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

Percentage Accurate: 94.7% → 98.2%

Time: 6.8s

Alternatives: 11

Speedup: 0.4×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.7% 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: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 (- INFINITY))
     (* y (/ x z))
     (if (<= t_1 2e+302) (* x t_1) (/ (* x y) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else if (t_1 <= 2e+302) {
		tmp = x * t_1;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else if (t_1 <= 2e+302) {
		tmp = x * t_1;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	elif t_1 <= 2e+302:
		tmp = x * t_1
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	elseif (t_1 <= 2e+302)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	elseif (t_1 <= 2e+302)
		tmp = x * t_1;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+302], N[(x * t$95$1), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0

   1. Initial program 66.7%

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

      1. clear-num 66.7%

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

      2. associate-/r/ 66.7%

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

   3. Applied egg-rr 66.7%

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

   4. Taylor expanded in y around inf 99.9%

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

      1. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2.0000000000000002e302

   1. Initial program 98.3%

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

   if 2.0000000000000002e302 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 53.8%

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

   2. Taylor expanded in y around inf 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(y, 1 - z, z \cdot \left(-t\right)\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 2e+296)
     t_1
     (/ (* x (fma y (- 1.0 z) (* z (- t)))) (* z (- 1.0 z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= 2e+296) {
		tmp = t_1;
	} else {
		tmp = (x * fma(y, (1.0 - z), (z * -t))) / (z * (1.0 - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_1 <= 2e+296)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * fma(y, Float64(1.0 - z), Float64(z * Float64(-t)))) / Float64(z * Float64(1.0 - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+296], t$95$1, N[(N[(x * N[(y * N[(1.0 - z), $MachinePrecision] + N[(z * (-t)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < 1.99999999999999996e296

   1. Initial program 96.5%

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

   if 1.99999999999999996e296 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

      2. frac-sub 81.3%

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

      3. associate-*l/ 100.0%

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

      4. cancel-sign-sub-inv 100.0%

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

      5. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \leq 2 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \mathsf{fma}\left(y, 1 - z, z \cdot \left(-t\right)\right)}{z \cdot \left(1 - z\right)}\\ \end{array} \]

Alternative 3: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -53000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -1.1e+67)
     t_1
     (if (<= t -4.4e+49)
       (/ (* x y) z)
       (if (<= t -53000000000.0)
         t_1
         (if (<= t -3.8e-179)
           (* x (- (/ y z) t))
           (if (<= t 3e+48) (* y (/ x z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.1e+67) {
		tmp = t_1;
	} else if (t <= -4.4e+49) {
		tmp = (x * y) / z;
	} else if (t <= -53000000000.0) {
		tmp = t_1;
	} else if (t <= -3.8e-179) {
		tmp = x * ((y / z) - t);
	} else if (t <= 3e+48) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / (z + (-1.0d0)))
    if (t <= (-1.1d+67)) then
        tmp = t_1
    else if (t <= (-4.4d+49)) then
        tmp = (x * y) / z
    else if (t <= (-53000000000.0d0)) then
        tmp = t_1
    else if (t <= (-3.8d-179)) then
        tmp = x * ((y / z) - t)
    else if (t <= 3d+48) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -1.1e+67) {
		tmp = t_1;
	} else if (t <= -4.4e+49) {
		tmp = (x * y) / z;
	} else if (t <= -53000000000.0) {
		tmp = t_1;
	} else if (t <= -3.8e-179) {
		tmp = x * ((y / z) - t);
	} else if (t <= 3e+48) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -1.1e+67:
		tmp = t_1
	elif t <= -4.4e+49:
		tmp = (x * y) / z
	elif t <= -53000000000.0:
		tmp = t_1
	elif t <= -3.8e-179:
		tmp = x * ((y / z) - t)
	elif t <= 3e+48:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -1.1e+67)
		tmp = t_1;
	elseif (t <= -4.4e+49)
		tmp = Float64(Float64(x * y) / z);
	elseif (t <= -53000000000.0)
		tmp = t_1;
	elseif (t <= -3.8e-179)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (t <= 3e+48)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -1.1e+67)
		tmp = t_1;
	elseif (t <= -4.4e+49)
		tmp = (x * y) / z;
	elseif (t <= -53000000000.0)
		tmp = t_1;
	elseif (t <= -3.8e-179)
		tmp = x * ((y / z) - t);
	elseif (t <= 3e+48)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e+67], t$95$1, If[LessEqual[t, -4.4e+49], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -53000000000.0], t$95$1, If[LessEqual[t, -3.8e-179], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+48], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1e67 or -4.4000000000000001e49 < t < -5.3e10 or 3e48 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in y around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. associate-*r* 74.8%

