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

Percentage Accurate: 94.5% → 95.5%

Time: 8.8s

Alternatives: 12

Speedup: 0.5×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (+ z -1.0))) (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_2 (- INFINITY)) (* t_1 (/ (* x (+ z (/ y t_1))) z)) t_2)))

C

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

Java

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

Python

def code(x, y, z, t):
	t_1 = t / (z + -1.0)
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 * ((x * (z + (y / t_1))) / z)
	else:
		tmp = t_2
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 81.0%

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

      1. frac-2neg 81.0%

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

      2. clear-num 81.0%

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

      3. frac-sub 77.7%

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

      4. fma-neg 77.7%

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

   3. Applied egg-rr 77.7%

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

      1. associate-*r/ 74.4%

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

      2. associate-/r/ 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 96.6%

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

      1. *-commutative 96.6%

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

      2. times-frac 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. associate-/l* 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

   8. Simplified 99.8%

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

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

   1. Initial program 97.0%

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

4. Final simplification 97.3%

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

Alternative 2: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+289}:\\ \;\;\;\;x \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+289) (* x t_1) (/ 1.0 (/ (/ z x) (+ 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 <= 2e+289) {
		tmp = x * t_1;
	} else {
		tmp = 1.0 / ((z / x) / (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) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 2d+289) then
        tmp = x * t_1
    else
        tmp = 1.0d0 / ((z / x) / (y + t))
    end if
    code = tmp
end function

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 <= 2e+289) {
		tmp = x * t_1;
	} else {
		tmp = 1.0 / ((z / x) / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 2e+289:
		tmp = x * t_1
	else:
		tmp = 1.0 / ((z / x) / (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 <= 2e+289)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(1.0 / Float64(Float64(z / x) / 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 <= 2e+289)
		tmp = x * t_1;
	else
		tmp = 1.0 / ((z / x) / (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, 2e+289], N[(x * t$95$1), $MachinePrecision], N[(1.0 / N[(N[(z / x), $MachinePrecision] / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 2.0000000000000001e289

   1. Initial program 96.7%

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

   if 2.0000000000000001e289 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 76.2%

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

   2. Taylor expanded in z around inf 76.2%

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

      1. cancel-sign-sub-inv 76.2%

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

      2. metadata-eval 76.2%

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

      3. *-lft-identity 76.2%

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

      4. +-commutative 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. +-commutative 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/r* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} - \frac{t}{1 - z} \leq 2 \cdot 10^{+289}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y + t}}\\ \end{array} \]

Alternative 3: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+175} \lor \neg \left(t \leq 4.5 \cdot 10^{+203}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- t))))
   (if (<= t -5.8e+181)
     t_1
     (if (<= t 1.95e+111)
       (* x (/ y z))
       (if (or (<= t 5.4e+175) (not (<= t 4.5e+203))) t_1 (* y (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double tmp;
	if (t <= -5.8e+181) {
		tmp = t_1;
	} else if (t <= 1.95e+111) {
		tmp = x * (y / z);
	} else if ((t <= 5.4e+175) || !(t <= 4.5e+203)) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -t
    if (t <= (-5.8d+181)) then
        tmp = t_1
    else if (t <= 1.95d+111) then
        tmp = x * (y / z)
    else if ((t <= 5.4d+175) .or. (.not. (t <= 4.5d+203))) then
        tmp = t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double tmp;
	if (t <= -5.8e+181) {
		tmp = t_1;
	} else if (t <= 1.95e+111) {
		tmp = x * (y / z);
	} else if ((t <= 5.4e+175) || !(t <= 4.5e+203)) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -t
	tmp = 0
	if t <= -5.8e+181:
		tmp = t_1
	elif t <= 1.95e+111:
		tmp = x * (y / z)
	elif (t <= 5.4e+175) or not (t <= 4.5e+203):
		tmp = t_1
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-t))
	tmp = 0.0
	if (t <= -5.8e+181)
		tmp = t_1;
	elseif (t <= 1.95e+111)
		tmp = Float64(x * Float64(y / z));
	elseif ((t <= 5.4e+175) || !(t <= 4.5e+203))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -t;
	tmp = 0.0;
	if (t <= -5.8e+181)
		tmp = t_1;
	elseif (t <= 1.95e+111)
		tmp = x * (y / z);
	elseif ((t <= 5.4e+175) || ~((t <= 4.5e+203)))
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-t)), $MachinePrecision]}, If[LessEqual[t, -5.8e+181], t$95$1, If[LessEqual[t, 1.95e+111], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 5.4e+175], N[Not[LessEqual[t, 4.5e+203]], $MachinePrecision]], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8e181 or 1.9499999999999999e111 < t < 5.4000000000000002e175 or 4.5000000000000003e203 < t

