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

Percentage Accurate: 94.6% → 97.7%

Time: 8.8s

Alternatives: 13

Speedup: 0.3×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-166} \lor \neg \left(t_1 \leq 5 \cdot 10^{-306}\right):\\ \;\;\;\;t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \end{array} \]

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 (or (<= t_1 -1e-166) (not (<= t_1 5e-306)))
       (* t_1 x)
       (* (/ x z) (+ y t))))))

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 <= -1e-166) || !(t_1 <= 5e-306)) {
		tmp = t_1 * x;
	} else {
		tmp = (x / z) * (y + t);
	}
	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 <= -1e-166) || !(t_1 <= 5e-306)) {
		tmp = t_1 * x;
	} else {
		tmp = (x / z) * (y + t);
	}
	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 <= -1e-166) or not (t_1 <= 5e-306):
		tmp = t_1 * x
	else:
		tmp = (x / z) * (y + t)
	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 <= -1e-166) || !(t_1 <= 5e-306))
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(Float64(x / z) * Float64(y + t));
	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 <= -1e-166) || ~((t_1 <= 5e-306)))
		tmp = t_1 * x;
	else
		tmp = (x / z) * (y + t);
	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[Or[LessEqual[t$95$1, -1e-166], N[Not[LessEqual[t$95$1, 5e-306]], $MachinePrecision]], N[(t$95$1 * x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 66.8%

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

      1. frac-2neg 66.8%

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

      2. div-inv 66.8%

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

      3. fma-neg 66.8%

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

      4. distribute-neg-frac 66.8%

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

   3. Applied egg-rr 66.8%

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

      1. fma-udef 66.8%

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

      2. +-commutative 66.8%

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

      3. distribute-lft-neg-out 66.8%

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

      4. unsub-neg 66.8%

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

      5. neg-mul-1 66.8%

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

      6. *-commutative 66.8%

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

      7. associate-*r/ 66.8%

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

      8. metadata-eval 66.8%

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

      9. associate-/r* 66.8%

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

      10. neg-mul-1 66.8%

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

      11. associate-*r/ 66.8%

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

      12. *-rgt-identity 66.8%

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

      13. neg-sub0 66.8%

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

      14. associate--r- 66.8%

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

      15. metadata-eval 66.8%

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

      16. neg-mul-1 66.8%

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

      17. associate-/r* 66.8%

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

      18. metadata-eval 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in t around 0 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.9%

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

   8. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -1.00000000000000004e-166 or 4.99999999999999998e-306 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 98.0%

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

   if -1.00000000000000004e-166 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 4.99999999999999998e-306

   1. Initial program 70.9%

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

   2. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 65.3%

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

      3. associate-/r/ 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. metadata-eval 99.9%

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

      6. *-lft-identity 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} - \frac{t}{1 - z} \leq -1 \cdot 10^{-166} \lor \neg \left(\frac{y}{z} - \frac{t}{1 - z} \leq 5 \cdot 10^{-306}\right):\\ \;\;\;\;\left(\frac{y}{z} - \frac{t}{1 - z}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]

Alternative 2: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 310000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -4.2e+185)
     t_1
     (if (<= t -2.95e+79)
       (* x (- (/ y z) t))
       (if (<= t 310000000.0) (/ (* 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 <= -4.2e+185) {
		tmp = t_1;
	} else if (t <= -2.95e+79) {
		tmp = x * ((y / z) - t);
	} else if (t <= 310000000.0) {
		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 <= (-4.2d+185)) then
        tmp = t_1
    else if (t <= (-2.95d+79)) then
        tmp = x * ((y / z) - t)
    else if (t <= 310000000.0d0) 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 <= -4.2e+185) {
		tmp = t_1;
	} else if (t <= -2.95e+79) {
		tmp = x * ((y / z) - t);
	} else if (t <= 310000000.0) {
		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 <= -4.2e+185:
		tmp = t_1
	elif t <= -2.95e+79:
		tmp = x * ((y / z) - t)
	elif t <= 310000000.0:
		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 <= -4.2e+185)
		tmp = t_1;
	elseif (t <= -2.95e+79)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (t <= 310000000.0)
		tmp = Float64(Float64(y * 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 <= -4.2e+185)
		tmp = t_1;
	elseif (t <= -2.95e+79)
		tmp = x * ((y / z) - t);
	elseif (t <= 310000000.0)
		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, -4.2e+185], t$95$1, If[LessEqual[t, -2.95e+79], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 310000000.0], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.2e185 or 3.1e8 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. associate-*r* 71.4%