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

      3. neg-mul-1 74.8%

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

      4. associate-*l/ 79.7%

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

      5. *-commutative 79.7%

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

      6. distribute-frac-neg 79.7%

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

      7. neg-mul-1 79.7%

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

      8. metadata-eval 79.7%

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

      9. times-frac 79.7%

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

      10. *-lft-identity 79.7%

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

      11. neg-mul-1 79.7%

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

      12. sub-neg 79.7%

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

      13. +-commutative 79.7%

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

      14. distribute-neg-in 79.7%

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

      15. remove-double-neg 79.7%

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

      16. metadata-eval 79.7%

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

   4. Simplified 79.7%

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

   if -1.1e67 < t < -4.4000000000000001e49

   1. Initial program 84.2%

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

   2. Taylor expanded in y around inf 97.3%

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

   if -5.3e10 < t < -3.79999999999999974e-179

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. associate-*l/ 89.3%

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

      4. distribute-rgt-out-- 89.4%

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

   4. Simplified 89.4%

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

   if -3.79999999999999974e-179 < t < 3e48

   1. Initial program 88.3%

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

      1. clear-num 87.8%

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

      2. associate-/r/ 88.3%

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

   3. Applied egg-rr 88.3%

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

   4. Taylor expanded in y around inf 84.7%

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

      1. associate-*r/ 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;t \leq -53000000000:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+48}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= z -2.6e+175)
     t_1
     (if (<= z -1.6e+27)
       (* x (/ y z))
       (if (<= z -6.8e+16)
         (/ t (/ z x))
         (if (<= z 1.6e+54) (* x (- (/ y z) t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (z <= -2.6e+175) {
		tmp = t_1;
	} else if (z <= -1.6e+27) {
		tmp = x * (y / z);
	} else if (z <= -6.8e+16) {
		tmp = t / (z / x);
	} else if (z <= 1.6e+54) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (z <= (-2.6d+175)) then
        tmp = t_1
    else if (z <= (-1.6d+27)) then
        tmp = x * (y / z)
    else if (z <= (-6.8d+16)) then
        tmp = t / (z / x)
    else if (z <= 1.6d+54) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (z <= -2.6e+175) {
		tmp = t_1;
	} else if (z <= -1.6e+27) {
		tmp = x * (y / z);
	} else if (z <= -6.8e+16) {
		tmp = t / (z / x);
	} else if (z <= 1.6e+54) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if z <= -2.6e+175:
		tmp = t_1
	elif z <= -1.6e+27:
		tmp = x * (y / z)
	elif z <= -6.8e+16:
		tmp = t / (z / x)
	elif z <= 1.6e+54:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (z <= -2.6e+175)
		tmp = t_1;
	elseif (z <= -1.6e+27)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= -6.8e+16)
		tmp = Float64(t / Float64(z / x));
	elseif (z <= 1.6e+54)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (z <= -2.6e+175)
		tmp = t_1;
	elseif (z <= -1.6e+27)
		tmp = x * (y / z);
	elseif (z <= -6.8e+16)
		tmp = t / (z / x);
	elseif (z <= 1.6e+54)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+175], t$95$1, If[LessEqual[z, -1.6e+27], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e+16], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+54], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6e175 or 1.6e54 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-/l* 94.6%

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

      3. neg-mul-1 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -2.6e175 < z < -1.60000000000000008e27

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 57.9%

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

      1. associate-*l/ 67.7%

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

   4. Simplified 67.7%

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

   if -1.60000000000000008e27 < z < -6.8e16

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.6%

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

      3. neg-mul-1 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. associate-*r/ 99.6%