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0 55.9%

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

      1. +-commutative 55.9%

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

      2. associate-*r/ 54.3%

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

      3. *-commutative 54.3%

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

      4. associate-*r* 54.3%

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

      5. neg-mul-1 54.3%

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

      6. distribute-rgt-out 56.1%

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

      7. unsub-neg 56.1%

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

   4. Simplified 56.1%

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

   5. Taylor expanded in y around 0 50.4%

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

      1. associate-*r* 50.4%

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

      2. neg-mul-1 50.4%

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

   7. Simplified 50.4%

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

   if -5.8e181 < t < 1.9499999999999999e111

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. associate-*r/ 72.2%

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

   4. Simplified 72.2%

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

   if 5.4000000000000002e175 < t < 4.5000000000000003e203

   1. Initial program 74.0%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. cancel-sign-sub-inv 65.0%

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

      2. metadata-eval 65.0%

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

      3. *-lft-identity 65.0%

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

      4. +-commutative 65.0%

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

   4. Simplified 65.0%

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

      1. associate-*r/ 73.9%

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

      2. +-commutative 73.9%

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

      3. *-un-lft-identity 73.9%

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

      4. metadata-eval 73.9%

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

      5. cancel-sign-sub-inv 73.9%

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

      6. associate-/l* 67.2%

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

      7. cancel-sign-sub-inv 67.2%

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

      8. metadata-eval 67.2%

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

      9. *-un-lft-identity 67.2%

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

      10. +-commutative 67.2%

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

   6. Applied egg-rr 67.2%

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

   7. Taylor expanded in t around 0 57.8%

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

      1. associate-*l/ 56.1%

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

      2. *-commutative 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+175} \lor \neg \left(t \leq 4.5 \cdot 10^{+203}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{+111}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.65e+39)
     t_1
     (if (<= t 1e+111) (* x (/ y z)) (if (<= t 1.32e+171) (* x (- t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.65e+39) {
		tmp = t_1;
	} else if (t <= 1e+111) {
		tmp = x * (y / z);
	} else if (t <= 1.32e+171) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (t <= (-2.65d+39)) then
        tmp = t_1
    else if (t <= 1d+111) then
        tmp = x * (y / z)
    else if (t <= 1.32d+171) then
        tmp = x * -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.65e+39) {
		tmp = t_1;
	} else if (t <= 1e+111) {
		tmp = x * (y / z);
	} else if (t <= 1.32e+171) {
		tmp = x * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.65e+39:
		tmp = t_1
	elif t <= 1e+111:
		tmp = x * (y / z)
	elif t <= 1.32e+171:
		tmp = x * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -2.65e+39)
		tmp = t_1;
	elseif (t <= 1e+111)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 1.32e+171)
		tmp = Float64(x * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (t <= -2.65e+39)
		tmp = t_1;
	elseif (t <= 1e+111)
		tmp = x * (y / z);
	elseif (t <= 1.32e+171)
		tmp = x * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.65e+39], t$95$1, If[LessEqual[t, 1e+111], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e+171], N[(x * (-t)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.64999999999999989e39 or 1.32000000000000009e171 < t