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

      3. neg-mul-1 71.4%

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

      4. associate-*l/ 80.4%

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

      5. *-commutative 80.4%

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

      6. neg-mul-1 80.4%

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

      7. *-commutative 80.4%

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

      8. associate-*r/ 80.4%

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

      9. metadata-eval 80.4%

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

      10. associate-/r* 80.4%

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

      11. neg-mul-1 80.4%

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

      12. associate-*r/ 80.4%

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

      13. *-rgt-identity 80.4%

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

      14. neg-sub0 80.4%

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

      15. associate--r- 80.4%

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

      16. metadata-eval 80.4%

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

   4. Simplified 80.4%

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

   if -4.2e185 < t < -2.95e79

   1. Initial program 92.7%

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

   2. Taylor expanded in z around 0 81.1%

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

      1. associate-*l/ 77.3%

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

      2. associate-*r* 77.3%

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

      3. neg-mul-1 77.3%

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

      4. distribute-rgt-out 77.3%

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

      5. unsub-neg 77.3%

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

   4. Simplified 77.3%

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

   if -2.95e79 < t < 3.1e8

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 82.3%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;t \leq 310000000:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]

Alternative 3: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+194}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.1e+194)
   (- (* t x))
   (if (<= t 4.2e-156)
     (* (/ y z) x)
     (if (<= t 1.9e+211) (* y (/ x z)) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e+194) {
		tmp = -(t * x);
	} else if (t <= 4.2e-156) {
		tmp = (y / z) * x;
	} else if (t <= 1.9e+211) {
		tmp = y * (x / z);
	} else {
		tmp = x * (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 (t <= (-5.1d+194)) then
        tmp = -(t * x)
    else if (t <= 4.2d-156) then
        tmp = (y / z) * x
    else if (t <= 1.9d+211) then
        tmp = y * (x / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.1e+194) {
		tmp = -(t * x);
	} else if (t <= 4.2e-156) {
		tmp = (y / z) * x;
	} else if (t <= 1.9e+211) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.1e+194:
		tmp = -(t * x)
	elif t <= 4.2e-156:
		tmp = (y / z) * x
	elif t <= 1.9e+211:
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.1e+194)
		tmp = Float64(-Float64(t * x));
	elseif (t <= 4.2e-156)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1.9e+211)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.1e+194)
		tmp = -(t * x);
	elseif (t <= 4.2e-156)
		tmp = (y / z) * x;
	elseif (t <= 1.9e+211)
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.1e+194], (-N[(t * x), $MachinePrecision]), If[LessEqual[t, 4.2e-156], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.9e+211], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.1000000000000002e194

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. neg-mul-1 74.4%

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

      4. associate-*l/ 85.4%

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

      5. *-commutative 85.4%

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

      6. neg-mul-1 85.4%

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

      7. *-commutative 85.4%

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

      8. associate-*r/ 85.2%

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

      9. metadata-eval 85.2%

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

      10. associate-/r* 85.2%

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

      11. neg-mul-1 85.2%

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

      12. associate-*r/ 85.4%

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

      13. *-rgt-identity 85.4%

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

      14. neg-sub0 85.4%

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

      15. associate--r- 85.4%

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

      16. metadata-eval 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. mul-1-neg 55.9%

