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

Percentage Accurate: 94.1% → 96.5%

Time: 7.3s

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: 94.1% 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: 96.5% accurate, 0.5× speedup

Math

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

FPCore

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

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) * (1.0 / z);
	} else {
		tmp = t_1 * x;
	}
	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) * (1.0 / z);
	} else {
		tmp = t_1 * x;
	}
	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) * (1.0 / z)
	else:
		tmp = t_1 * x
	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(Float64(y * x) * Float64(1.0 / z));
	else
		tmp = Float64(t_1 * x);
	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) * (1.0 / z);
	else
		tmp = t_1 * x;
	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[(N[(y * x), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 60.9%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. associate-/l* 63.0%

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

   4. Simplified 63.0%

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

      1. associate-/l* 99.7%

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

      2. div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

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

   1. Initial program 97.6%

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

4. Final simplification 97.7%

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

Alternative 2: 68.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -4.8e+145)
     t_1
     (if (<= t -3.4e-279)
       (* y (/ x z))
       (if (<= t 1.05e+133) (/ x (/ z y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -4.8e+145) {
		tmp = t_1;
	} else if (t <= -3.4e-279) {
		tmp = y * (x / z);
	} else if (t <= 1.05e+133) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-4.8d+145)) then
        tmp = t_1
    else if (t <= (-3.4d-279)) then
        tmp = y * (x / z)
    else if (t <= 1.05d+133) then
        tmp = x / (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -4.8e+145) {
		tmp = t_1;
	} else if (t <= -3.4e-279) {
		tmp = y * (x / z);
	} else if (t <= 1.05e+133) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -4.8e+145:
		tmp = t_1
	elif t <= -3.4e-279:
		tmp = y * (x / z)
	elif t <= 1.05e+133:
		tmp = x / (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -4.8e+145)
		tmp = t_1;
	elseif (t <= -3.4e-279)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 1.05e+133)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -4.8e+145)
		tmp = t_1;
	elseif (t <= -3.4e-279)
		tmp = y * (x / z);
	elseif (t <= 1.05e+133)
		tmp = x / (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+145], t$95$1, If[LessEqual[t, -3.4e-279], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+133], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.79999999999999984e145 or 1.05e133 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 60.7%

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

      1. associate-/l* 73.4%

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

      2. cancel-sign-sub-inv 73.4%

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

      3. metadata-eval 73.4%

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

      4. *-lft-identity 73.4%

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

      5. +-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around inf 62.2%

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

   if -4.79999999999999984e145 < t < -3.40000000000000015e-279

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 70.4%

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

      2. associate-/r/ 74.7%

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

   4. Simplified 74.7%

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

   if -3.40000000000000015e-279 < t < 1.05e133

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 70.5%

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

      1. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 3: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -3.6e+145)
     t_1
     (if (<= t -5e-270)
       (/ y (/ z x))
       (if (<= t 1.6e+131) (/ x (/ z y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -3.6e+145) {
		tmp = t_1;
	} else if (t <= -5e-270) {
		tmp = y / (z / x);
	} else if (t <= 1.6e+131) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-3.6d+145)) then
        tmp = t_1
    else if (t <= (-5d-270)) then
        tmp = y / (z / x)
    else if (t <= 1.6d+131) then
        tmp = x / (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -3.6e+145) {
		tmp = t_1;
	} else if (t <= -5e-270) {
		tmp = y / (z / x);
	} else if (t <= 1.6e+131) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -3.6e+145:
		tmp = t_1
	elif t <= -5e-270:
		tmp = y / (z / x)
	elif t <= 1.6e+131:
		tmp = x / (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -3.6e+145)
		tmp = t_1;
	elseif (t <= -5e-270)
		tmp = Float64(y / Float64(z / x));
	elseif (t <= 1.6e+131)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -3.6e+145)
		tmp = t_1;
	elseif (t <= -5e-270)
		tmp = y / (z / x);
	elseif (t <= 1.6e+131)
		tmp = x / (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+145], t$95$1, If[LessEqual[t, -5e-270], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+131], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999974e145 or 1.6000000000000001e131 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 60.7%