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. cancel-sign-sub-inv 68.9%

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

      2. metadata-eval 68.9%

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

      3. *-lft-identity 68.9%

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

      4. +-commutative 68.9%

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

   4. Simplified 68.9%

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

   5. Taylor expanded in t around inf 50.1%

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

      1. associate-/l* 46.5%

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

   7. Simplified 46.5%

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

      1. associate-/r/ 58.9%

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

   9. Applied egg-rr 58.9%

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

   if -2.64999999999999989e39 < t < 9.99999999999999957e110

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 78.7%

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

   4. Simplified 78.7%

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

   if 9.99999999999999957e110 < t < 1.32000000000000009e171

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*r/ 68.1%

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

      3. *-commutative 68.1%

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

      4. associate-*r* 68.1%

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

      5. neg-mul-1 68.1%

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

      6. distribute-rgt-out 68.1%

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

      7. unsub-neg 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in y around 0 62.5%

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

      1. associate-*r* 62.5%

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

      2. neg-mul-1 62.5%

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

   7. Simplified 62.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 10^{+111}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.4e+36)
   (/ x (/ z t))
   (if (<= t 7.2e+110)
     (* x (/ y z))
     (if (<= t 2.3e+171) (* x (- t)) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.4e+36) {
		tmp = x / (z / t);
	} else if (t <= 7.2e+110) {
		tmp = x * (y / z);
	} else if (t <= 2.3e+171) {
		tmp = x * -t;
	} 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 <= (-4.4d+36)) then
        tmp = x / (z / t)
    else if (t <= 7.2d+110) then
        tmp = x * (y / z)
    else if (t <= 2.3d+171) then
        tmp = x * -t
    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 <= -4.4e+36) {
		tmp = x / (z / t);
	} else if (t <= 7.2e+110) {
		tmp = x * (y / z);
	} else if (t <= 2.3e+171) {
		tmp = x * -t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.4e+36:
		tmp = x / (z / t)
	elif t <= 7.2e+110:
		tmp = x * (y / z)
	elif t <= 2.3e+171:
		tmp = x * -t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.4e+36)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 7.2e+110)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 2.3e+171)
		tmp = Float64(x * Float64(-t));
	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 <= -4.4e+36)
		tmp = x / (z / t);
	elseif (t <= 7.2e+110)
		tmp = x * (y / z);
	elseif (t <= 2.3e+171)
		tmp = x * -t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.4e+36], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+110], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+171], N[(x * (-t)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.40000000000000001e36

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 67.6%

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

      1. cancel-sign-sub-inv 67.6%

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

      2. metadata-eval 67.6%

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

      3. *-lft-identity 67.6%

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

      4. +-commutative 67.6%

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

   4. Simplified 67.6%

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

      1. associate-*r/ 59.2%

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

      2. +-commutative 59.2%

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

      3. *-un-lft-identity 59.2%

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

      4. metadata-eval 59.2%

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

      5. cancel-sign-sub-inv 59.2%

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

      6. associate-/l* 67.6%

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

      7. cancel-sign-sub-inv 67.6%

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

      8. metadata-eval 67.6%

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

      9. *-un-lft-identity 67.6%

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

      10. +-commutative 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in t around inf 55.6%

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

   if -4.40000000000000001e36 < t < 7.1999999999999994e110

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 78.7%

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

   4. Simplified 78.7%

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

   if 7.1999999999999994e110 < t < 2.30000000000000017e171

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 73.3%

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

      1. +-commutative 73.3%

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

      2. associate-*r/ 68.1%

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

      3. *-commutative 68.1%

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

      4. associate-*r* 68.1%

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

      5. neg-mul-1 68.1%

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

      6. distribute-rgt-out 68.1%

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

      7. unsub-neg 68.1%

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

   4. Simplified 68.1%

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

   5. Taylor expanded in y around 0 62.5%

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

      1. associate-*r* 62.5%

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

      2. neg-mul-1 62.5%

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

   7. Simplified 62.5%

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

   if 2.30000000000000017e171 < t

   1. Initial program 90.3%

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

   2. Taylor expanded in z around inf 70.9%

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

      1. cancel-sign-sub-inv 70.9%

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

      2. metadata-eval 70.9%

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

      3. *-lft-identity 70.9%

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

      4. +-commutative 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in t around inf 51.7%