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

   7. Simplified 55.9%

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

   if -5.1000000000000002e194 < t < 4.20000000000000025e-156

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 78.0%

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

      1. associate-*l/ 76.9%

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

   4. Simplified 76.9%

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

   if 4.20000000000000025e-156 < t < 1.90000000000000008e211

   1. Initial program 90.3%

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

      1. frac-2neg 90.3%

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

      2. div-inv 90.4%

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

      3. fma-neg 90.4%

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

      4. distribute-neg-frac 90.4%

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

   3. Applied egg-rr 90.4%

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

      1. fma-udef 90.4%

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

      2. +-commutative 90.4%

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

      3. distribute-lft-neg-out 90.4%

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

      4. unsub-neg 90.4%

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

      5. neg-mul-1 90.4%

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

      6. *-commutative 90.4%

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

      7. associate-*r/ 90.4%

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

      8. metadata-eval 90.4%

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

      9. associate-/r* 90.4%

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

      10. neg-mul-1 90.4%

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

      11. associate-*r/ 90.4%

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

      12. *-rgt-identity 90.4%

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

      13. neg-sub0 90.4%

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

      14. associate--r- 90.4%

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

      15. metadata-eval 90.4%

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

      16. neg-mul-1 90.4%

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

      17. associate-/r* 90.4%

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

      18. metadata-eval 90.4%

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

   5. Simplified 90.4%

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

   6. Taylor expanded in t around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. associate-*l/ 66.9%

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

   8. Simplified 66.9%

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

   if 1.90000000000000008e211 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-mul-1 94.4%

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

      7. *-commutative 94.4%

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

      8. associate-*r/ 94.4%

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

      9. metadata-eval 94.4%

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

      10. associate-/r* 94.4%

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

      11. neg-mul-1 94.4%

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

      12. associate-*r/ 94.4%

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

      13. *-rgt-identity 94.4%

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

      14. neg-sub0 94.4%

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

      15. associate--r- 94.4%

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

      16. metadata-eval 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in z around inf 72.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+194}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+211}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+196}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e+196)
   (- (* t x))
   (if (<= t -4.6e-287)
     (/ x (/ z y))
     (if (<= t 1.5e+210) (* y (/ x z)) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+196) {
		tmp = -(t * x);
	} else if (t <= -4.6e-287) {
		tmp = x / (z / y);
	} else if (t <= 1.5e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x * (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 (t <= (-4.8d+196)) then
        tmp = -(t * x)
    else if (t <= (-4.6d-287)) then
        tmp = x / (z / y)
    else if (t <= 1.5d+210) then
        tmp = y * (x / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+196) {
		tmp = -(t * x);
	} else if (t <= -4.6e-287) {
		tmp = x / (z / y);
	} else if (t <= 1.5e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e+196:
		tmp = -(t * x)
	elif t <= -4.6e-287:
		tmp = x / (z / y)
	elif t <= 1.5e+210:
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e+196)
		tmp = Float64(-Float64(t * x));
	elseif (t <= -4.6e-287)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 1.5e+210)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e+196)
		tmp = -(t * x);
	elseif (t <= -4.6e-287)
		tmp = x / (z / y);
	elseif (t <= 1.5e+210)
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e+196], (-N[(t * x), $MachinePrecision]), If[LessEqual[t, -4.6e-287], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+210], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.8000000000000001e196

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 74.4%

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

      1. associate-*r/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. neg-mul-1 74.4%