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

   7. Simplified 99.6%

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

      1. clear-num 99.6%

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

      2. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -6.8e16 < z < 1.6e54

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

      3. associate-*l/ 81.5%

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

      4. distribute-rgt-out-- 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{+16}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 5: 42.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-19} \lor \neg \left(z \leq -2.9 \cdot 10^{-242} \lor \neg \left(z \leq 1.4 \cdot 10^{-280}\right) \land z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e-19)
         (not (or (<= z -2.9e-242) (and (not (<= z 1.4e-280)) (<= z 1.0)))))
   (* t (/ x z))
   (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e-19) || !((z <= -2.9e-242) || (!(z <= 1.4e-280) && (z <= 1.0)))) {
		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 <= (-1d-19)) .or. (.not. (z <= (-2.9d-242)) .or. (.not. (z <= 1.4d-280)) .and. (z <= 1.0d0))) 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 <= -1e-19) || !((z <= -2.9e-242) || (!(z <= 1.4e-280) && (z <= 1.0)))) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e-19) or not ((z <= -2.9e-242) or (not (z <= 1.4e-280) and (z <= 1.0))):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e-19) || !((z <= -2.9e-242) || (!(z <= 1.4e-280) && (z <= 1.0))))
		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 <= -1e-19) || ~(((z <= -2.9e-242) || (~((z <= 1.4e-280)) && (z <= 1.0)))))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e-19], N[Not[Or[LessEqual[z, -2.9e-242], And[N[Not[LessEqual[z, 1.4e-280]], $MachinePrecision], LessEqual[z, 1.0]]]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999998e-20 or -2.9000000000000001e-242 < z < 1.40000000000000009e-280 or 1 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-/l* 91.4%

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

      3. neg-mul-1 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in y around 0 52.4%

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

      1. associate-*r/ 51.6%

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

   7. Simplified 51.6%

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

   if -9.9999999999999998e-20 < z < -2.9000000000000001e-242 or 1.40000000000000009e-280 < z < 1

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-*l/ 85.5%

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

      4. distribute-rgt-out-- 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in y around 0 38.1%

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

      1. associate-*r* 38.1%

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

      2. mul-1-neg 38.1%

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

   7. Simplified 38.1%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-19} \lor \neg \left(z \leq -2.9 \cdot 10^{-242} \lor \neg \left(z \leq 1.4 \cdot 10^{-280}\right) \land z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 6: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-18} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-18) (not (<= z 1.0)))
   (* (/ x z) (+ y t))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-18) || !(z <= 1.0)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-18)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / z) * (y + t)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-18) || !(z <= 1.0)) {
		tmp = (x / z) * (y + t);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-18) or not (z <= 1.0):
		tmp = (x / z) * (y + t)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-18) || !(z <= 1.0))
		tmp = Float64(Float64(x / z) * Float64(y + t));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-18) || ~((z <= 1.0)))
		tmp = (x / z) * (y + t);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-18], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000002e-18 or 1 < z

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-/l* 94.2%

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

      3. associate-/r/ 88.9%

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

      4. cancel-sign-sub-inv 88.9%

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

      5. metadata-eval 88.9%

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

      6. *-lft-identity 88.9%

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

   4. Simplified 88.9%

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

   if -1.95000000000000002e-18 < z < 1

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. unsub-neg 90.5%

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

      3. associate-*l/ 85.3%

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

      4. distribute-rgt-out-- 90.3%

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

   4. Simplified 90.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-18} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 7: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-/l* 94.8%

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

      3. neg-mul-1 94.8%

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

   4. Simplified 94.8%

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

   5. Taylor expanded in z around 0 94.8%

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

      1. associate-/l* 88.4%

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

      2. associate-*r/ 95.6%

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

      3. *-commutative 95.6%

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

   7. Applied egg-rr 95.6%

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

   if -1 < z < 1

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 90.6%

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

      1. mul-1-neg 90.6%

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

      2. unsub-neg 90.6%

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

      3. associate-*l/ 84.7%

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

      4. distribute-rgt-out-- 89.7%

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

   4. Simplified 89.7%

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

4. Final simplification 92.8%

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

Alternative 8: 94.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\frac{t_1}{\frac{1}{x}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ y t) z)))
   (if (<= z -1.05)
     (/ t_1 (/ 1.0 x))
     (if (<= z 1.0) (* x (- (/ y z) t)) (* x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y + t) / z;
	double tmp;
	if (z <= -1.05) {
		tmp = t_1 / (1.0 / x);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * 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 = (y + t) / z
    if (z <= (-1.05d0)) then
        tmp = t_1 / (1.0d0 / x)
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y + t) / z;
	double tmp;
	if (z <= -1.05) {
		tmp = t_1 / (1.0 / x);
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y + t) / z
	tmp = 0
	if z <= -1.05:
		tmp = t_1 / (1.0 / x)
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y + t) / z)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(t_1 / Float64(1.0 / x));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y + t) / z;
	tmp = 0.0;
	if (z <= -1.05)
		tmp = t_1 / (1.0 / x);
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = x * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 95.5%