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

      1. associate-/l* 48.7%

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

   7. Simplified 48.7%

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

      1. associate-/r/ 64.0%

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

   9. Applied egg-rr 64.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e+39)
   (/ x (/ z t))
   (if (<= t 7e+104)
     (/ x (/ z y))
     (if (<= t 1.2e+171) (* x (- t)) (* x (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e+39) {
		tmp = x / (z / t);
	} else if (t <= 7e+104) {
		tmp = x / (z / y);
	} else if (t <= 1.2e+171) {
		tmp = x * -t;
	} 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 <= (-4.2d+39)) then
        tmp = x / (z / t)
    else if (t <= 7d+104) then
        tmp = x / (z / y)
    else if (t <= 1.2d+171) then
        tmp = x * -t
    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 <= -4.2e+39) {
		tmp = x / (z / t);
	} else if (t <= 7e+104) {
		tmp = x / (z / y);
	} else if (t <= 1.2e+171) {
		tmp = x * -t;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e+39:
		tmp = x / (z / t)
	elif t <= 7e+104:
		tmp = x / (z / y)
	elif t <= 1.2e+171:
		tmp = x * -t
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e+39)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 7e+104)
		tmp = Float64(x / Float64(z / y));
	elseif (t <= 1.2e+171)
		tmp = Float64(x * Float64(-t));
	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 <= -4.2e+39)
		tmp = x / (z / t);
	elseif (t <= 7e+104)
		tmp = x / (z / y);
	elseif (t <= 1.2e+171)
		tmp = x * -t;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e+39], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+104], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+171], N[(x * (-t)), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.1999999999999997e39

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 67.6%

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

      1. cancel-sign-sub-inv 67.6%

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

      2. metadata-eval 67.6%

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

      3. *-lft-identity 67.6%

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

      4. +-commutative 67.6%

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

   4. Simplified 67.6%

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

      1. associate-*r/ 59.2%

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

      2. +-commutative 59.2%

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

      3. *-un-lft-identity 59.2%

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

      4. metadata-eval 59.2%

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

      5. cancel-sign-sub-inv 59.2%

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

      6. associate-/l* 67.6%

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

      7. cancel-sign-sub-inv 67.6%

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

      8. metadata-eval 67.6%

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

      9. *-un-lft-identity 67.6%

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

      10. +-commutative 67.6%

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

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in t around inf 55.6%

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

   if -4.1999999999999997e39 < t < 7.0000000000000003e104

   1. Initial program 94.7%

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

      1. frac-2neg 94.7%

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

      2. div-inv 94.6%

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

      3. fma-neg 94.6%

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

      4. distribute-neg-frac 94.6%

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

   3. Applied egg-rr 94.6%

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

      1. fma-udef 94.6%

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

      2. +-commutative 94.6%

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

      3. distribute-lft-neg-out 94.6%

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

      4. unsub-neg 94.6%

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

      5. neg-mul-1 94.6%

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

      6. *-commutative 94.6%

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

      7. associate-*r/ 94.6%

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

      8. metadata-eval 94.6%

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

      9. associate-/r* 94.6%

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

      10. neg-mul-1 94.6%

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

      11. associate-*r/ 94.6%

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

      12. *-rgt-identity 94.6%

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

      13. neg-sub0 94.6%

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

      14. associate--r- 94.6%

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

      15. metadata-eval 94.6%

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

      16. neg-mul-1 94.6%

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

      17. associate-/r* 94.6%

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

      18. metadata-eval 94.6%

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

   5. Simplified 94.6%

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

   6. Taylor expanded in t around 0 76.0%

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

      1. associate-/l* 79.4%

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

   8. Simplified 79.4%

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

   if 7.0000000000000003e104 < t < 1.19999999999999999e171

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 75.9%

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

      1. +-commutative 75.9%

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

      2. associate-*r/ 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-*r* 71.3%

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

      5. neg-mul-1 71.3%

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

      6. distribute-rgt-out 71.3%

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

      7. unsub-neg 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in y around 0 61.3%