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

      4. associate-*l/ 85.4%

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

      5. *-commutative 85.4%

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

      6. neg-mul-1 85.4%

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

      7. *-commutative 85.4%

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

      8. associate-*r/ 85.2%

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

      9. metadata-eval 85.2%

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

      10. associate-/r* 85.2%

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

      11. neg-mul-1 85.2%

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

      12. associate-*r/ 85.4%

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

      13. *-rgt-identity 85.4%

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

      14. neg-sub0 85.4%

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

      15. associate--r- 85.4%

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

      16. metadata-eval 85.4%

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

   4. Simplified 85.4%

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

   5. Taylor expanded in z around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. mul-1-neg 55.9%

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

   7. Simplified 55.9%

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

   if -4.8000000000000001e196 < t < -4.59999999999999972e-287

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 74.0%

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

      1. associate-*l/ 71.5%

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

   4. Simplified 71.5%

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

      1. *-commutative 71.5%

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

      2. clear-num 70.9%

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

      3. un-div-inv 71.7%

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

   6. Applied egg-rr 71.7%

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

   if -4.59999999999999972e-287 < t < 1.50000000000000011e210

   1. Initial program 91.0%

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

      1. frac-2neg 91.0%

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

      2. div-inv 90.9%

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

      3. fma-neg 90.9%

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

      4. distribute-neg-frac 90.9%

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

   3. Applied egg-rr 90.9%

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

      1. fma-udef 90.9%

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

      2. +-commutative 90.9%

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

      3. distribute-lft-neg-out 90.9%

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

      4. unsub-neg 90.9%

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

      5. neg-mul-1 90.9%

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

      6. *-commutative 90.9%

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

      7. associate-*r/ 90.9%

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

      8. metadata-eval 90.9%

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

      9. associate-/r* 90.9%

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

      10. neg-mul-1 90.9%

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

      11. associate-*r/ 90.9%

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

      12. *-rgt-identity 90.9%

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

      13. neg-sub0 90.9%

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

      14. associate--r- 90.9%

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

      15. metadata-eval 90.9%

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

      16. neg-mul-1 90.9%

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

      17. associate-/r* 90.9%

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

      18. metadata-eval 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in t around 0 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*l/ 76.6%

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

   8. Simplified 76.6%

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

   if 1.50000000000000011e210 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-mul-1 94.4%

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

      7. *-commutative 94.4%

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

      8. associate-*r/ 94.4%

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

      9. metadata-eval 94.4%

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

      10. associate-/r* 94.4%

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

      11. neg-mul-1 94.4%

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

      12. associate-*r/ 94.4%

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

      13. *-rgt-identity 94.4%

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

      14. neg-sub0 94.4%

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

      15. associate--r- 94.4%

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

      16. metadata-eval 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in z around inf 72.5%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+196}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 88.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+14) (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 <= -8e+14) || !(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 <= (-8d+14)) .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 <= -8e+14) || !(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 <= -8e+14) 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 <= -8e+14) || !(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 <= -8e+14) || ~((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, -8e+14], 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 < -8e14 or 1 < z

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-/l* 90.0%

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

      3. associate-/r/ 89.0%

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

      4. cancel-sign-sub-inv 89.0%

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

      5. metadata-eval 89.0%

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

      6. *-lft-identity 89.0%

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

   4. Simplified 89.0%

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

   if -8e14 < z < 1

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 97.3%

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

      1. associate-*l/ 93.5%

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

      2. associate-*r* 93.5%

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

      3. neg-mul-1 93.5%

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

      4. distribute-rgt-out 93.5%

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

      5. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 6: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.4e+72)
   (* x (/ t z))
   (if (<= z 1.04e+82) (* x (- (/ y z) t)) (/ t (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+72) {
		tmp = x * (t / z);
	} else if (z <= 1.04e+82) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.4d+72)) then
        tmp = x * (t / z)
    else if (z <= 1.04d+82) then
        tmp = x * ((y / z) - t)
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+72) {
		tmp = x * (t / z);
	} else if (z <= 1.04e+82) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.4e+72:
		tmp = x * (t / z)
	elif z <= 1.04e+82:
		tmp = x * ((y / z) - t)
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.4e+72)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 1.04e+82)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.4e+72)
		tmp = x * (t / z);
	elseif (z <= 1.04e+82)
		tmp = x * ((y / z) - t);
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.4e+72], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.04e+82], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000001e72