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

      1. associate-/l* 73.4%

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

      2. cancel-sign-sub-inv 73.4%

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

      3. metadata-eval 73.4%

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

      4. *-lft-identity 73.4%

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

      5. +-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around inf 62.2%

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

   if -3.59999999999999974e145 < t < -4.9999999999999998e-270

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. associate-/l* 70.4%

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

      2. associate-/r/ 74.7%

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

   4. Simplified 74.7%

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

      1. *-commutative 74.7%

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

      2. clear-num 74.1%

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

      3. un-div-inv 74.9%

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

   6. Applied egg-rr 74.9%

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

   if -4.9999999999999998e-270 < t < 1.6000000000000001e131

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf 70.5%

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

      1. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-270}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 4: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.25e+22) (not (<= z 0.00059)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.25e+22) || !(z <= 0.00059)) {
		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 <= (-2.25d+22)) .or. (.not. (z <= 0.00059d0))) 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 <= -2.25e+22) || !(z <= 0.00059)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.25e+22) or not (z <= 0.00059):
		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 <= -2.25e+22) || !(z <= 0.00059))
		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 <= -2.25e+22) || ~((z <= 0.00059)))
		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, -2.25e+22], N[Not[LessEqual[z, 0.00059]], $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 < -2.2499999999999999e22 or 5.9000000000000003e-4 < z

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 97.1%

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

      1. cancel-sign-sub-inv 97.1%

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

      2. metadata-eval 97.1%

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

      3. *-lft-identity 97.1%

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

      4. +-commutative 97.1%

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

   4. Simplified 97.1%

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

   if -2.2499999999999999e22 < z < 5.9000000000000003e-4

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r* 88.0%

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

      5. neg-mul-1 88.0%

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

      6. distribute-rgt-out 93.7%

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

      7. unsub-neg 93.7%

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

   4. Simplified 93.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 5: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+42)
   (* x (/ t z))
   (if (<= z 0.00059) (* x (- (/ y z) t)) (/ x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+42) {
		tmp = x * (t / z);
	} else if (z <= 0.00059) {
		tmp = x * ((y / z) - t);
	} 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 (z <= (-2.2d+42)) then
        tmp = x * (t / z)
    else if (z <= 0.00059d0) then
        tmp = x * ((y / z) - t)
    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 (z <= -2.2e+42) {
		tmp = x * (t / z);
	} else if (z <= 0.00059) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+42:
		tmp = x * (t / z)
	elif z <= 0.00059:
		tmp = x * ((y / z) - t)
	else:
		tmp = x / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = Float64(x * Float64(t / z));
	elseif (z <= 0.00059)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = x * (t / z);
	elseif (z <= 0.00059)
		tmp = x * ((y / z) - t);
	else
		tmp = x / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+42], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00059], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e42

   1. Initial program 97.7%

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

   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. Taylor expanded in t around inf 70.8%

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

   if -2.2000000000000001e42 < z < 5.9000000000000003e-4

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. associate-*r/ 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-*r* 87.7%

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

      5. neg-mul-1 87.7%

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

      6. distribute-rgt-out 93.2%

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

      7. unsub-neg 93.2%

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

   4. Simplified 93.2%

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

   if 5.9000000000000003e-4 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in y around inf 52.4%

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

      1. associate-/l* 60.4%

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

   4. Simplified 60.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 6: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+22)
   (* x (/ (+ y t) z))
   (if (<= z 0.00059) (* x (- (/ y z) t)) (/ x (/ z (+ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+22) {
		tmp = x * ((y + t) / z);
	} else if (z <= 0.00059) {
		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 <= (-2.25d+22)) then
        tmp = x * ((y + t) / z)
    else if (z <= 0.00059d0) 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 <= -2.25e+22) {
		tmp = x * ((y + t) / z);
	} else if (z <= 0.00059) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+22:
		tmp = x * ((y + t) / z)
	elif z <= 0.00059:
		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 <= -2.25e+22)
		tmp = Float64(x * Float64(Float64(y + t) / z));
	elseif (z <= 0.00059)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.25e+22)
		tmp = x * ((y + t) / z);
	elseif (z <= 0.00059)
		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, -2.25e+22], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00059], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e22