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

      3. neg-mul-1 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in z around 0 95.5%

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

      1. associate-/l* 85.0%

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

      2. associate-*r/ 96.2%

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

      3. *-commutative 96.2%

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

   7. Applied egg-rr 96.2%

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

      1. associate-/r/ 87.7%

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

      2. div-inv 87.7%

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

      3. associate-/r* 96.3%

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

   9. Applied egg-rr 96.3%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 90.6%

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

      1. mul-1-neg 90.6%

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

      2. unsub-neg 90.6%

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

      3. associate-*l/ 84.7%

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

      4. distribute-rgt-out-- 89.7%

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

   4. Simplified 89.7%

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

   if 1 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-/l* 93.9%

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

      3. neg-mul-1 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in z around 0 93.9%

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

      1. associate-/l* 92.5%

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

      2. associate-*r/ 94.8%

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

      3. *-commutative 94.8%

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

   7. Applied egg-rr 94.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\frac{\frac{y + t}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 9: 64.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+101}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.5e+67) (not (<= t 8e+101))) (* t (/ x z)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e+67) || !(t <= 8e+101)) {
		tmp = t * (x / 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 <= (-7.5d+67)) .or. (.not. (t <= 8d+101))) then
        tmp = t * (x / 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 <= -7.5e+67) || !(t <= 8e+101)) {
		tmp = t * (x / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.5e+67) or not (t <= 8e+101):
		tmp = t * (x / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.5e+67) || !(t <= 8e+101))
		tmp = Float64(t * Float64(x / 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 <= -7.5e+67) || ~((t <= 8e+101)))
		tmp = t * (x / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.5e+67], N[Not[LessEqual[t, 8e+101]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000005e67 or 7.9999999999999998e101 < t

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 69.5%

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

      3. neg-mul-1 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. associate-*r/ 50.3%

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

   7. Simplified 50.3%

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

   if -7.5000000000000005e67 < t < 7.9999999999999998e101

   1. Initial program 92.0%

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

      1. clear-num 91.7%

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

      2. associate-/r/ 92.0%

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

   3. Applied egg-rr 92.0%

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

   4. Taylor expanded in y around inf 79.1%

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

      1. associate-*r/ 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+101}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 67.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+67} \lor \neg \left(t \leq 7.4 \cdot 10^{+101}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e+67) (not (<= t 7.4e+101))) (/ x (/ z t)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+67) || !(t <= 7.4e+101)) {
		tmp = x / (z / t);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.6d+67)) .or. (.not. (t <= 7.4d+101))) then
        tmp = x / (z / t)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+67) || !(t <= 7.4e+101)) {
		tmp = x / (z / t);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e+67) or not (t <= 7.4e+101):
		tmp = x / (z / t)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e+67) || !(t <= 7.4e+101))
		tmp = Float64(x / Float64(z / t));
	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 <= -6.6e+67) || ~((t <= 7.4e+101)))
		tmp = x / (z / t);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e+67], N[Not[LessEqual[t, 7.4e+101]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000006e67 or 7.3999999999999995e101 < t

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-/l* 69.5%

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

      3. neg-mul-1 69.5%

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

   4. Simplified 69.5%

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

   5. Taylor expanded in y around 0 58.4%

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

   if -6.6000000000000006e67 < t < 7.3999999999999995e101

   1. Initial program 92.0%

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

      1. clear-num 91.7%

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

      2. associate-/r/ 92.0%

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

   3. Applied egg-rr 92.0%

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

   4. Taylor expanded in y around inf 79.1%

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

      1. associate-*r/ 80.7%

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

   6. Simplified 80.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+67} \lor \neg \left(t \leq 7.4 \cdot 10^{+101}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 23.4% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

2. Taylor expanded in z around 0 63.0%

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

   1. mul-1-neg 63.0%

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

   2. unsub-neg 63.0%

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

   3. associate-*l/ 61.7%

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

   4. distribute-rgt-out-- 64.0%

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

4. Simplified 64.0%

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

5. Taylor expanded in y around 0 23.3%

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

   1. associate-*r* 23.3%

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

   2. mul-1-neg 23.3%

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

7. Simplified 23.3%

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

8. Final simplification 23.3%

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

Developer target: 95.1% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

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

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