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 47.9%

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

      1. associate-*r/ 47.9%

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

      2. associate-*r* 47.9%

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

      3. neg-mul-1 47.9%

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

      4. associate-*l/ 54.2%

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

      5. *-commutative 54.2%

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

      6. neg-mul-1 54.2%

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

      7. *-commutative 54.2%

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

      8. associate-*r/ 54.2%

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

      9. metadata-eval 54.2%

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

      10. associate-/r* 54.2%

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

      11. neg-mul-1 54.2%

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

      12. associate-*r/ 54.2%

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

      13. *-rgt-identity 54.2%

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

      14. neg-sub0 54.2%

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

      15. associate--r- 54.2%

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

      16. metadata-eval 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -5.4000000000000001e72 < z < 1.03999999999999997e82

   1. Initial program 94.9%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*l/ 89.2%

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

      2. associate-*r* 89.2%

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

      3. neg-mul-1 89.2%

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

      4. distribute-rgt-out 89.2%

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

      5. unsub-neg 89.2%

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

   4. Simplified 89.2%

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

   if 1.03999999999999997e82 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*r/ 57.3%

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

      2. associate-*r* 57.3%

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

      3. neg-mul-1 57.3%

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

      4. associate-*l/ 62.9%

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

      5. *-commutative 62.9%

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

      6. neg-mul-1 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-*r/ 62.8%

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

      9. metadata-eval 62.8%

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

      10. associate-/r* 62.8%

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

      11. neg-mul-1 62.8%

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

      12. associate-*r/ 62.9%

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

      13. *-rgt-identity 62.9%

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

      14. neg-sub0 62.9%

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

      15. associate--r- 62.9%

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

      16. metadata-eval 62.9%

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

   4. Simplified 62.9%

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

   5. Taylor expanded in z around inf 57.3%

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

      1. associate-/l* 62.9%

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

   7. Simplified 62.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e+14)
   (/ x (/ z (+ y t)))
   (if (<= z 1.0) (* x (- (/ y z) t)) (* (/ x z) (+ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+14) {
		tmp = x / (z / (y + t));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x / z) * (y + 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 <= (-8d+14)) then
        tmp = x / (z / (y + t))
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (x / z) * (y + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+14) {
		tmp = x / (z / (y + t));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8e+14:
		tmp = x / (z / (y + t))
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (x / z) * (y + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e+14)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(x / z) * Float64(y + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e+14)
		tmp = x / (z / (y + t));
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (x / z) * (y + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8e+14], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e14

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-/l* 92.3%

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

      3. neg-mul-1 92.3%

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

   4. Simplified 92.3%

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

   if -8e14 < z < 1

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 97.3%

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

      1. associate-*l/ 93.5%

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

      2. associate-*r* 93.5%

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

      3. neg-mul-1 93.5%

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

      4. distribute-rgt-out 93.5%

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

      5. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

   if 1 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/l* 87.1%

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

      3. associate-/r/ 91.1%

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

      4. cancel-sign-sub-inv 91.1%

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

      5. metadata-eval 91.1%

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

      6. *-lft-identity 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]

Alternative 8: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e+14)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 1.0) (* x (- (/ y z) t)) (* (/ x z) (+ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+14) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x / z) * (y + 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 <= (-8d+14)) then
        tmp = x * ((y / z) + (t / z))
    else if (z <= 1.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (x / z) * (y + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+14) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 1.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (x / z) * (y + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8e+14:
		tmp = x * ((y / z) + (t / z))
	elif z <= 1.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (x / z) * (y + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e+14)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(x / z) * Float64(y + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e+14)
		tmp = x * ((y / z) + (t / z));
	elseif (z <= 1.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (x / z) * (y + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8e+14], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e14