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

      1. associate-*r* 61.3%

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

      2. neg-mul-1 61.3%

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

   7. Simplified 61.3%

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

   if 1.19999999999999999e171 < t

   1. Initial program 90.3%

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

   2. Taylor expanded in z around inf 70.9%

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

      1. cancel-sign-sub-inv 70.9%

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

      2. metadata-eval 70.9%

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

      3. *-lft-identity 70.9%

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

      4. +-commutative 70.9%

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

   4. Simplified 70.9%

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

   5. Taylor expanded in t around inf 51.7%

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

      1. associate-/l* 48.7%

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

   7. Simplified 48.7%

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

      1. associate-/r/ 64.0%

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

   9. Applied egg-rr 64.0%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 48:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+72)
   (/ x (/ z t))
   (if (<= z 48.0)
     (* x (- (/ y z) t))
     (if (<= z 2.3e+84) (* x (/ t z)) (* x (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+72) {
		tmp = x / (z / t);
	} else if (z <= 48.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 2.3e+84) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.7d+72)) then
        tmp = x / (z / t)
    else if (z <= 48.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 2.3d+84) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+72) {
		tmp = x / (z / t);
	} else if (z <= 48.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 2.3e+84) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+72:
		tmp = x / (z / t)
	elif z <= 48.0:
		tmp = x * ((y / z) - t)
	elif z <= 2.3e+84:
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+72)
		tmp = Float64(x / Float64(z / t));
	elseif (z <= 48.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 2.3e+84)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e+72)
		tmp = x / (z / t);
	elseif (z <= 48.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 2.3e+84)
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+72], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 48.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+84], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6999999999999999e72

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 97.6%

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

      1. cancel-sign-sub-inv 97.6%

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

      2. metadata-eval 97.6%

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

      3. *-lft-identity 97.6%

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

      4. +-commutative 97.6%

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

   4. Simplified 97.6%

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

      1. associate-*r/ 77.7%

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

      2. +-commutative 77.7%

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

      3. *-un-lft-identity 77.7%

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

      4. metadata-eval 77.7%

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

      5. cancel-sign-sub-inv 77.7%

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

      6. associate-/l* 97.6%

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

      7. cancel-sign-sub-inv 97.6%

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

      8. metadata-eval 97.6%

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

      9. *-un-lft-identity 97.6%

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

      10. +-commutative 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in t around inf 64.8%

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

   if -1.6999999999999999e72 < z < 48

   1. Initial program 94.4%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. associate-*r/ 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r* 89.3%

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

      5. neg-mul-1 89.3%

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

      6. distribute-rgt-out 90.6%

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

      7. unsub-neg 90.6%

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

   4. Simplified 90.6%

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

   if 48 < z < 2.2999999999999999e84

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 99.6%

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

      1. cancel-sign-sub-inv 99.6%

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

      2. metadata-eval 99.6%

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

      3. *-lft-identity 99.6%

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

      4. +-commutative 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in t around inf 73.3%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

      1. associate-/r/ 73.5%

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

   9. Applied egg-rr 73.5%

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

   if 2.2999999999999999e84 < z

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 54.6%

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

      1. associate-*r/ 59.2%

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

   4. Simplified 59.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 48:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 8: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+39} \lor \neg \left(t \leq 1.16 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e+39) (not (<= t 1.16e+71)))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+39) || !(t <= 1.16e+71)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.1d+39)) .or. (.not. (t <= 1.16d+71))) then
        tmp = x * (t / (z + (-1.0d0)))
    else
        tmp = x / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+39) || !(t <= 1.16e+71)) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.1e+39) or not (t <= 1.16e+71):
		tmp = x * (t / (z + -1.0))
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.1e+39) || !(t <= 1.16e+71))
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.1e+39) || ~((t <= 1.16e+71)))
		tmp = x * (t / (z + -1.0));
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.1e+39], N[Not[LessEqual[t, 1.16e+71]], $MachinePrecision]], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000003e39 or 1.1599999999999999e71 < t

