e144

   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 90.5%

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

      1. associate-*r/ 90.5%

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

      2. associate-*r* 90.5%

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

      3. neg-mul-1 90.5%

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

      4. *-commutative 90.5%

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

      5. times-frac 84.5%

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

      6. distribute-frac-neg 84.5%

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

      7. distribute-neg-frac2 84.5%

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

      8. neg-sub0 84.5%

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

      9. associate--r- 84.5%

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

      10. metadata-eval 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in t around 0 78.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+72} \lor \neg \left(t \leq 2.2 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+71} \lor \neg \left(t \leq 4.8 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.6e+71) (not (<= t 4.8e+139))) (* x (/ t z)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.6e+71) || !(t <= 4.8e+139)) {
		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 ((t <= (-8.6d+71)) .or. (.not. (t <= 4.8d+139))) 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 ((t <= -8.6e+71) || !(t <= 4.8e+139)) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.6e+71) or not (t <= 4.8e+139):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.6e+71) || !(t <= 4.8e+139))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.6e+71) || ~((t <= 4.8e+139)))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.6e+71], N[Not[LessEqual[t, 4.8e+139]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.59999999999999967e71 or 4.80000000000000016e139 < t

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. distribute-neg-frac2 81.1%

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

      3. neg-sub0 81.1%

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

      4. associate--r- 81.1%

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

      5. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in z around inf 62.0%

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

   if -8.59999999999999967e71 < t < 4.80000000000000016e139

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 78.7%

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

      1. associate-*r/ 77.3%

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

   5. Simplified 77.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+71} \lor \neg \left(t \leq 4.8 \cdot 10^{+139}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 23.6% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

3. Taylor expanded in y around 0 46.6%

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

   1. mul-1-neg 46.6%

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

   2. distribute-neg-frac2 46.6%

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

   3. neg-sub0 46.6%

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

   4. associate--r- 46.6%

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

   5. metadata-eval 46.6%

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

5. Simplified 46.6%

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

6. Taylor expanded in z around 0 22.9%

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

   1. mul-1-neg 22.9%

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

8. Simplified 22.9%

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

9. Final simplification 22.9%

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

Developer target: 95.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) -7.623226303312042e-196) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))) (if (< (* x (- (/ y z) (/ t (- 1.0 z)))) 1.4133944927702302e-211) (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z)))) (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z)))))))

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