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 94.2%

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

      1. associate-*r/ 94.2%

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

      2. neg-mul-1 94.2%

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

   4. Simplified 94.2%

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

   if -8e14 < z < 1

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 97.3%

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

      1. associate-*l/ 93.5%

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

      2. associate-*r* 93.5%

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

      3. neg-mul-1 93.5%

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

      4. distribute-rgt-out 93.5%

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

      5. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

   if 1 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/l* 87.1%

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

      3. associate-/r/ 91.1%

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

      4. cancel-sign-sub-inv 91.1%

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

      5. metadata-eval 91.1%

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

      6. *-lft-identity 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + t\right)\\ \end{array} \]

Alternative 9: 43.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+14) (not (<= z 1.0))) (* t (/ x z)) (- (* t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+14) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = -(t * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+14)) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / z)
    else
        tmp = -(t * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+14) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = -(t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+14) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = -(t * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+14) || !(z <= 1.0))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(-Float64(t * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+14) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = -(t * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+14], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], (-N[(t * x), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < -8e14 or 1 < z

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-/l* 90.0%

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

      3. associate-/r/ 89.0%

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

      4. cancel-sign-sub-inv 89.0%

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

      5. metadata-eval 89.0%

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

      6. *-lft-identity 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in y around 0 49.7%

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

      1. *-commutative 49.7%

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

      2. associate-*l/ 52.5%

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

      3. *-commutative 52.5%

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

   7. Simplified 52.5%

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

   if -8e14 < z < 1

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 32.1%

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

      1. associate-*r/ 32.1%

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

      2. associate-*r* 32.1%

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

      3. neg-mul-1 32.1%

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

      4. associate-*l/ 32.1%

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

      5. *-commutative 32.1%

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

      6. neg-mul-1 32.1%

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

      7. *-commutative 32.1%

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

      8. associate-*r/ 32.1%

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

      9. metadata-eval 32.1%

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

      10. associate-/r* 32.1%

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

      11. neg-mul-1 32.1%

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

      12. associate-*r/ 32.1%

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

      13. *-rgt-identity 32.1%

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

      14. neg-sub0 32.1%

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

      15. associate--r- 32.1%

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

      16. metadata-eval 32.1%

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

   4. Simplified 32.1%

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

   5. Taylor expanded in z around 0 31.6%

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

      1. associate-*r* 31.6%

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

      2. mul-1-neg 31.6%

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

   7. Simplified 31.6%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot x\\ \end{array} \]

Alternative 10: 45.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e+14) (not (<= z 1.0))) (* x (/ t z)) (- (* t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+14) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = -(t * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8d+14)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / z)
    else
        tmp = -(t * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e+14) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = -(t * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e+14) or not (z <= 1.0):
		tmp = x * (t / z)
	else:
		tmp = -(t * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e+14) || !(z <= 1.0))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(-Float64(t * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8e+14) || ~((z <= 1.0)))
		tmp = x * (t / z);
	else
		tmp = -(t * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e+14], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], (-N[(t * x), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < -8e14 or 1 < z

   1. Initial program 92.4%

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

   2. Taylor expanded in y around 0 50.4%

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

      1. associate-*r/ 50.4%

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

      2. associate-*r* 50.4%

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

      3. neg-mul-1 50.4%

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

      4. associate-*l/ 54.9%

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

      5. *-commutative 54.9%

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

      6. neg-mul-1 54.9%

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

      7. *-commutative 54.9%

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

      8. associate-*r/ 54.8%

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

      9. metadata-eval 54.8%

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

      10. associate-/r* 54.8%

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

      11. neg-mul-1 54.8%

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

      12. associate-*r/ 54.9%

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

      13. *-rgt-identity 54.9%

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

      14. neg-sub0 54.9%

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

      15. associate--r- 54.9%

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

      16. metadata-eval 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -8e14 < z < 1