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 97.8%

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

      1. cancel-sign-sub-inv 97.8%

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

      2. metadata-eval 97.8%

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

      3. *-lft-identity 97.8%

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

      4. +-commutative 97.8%

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

   4. Simplified 97.8%

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

   if -2.2499999999999999e22 < z < 5.9000000000000003e-4

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r* 88.0%

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

      5. neg-mul-1 88.0%

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

      6. distribute-rgt-out 93.7%

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

      7. unsub-neg 93.7%

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

   4. Simplified 93.7%

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

   if 5.9000000000000003e-4 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-/l* 96.5%

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

      2. cancel-sign-sub-inv 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-lft-identity 96.5%

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

      5. +-commutative 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 7: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+22)
   (* x (+ (/ y z) (/ t z)))
   (if (<= z 0.00059) (* x (- (/ y z) t)) (/ x (/ z (+ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+22) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 0.00059) {
		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 <= (-2.25d+22)) then
        tmp = x * ((y / z) + (t / z))
    else if (z <= 0.00059d0) 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 <= -2.25e+22) {
		tmp = x * ((y / z) + (t / z));
	} else if (z <= 0.00059) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x / (z / (y + t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+22:
		tmp = x * ((y / z) + (t / z))
	elif z <= 0.00059:
		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 <= -2.25e+22)
		tmp = Float64(x * Float64(Float64(y / z) + Float64(t / z)));
	elseif (z <= 0.00059)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x / Float64(z / Float64(y + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.25e+22)
		tmp = x * ((y / z) + (t / z));
	elseif (z <= 0.00059)
		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, -2.25e+22], N[(x * N[(N[(y / z), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00059], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e22

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 97.8%

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

      1. associate-*r/ 97.8%

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

      2. neg-mul-1 97.8%

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

   4. Simplified 97.8%

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

   if -2.2499999999999999e22 < z < 5.9000000000000003e-4

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r* 88.0%

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

      5. neg-mul-1 88.0%

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

      6. distribute-rgt-out 93.7%

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

      7. unsub-neg 93.7%

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

   4. Simplified 93.7%

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

   if 5.9000000000000003e-4 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 83.4%

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

      1. associate-/l* 96.5%

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

      2. cancel-sign-sub-inv 96.5%

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

      3. metadata-eval 96.5%

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

      4. *-lft-identity 96.5%

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

      5. +-commutative 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} + \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 0.00059:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \end{array} \]

Alternative 8: 41.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-35} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e-35) (not (<= z 0.00059))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e-35) || !(z <= 0.00059)) {
		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 <= (-3.5d-35)) .or. (.not. (z <= 0.00059d0))) 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 <= -3.5e-35) || !(z <= 0.00059)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e-35) or not (z <= 0.00059):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e-35) || !(z <= 0.00059))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e-35) || ~((z <= 0.00059)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e-35], N[Not[LessEqual[z, 0.00059]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999996e-35 or 5.9000000000000003e-4 < z

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 96.8%

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

      2. cancel-sign-sub-inv 96.8%

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

      3. metadata-eval 96.8%

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

      4. *-lft-identity 96.8%

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

      5. +-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in t around inf 54.9%

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

      1. associate-*r/ 51.9%

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

   7. Simplified 51.9%

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

   if -3.49999999999999996e-35 < z < 5.9000000000000003e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-*r* 88.4%

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

      5. neg-mul-1 88.4%

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

      6. distribute-rgt-out 93.5%

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

      7. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. distribute-lft-neg-out 35.2%

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

      3. *-commutative 35.2%

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

   7. Simplified 35.2%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-35} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 9: 43.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-35} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e-35) (not (<= z 0.00059))) (* x (/ t z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e-35) || !(z <= 0.00059)) {
		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 <= (-3.5d-35)) .or. (.not. (z <= 0.00059d0))) 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 <= -3.5e-35) || !(z <= 0.00059)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.5e-35) or not (z <= 0.00059):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.5e-35) || !(z <= 0.00059))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(t * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.5e-35) || ~((z <= 0.00059)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.5e-35], N[Not[LessEqual[z, 0.00059]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999996e-35 or 5.9000000000000003e-4 < z