   1. Initial program 96.0%

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

   2. Taylor expanded in y around 0 69.5%

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

      1. associate-*r/ 69.5%

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

      2. associate-*r* 69.5%

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

      3. neg-mul-1 69.5%

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

      4. associate-*l/ 77.0%

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

      5. *-commutative 77.0%

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

      6. distribute-frac-neg 77.0%

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

      7. mul-1-neg 77.0%

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

      8. associate-*r/ 77.0%

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

      9. *-commutative 77.0%

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

      10. associate-*r/ 76.9%

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

      11. metadata-eval 76.9%

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

      12. associate-/r* 76.9%

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

      13. neg-mul-1 76.9%

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

      14. associate-*r/ 77.0%

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

      15. *-rgt-identity 77.0%

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

      16. neg-sub0 77.0%

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

      17. associate--r- 77.0%

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

      18. metadata-eval 77.0%

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

   4. Simplified 77.0%

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

   if -3.1000000000000003e39 < t < 1.1599999999999999e71

   1. Initial program 94.5%

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

      1. frac-2neg 94.5%

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

      2. div-inv 94.4%

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

      3. fma-neg 94.4%

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

      4. distribute-neg-frac 94.4%

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

   3. Applied egg-rr 94.4%

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

      1. fma-udef 94.4%

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

      2. +-commutative 94.4%

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

      3. distribute-lft-neg-out 94.4%

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

      4. unsub-neg 94.4%

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

      5. neg-mul-1 94.4%

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

      6. *-commutative 94.4%

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

      7. associate-*r/ 94.4%

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

      8. metadata-eval 94.4%

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

      9. associate-/r* 94.4%

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

      10. neg-mul-1 94.4%

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

      11. associate-*r/ 94.4%

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

      12. *-rgt-identity 94.4%

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

      13. neg-sub0 94.4%

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

      14. associate--r- 94.4%

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

      15. metadata-eval 94.4%

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

      16. neg-mul-1 94.4%

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

      17. associate-/r* 94.4%

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

      18. metadata-eval 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in t around 0 78.1%

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

      1. associate-/l* 81.0%

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

   8. Simplified 81.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+39} \lor \neg \left(t \leq 1.16 \cdot 10^{+71}\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 9: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700 \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1700.0) (not (<= z 5.8e-8)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1700.0) || !(z <= 5.8e-8)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1700.0d0)) .or. (.not. (z <= 5.8d-8))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1700.0) || !(z <= 5.8e-8)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1700.0) or not (z <= 5.8e-8):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1700.0) || !(z <= 5.8e-8))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1700.0) || ~((z <= 5.8e-8)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1700.0], N[Not[LessEqual[z, 5.8e-8]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1700 or 5.8000000000000003e-8 < z

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 96.2%

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

      1. cancel-sign-sub-inv 96.2%

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

      2. metadata-eval 96.2%

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

      3. *-lft-identity 96.2%

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

      4. +-commutative 96.2%

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

   4. Simplified 96.2%

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

   if -1700 < z < 5.8000000000000003e-8

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*r* 91.5%

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

      5. neg-mul-1 91.5%

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

      6. distribute-rgt-out 92.9%

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

      7. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700 \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 10: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1700.0)
   (/ x (/ z (+ y t)))
   (if (<= z 5.8e-8) (* x (- (/ y z) t)) (* x (/ (+ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1700.0) {
		tmp = x / (z / (y + t));
	} else if (z <= 5.8e-8) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1700.0d0)) then
        tmp = x / (z / (y + t))
    else if (z <= 5.8d-8) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * ((y + t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1700.0) {
		tmp = x / (z / (y + t));
	} else if (z <= 5.8e-8) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * ((y + t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1700.0:
		tmp = x / (z / (y + t))
	elif z <= 5.8e-8:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * ((y + t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1700.0)
		tmp = Float64(x / Float64(z / Float64(y + t)));
	elseif (z <= 5.8e-8)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(Float64(y + t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1700.0)
		tmp = x / (z / (y + t));
	elseif (z <= 5.8e-8)
		tmp = x * ((y / z) - t);
	else
		tmp = x * ((y + t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1700.0], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-8], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1700