   1. Initial program 94.0%

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

   2. Taylor expanded in y around 0 32.1%

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

      1. associate-*r/ 32.1%

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

      2. associate-*r* 32.1%

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

      3. neg-mul-1 32.1%

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

      4. associate-*l/ 32.1%

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

      5. *-commutative 32.1%

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

      6. neg-mul-1 32.1%

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

      7. *-commutative 32.1%

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

      8. associate-*r/ 32.1%

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

      9. metadata-eval 32.1%

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

      10. associate-/r* 32.1%

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

      11. neg-mul-1 32.1%

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

      12. associate-*r/ 32.1%

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

      13. *-rgt-identity 32.1%

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

      14. neg-sub0 32.1%

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

      15. associate--r- 32.1%

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

      16. metadata-eval 32.1%

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

   4. Simplified 32.1%

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

   5. Taylor expanded in z around 0 31.6%

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

      1. associate-*r* 31.6%

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

      2. mul-1-neg 31.6%

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

   7. Simplified 31.6%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot x\\ \end{array} \]

Alternative 11: 64.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+207}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e+207)
   (- (* t x))
   (if (<= t 1.6e+210) (* y (/ x z)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+207) {
		tmp = -(t * x);
	} else if (t <= 1.6e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x * (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 (t <= (-2.2d+207)) then
        tmp = -(t * x)
    else if (t <= 1.6d+210) then
        tmp = y * (x / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+207) {
		tmp = -(t * x);
	} else if (t <= 1.6e+210) {
		tmp = y * (x / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.2e+207:
		tmp = -(t * x)
	elif t <= 1.6e+210:
		tmp = y * (x / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.2e+207)
		tmp = Float64(-Float64(t * x));
	elseif (t <= 1.6e+210)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.2e+207)
		tmp = -(t * x);
	elseif (t <= 1.6e+210)
		tmp = y * (x / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.2e+207], (-N[(t * x), $MachinePrecision]), If[LessEqual[t, 1.6e+210], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000009e207

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. associate-*r* 79.3%

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

      3. neg-mul-1 79.3%

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

      4. associate-*l/ 91.6%

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

      5. *-commutative 91.6%

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

      6. neg-mul-1 91.6%

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

      7. *-commutative 91.6%

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

      8. associate-*r/ 91.5%

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

      9. metadata-eval 91.5%

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

      10. associate-/r* 91.5%

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

      11. neg-mul-1 91.5%

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

      12. associate-*r/ 91.6%

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

      13. *-rgt-identity 91.6%

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

      14. neg-sub0 91.6%

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

      15. associate--r- 91.6%

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

      16. metadata-eval 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 58.4%

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

      1. associate-*r* 58.4%

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

      2. mul-1-neg 58.4%

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

   7. Simplified 58.4%

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

   if -2.20000000000000009e207 < t < 1.6000000000000001e210

   1. Initial program 92.1%

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

      1. frac-2neg 92.1%

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

      2. div-inv 92.0%

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

      3. fma-neg 92.0%

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

      4. distribute-neg-frac 92.0%

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

   3. Applied egg-rr 92.0%

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

      1. fma-udef 92.0%

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

      2. +-commutative 92.0%

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

      3. distribute-lft-neg-out 92.0%

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

      4. unsub-neg 92.0%

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

      5. neg-mul-1 92.0%

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

      6. *-commutative 92.0%

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

      7. associate-*r/ 92.0%

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

      8. metadata-eval 92.0%

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

      9. associate-/r* 92.0%

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

      10. neg-mul-1 92.0%

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

      11. associate-*r/ 92.0%

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

      12. *-rgt-identity 92.0%

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

      13. neg-sub0 92.0%

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

      14. associate--r- 92.0%

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

      15. metadata-eval 92.0%

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

      16. neg-mul-1 92.0%

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

      17. associate-/r* 92.0%

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

      18. metadata-eval 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in t around 0 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*l/ 71.6%

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

   8. Simplified 71.6%

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

   if 1.6000000000000001e210 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-mul-1 94.4%