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 97.2%

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

      1. cancel-sign-sub-inv 97.2%

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

      2. metadata-eval 97.2%

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

      3. *-lft-identity 97.2%

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

      4. +-commutative 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in t around inf 60.2%

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

   if -3.49999999999999996e-35 < z < 5.9000000000000003e-4

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*r/ 88.4%

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

      3. *-commutative 88.4%

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

      4. associate-*r* 88.4%

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

      5. neg-mul-1 88.4%

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

      6. distribute-rgt-out 93.5%

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

      7. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in y around 0 35.2%

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

      1. mul-1-neg 35.2%

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

      2. distribute-lft-neg-out 35.2%

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

      3. *-commutative 35.2%

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

   7. Simplified 35.2%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-35} \lor \neg \left(z \leq 0.00059\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]

Alternative 10: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+145} \lor \neg \left(t \leq 3 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.9e+145) (not (<= t 3e+131))) (* x (/ t z)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+145) || !(t <= 3e+131)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.9d+145)) .or. (.not. (t <= 3d+131))) then
        tmp = x * (t / z)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+145) || !(t <= 3e+131)) {
		tmp = x * (t / z);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.9e+145) or not (t <= 3e+131):
		tmp = x * (t / z)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.9e+145) || !(t <= 3e+131))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.9e+145) || ~((t <= 3e+131)))
		tmp = x * (t / z);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.9e+145], N[Not[LessEqual[t, 3e+131]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8999999999999998e145 or 3.0000000000000001e131 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 73.4%

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

      1. cancel-sign-sub-inv 73.4%

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

      2. metadata-eval 73.4%

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

      3. *-lft-identity 73.4%

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

      4. +-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around inf 62.1%

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

   if -3.8999999999999998e145 < t < 3.0000000000000001e131

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. associate-*r/ 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+145} \lor \neg \left(t \leq 3 \cdot 10^{+131}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 11: 68.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+147} \lor \neg \left(t \leq 1.5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1e+147) (not (<= t 1.5e+130))) (/ x (/ z t)) (* (/ y z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1e+147) || !(t <= 1.5e+130)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1d+147)) .or. (.not. (t <= 1.5d+130))) then
        tmp = x / (z / t)
    else
        tmp = (y / z) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1e+147) || !(t <= 1.5e+130)) {
		tmp = x / (z / t);
	} else {
		tmp = (y / z) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1e+147) or not (t <= 1.5e+130):
		tmp = x / (z / t)
	else:
		tmp = (y / z) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1e+147) || !(t <= 1.5e+130))
		tmp = Float64(x / Float64(z / t));
	else
		tmp = Float64(Float64(y / z) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1e+147) || ~((t <= 1.5e+130)))
		tmp = x / (z / t);
	else
		tmp = (y / z) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1e+147], N[Not[LessEqual[t, 1.5e+130]], $MachinePrecision]], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.9999999999999998e146 or 1.5e130 < t

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 60.7%

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

      1. associate-/l* 73.4%

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

      2. cancel-sign-sub-inv 73.4%

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

      3. metadata-eval 73.4%

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

      4. *-lft-identity 73.4%

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

      5. +-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in t around inf 62.2%

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

   if -9.9999999999999998e146 < t < 1.5e130

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 70.4%

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

      1. associate-*r/ 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+147} \lor \neg \left(t \leq 1.5 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 12: 22.1% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

2. Taylor expanded in z around 0 59.3%

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

   1. +-commutative 59.3%

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

   2. associate-*r/ 59.3%

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

   3. *-commutative 59.3%

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

   4. associate-*r* 59.3%

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

   5. neg-mul-1 59.3%

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

   6. distribute-rgt-out 62.1%

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

   7. unsub-neg 62.1%

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

4. Simplified 62.1%

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

5. Taylor expanded in y around 0 22.5%

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

   1. mul-1-neg 22.5%

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

   2. distribute-lft-neg-out 22.5%

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

   3. *-commutative 22.5%

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

7. Simplified 22.5%

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

8. Final simplification 22.5%

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

Developer target: 94.7% 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 2023320 
(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)))))