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 97.3%

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

      1. cancel-sign-sub-inv 97.3%

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

      2. metadata-eval 97.3%

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

      3. *-lft-identity 97.3%

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

      4. +-commutative 97.3%

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

   4. Simplified 97.3%

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

      1. associate-*r/ 81.9%

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

      2. +-commutative 81.9%

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

      3. *-un-lft-identity 81.9%

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

      4. metadata-eval 81.9%

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

      5. cancel-sign-sub-inv 81.9%

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

      6. associate-/l* 97.3%

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

      7. cancel-sign-sub-inv 97.3%

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

      8. metadata-eval 97.3%

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

      9. *-un-lft-identity 97.3%

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

      10. +-commutative 97.3%

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

   6. Applied egg-rr 97.3%

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

   if -1700 < z < 5.8000000000000003e-8

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-*r/ 91.5%

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

      3. *-commutative 91.5%

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

      4. associate-*r* 91.5%

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

      5. neg-mul-1 91.5%

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

      6. distribute-rgt-out 92.9%

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

      7. unsub-neg 92.9%

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

   4. Simplified 92.9%

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

   if 5.8000000000000003e-8 < z

   1. Initial program 95.0%

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

   2. Taylor expanded in z around inf 95.0%

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

      1. cancel-sign-sub-inv 95.0%

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

      2. metadata-eval 95.0%

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

      3. *-lft-identity 95.0%

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

      4. +-commutative 95.0%

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

   4. Simplified 95.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \end{array} \]

Alternative 11: 64.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+182} \lor \neg \left(t \leq 3.9 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e+182) (not (<= t 3.9e+111))) (* x (- t)) (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+182) || !(t <= 3.9e+111)) {
		tmp = x * -t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.05d+182)) .or. (.not. (t <= 3.9d+111))) then
        tmp = x * -t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+182) || !(t <= 3.9e+111)) {
		tmp = x * -t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e+182) or not (t <= 3.9e+111):
		tmp = x * -t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e+182) || !(t <= 3.9e+111))
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e+182) || ~((t <= 3.9e+111)))
		tmp = x * -t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e+182], N[Not[LessEqual[t, 3.9e+111]], $MachinePrecision]], N[(x * (-t)), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.0499999999999999e182 or 3.89999999999999979e111 < t

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 54.4%

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

      1. +-commutative 54.4%

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

      2. associate-*r/ 48.8%

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

      3. *-commutative 48.8%

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

      4. associate-*r* 48.8%

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

      5. neg-mul-1 48.8%

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

      6. distribute-rgt-out 51.8%

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

      7. unsub-neg 51.8%

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

   4. Simplified 51.8%

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

   5. Taylor expanded in y around 0 44.1%

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

      1. associate-*r* 44.1%

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

      2. neg-mul-1 44.1%

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

   7. Simplified 44.1%

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

   if -1.0499999999999999e182 < t < 3.89999999999999979e111

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 69.2%

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

      1. associate-*r/ 72.2%

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

   4. Simplified 72.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+182} \lor \neg \left(t \leq 3.9 \cdot 10^{+111}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12: 23.3% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

2. Taylor expanded in z around 0 65.5%

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

   1. +-commutative 65.5%

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

   2. associate-*r/ 66.5%

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

   3. *-commutative 66.5%

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

   4. associate-*r* 66.5%

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

   5. neg-mul-1 66.5%

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

   6. distribute-rgt-out 67.6%

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

   7. unsub-neg 67.6%

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

4. Simplified 67.6%

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

5. Taylor expanded in y around 0 22.1%

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

   1. associate-*r* 22.1%

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

   2. neg-mul-1 22.1%

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

7. Simplified 22.1%

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

8. Final simplification 22.1%

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

Developer target: 95.0% 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 2023271 
(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)))))