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

      7. *-commutative 94.4%

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

      8. associate-*r/ 94.4%

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

      9. metadata-eval 94.4%

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

      10. associate-/r* 94.4%

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

      11. neg-mul-1 94.4%

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

      12. associate-*r/ 94.4%

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

      13. *-rgt-identity 94.4%

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

      14. neg-sub0 94.4%

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

      15. associate--r- 94.4%

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

      16. metadata-eval 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in z around inf 72.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+207}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 12: 64.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+207}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e+207)
   (- (* t x))
   (if (<= t 3.2e+210) (/ (* y x) z) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+207) {
		tmp = -(t * x);
	} else if (t <= 3.2e+210) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (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 (t <= (-1.5d+207)) then
        tmp = -(t * x)
    else if (t <= 3.2d+210) then
        tmp = (y * x) / z
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e+207) {
		tmp = -(t * x);
	} else if (t <= 3.2e+210) {
		tmp = (y * x) / z;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e+207:
		tmp = -(t * x)
	elif t <= 3.2e+210:
		tmp = (y * x) / z
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e+207)
		tmp = Float64(-Float64(t * x));
	elseif (t <= 3.2e+210)
		tmp = Float64(Float64(y * x) / z);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e+207)
		tmp = -(t * x);
	elseif (t <= 3.2e+210)
		tmp = (y * x) / z;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e+207], (-N[(t * x), $MachinePrecision]), If[LessEqual[t, 3.2e+210], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999992e207

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. associate-*r* 79.3%

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

      3. neg-mul-1 79.3%

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

      4. associate-*l/ 91.6%

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

      5. *-commutative 91.6%

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

      6. neg-mul-1 91.6%

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

      7. *-commutative 91.6%

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

      8. associate-*r/ 91.5%

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

      9. metadata-eval 91.5%

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

      10. associate-/r* 91.5%

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

      11. neg-mul-1 91.5%

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

      12. associate-*r/ 91.6%

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

      13. *-rgt-identity 91.6%

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

      14. neg-sub0 91.6%

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

      15. associate--r- 91.6%

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

      16. metadata-eval 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in z around 0 58.4%

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

      1. associate-*r* 58.4%

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

      2. mul-1-neg 58.4%

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

   7. Simplified 58.4%

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

   if -1.49999999999999992e207 < t < 3.2000000000000002e210

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 74.4%

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

   if 3.2000000000000002e210 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. associate-*r* 73.6%

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

      3. neg-mul-1 73.6%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-mul-1 94.4%

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

      7. *-commutative 94.4%

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

      8. associate-*r/ 94.4%

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

      9. metadata-eval 94.4%

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

      10. associate-/r* 94.4%

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

      11. neg-mul-1 94.4%

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

      12. associate-*r/ 94.4%

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

      13. *-rgt-identity 94.4%

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

      14. neg-sub0 94.4%

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

      15. associate--r- 94.4%

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

      16. metadata-eval 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in z around inf 72.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+207}:\\ \;\;\;\;-t \cdot x\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+210}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 13: 23.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ -t \cdot x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

2. Taylor expanded in y around 0 40.0%

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

   1. associate-*r/ 40.0%

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

   2. associate-*r* 40.0%

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

   3. neg-mul-1 40.0%

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

   4. associate-*l/ 42.0%

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

   5. *-commutative 42.0%

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

   6. neg-mul-1 42.0%

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

   7. *-commutative 42.0%

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

   8. associate-*r/ 42.0%

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

   9. metadata-eval 42.0%

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

   10. associate-/r* 42.0%

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

   11. neg-mul-1 42.0%

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

   12. associate-*r/ 42.0%

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

   13. *-rgt-identity 42.0%

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

   14. neg-sub0 42.0%

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

   15. associate--r- 42.0%

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

   16. metadata-eval 42.0%

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

4. Simplified 42.0%

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

5. Taylor expanded in z around 0 23.0%

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

   1. associate-*r* 23.0%

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

   2. mul-1-neg 23.0%

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

7. Simplified 23.0%

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

8. Final simplification 23.0%

   \[\leadsto -t \cdot x \]

Developer target: 95.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(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)))))