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

Percentage Accurate: 94.4% → 98.3%

Time: 12.3s

Alternatives: 13

Speedup: 0.4×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (* y (/ x z))
     (* x t_1))))

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)) || !(t_1 <= 5e+306)) {
		tmp = y * (x / z);
	} else {
		tmp = x * t_1;
	}
	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) || !(t_1 <= 5e+306)) {
		tmp = y * (x / z);
	} else {
		tmp = x * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = y * (x / z)
	else:
		tmp = x * t_1
	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)) || !(t_1 <= 5e+306))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(x * t_1);
	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) || ~((t_1 <= 5e+306)))
		tmp = y * (x / z);
	else
		tmp = x * t_1;
	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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < -inf.0 or 4.99999999999999993e306 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

   1. Initial program 61.8%

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

   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* 69.1%

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

      2. associate-/r/ 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) < 4.99999999999999993e306

   1. Initial program 99.4%

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

4. Final simplification 99.4%

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

Alternative 2: 96.3% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 (- INFINITY))
     (/ (* x (fma y (- 1.0 z) (- (* z t)))) (* z (- 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 - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * fma(y, (1.0 - z), -(z * t))) / (z * (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 - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * fma(y, Float64(1.0 - z), Float64(-Float64(z * t)))) / Float64(z * Float64(1.0 - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

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

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 80.8%

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

      1. *-commutative 80.8%

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

      2. frac-sub 80.8%

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

      3. associate-*l/ 99.8%

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

      4. cancel-sign-sub-inv 99.8%

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

      5. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

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

   1. Initial program 97.7%

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

4. Final simplification 97.9%

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

Alternative 3: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -10000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (* t (/ x z))))
   (if (<= z -7.5e+97)
     t_1
     (if (<= z -10000000.0)
       t_2
       (if (<= z 1.1e+18)
         (* y (/ x z))
         (if (<= z 2.4e+114) t_2 (if (<= z 1.05e+192) t_1 (* x (/ t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = t * (x / z);
	double tmp;
	if (z <= -7.5e+97) {
		tmp = t_1;
	} else if (z <= -10000000.0) {
		tmp = t_2;
	} else if (z <= 1.1e+18) {
		tmp = y * (x / z);
	} else if (z <= 2.4e+114) {
		tmp = t_2;
	} else if (z <= 1.05e+192) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = t * (x / z)
    if (z <= (-7.5d+97)) then
        tmp = t_1
    else if (z <= (-10000000.0d0)) then
        tmp = t_2
    else if (z <= 1.1d+18) then
        tmp = y * (x / z)
    else if (z <= 2.4d+114) then
        tmp = t_2
    else if (z <= 1.05d+192) then
        tmp = t_1
    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 t_1 = x * (y / z);
	double t_2 = t * (x / z);
	double tmp;
	if (z <= -7.5e+97) {
		tmp = t_1;
	} else if (z <= -10000000.0) {
		tmp = t_2;
	} else if (z <= 1.1e+18) {
		tmp = y * (x / z);
	} else if (z <= 2.4e+114) {
		tmp = t_2;
	} else if (z <= 1.05e+192) {
		tmp = t_1;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	t_2 = t * (x / z)
	tmp = 0
	if z <= -7.5e+97:
		tmp = t_1
	elif z <= -10000000.0:
		tmp = t_2
	elif z <= 1.1e+18:
		tmp = y * (x / z)
	elif z <= 2.4e+114:
		tmp = t_2
	elif z <= 1.05e+192:
		tmp = t_1
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (z <= -7.5e+97)
		tmp = t_1;
	elseif (z <= -10000000.0)
		tmp = t_2;
	elseif (z <= 1.1e+18)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 2.4e+114)
		tmp = t_2;
	elseif (z <= 1.05e+192)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (z <= -7.5e+97)
		tmp = t_1;
	elseif (z <= -10000000.0)
		tmp = t_2;
	elseif (z <= 1.1e+18)
		tmp = y * (x / z);
	elseif (z <= 2.4e+114)
		tmp = t_2;
	elseif (z <= 1.05e+192)
		tmp = t_1;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+97], t$95$1, If[LessEqual[z, -10000000.0], t$95$2, If[LessEqual[z, 1.1e+18], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+114], t$95$2, If[LessEqual[z, 1.05e+192], t$95$1, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5000000000000004e97 or 2.4e114 < z < 1.04999999999999997e192

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 74.2%

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

   4. Simplified 74.2%

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

   if -7.5000000000000004e97 < z < -1e7 or 1.1e18 < z < 2.4e114

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 97.1%

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

      2. associate-/r/ 92.7%

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

      3. cancel-sign-sub-inv 92.7%

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

      4. metadata-eval 92.7%

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

      5. *-lft-identity 92.7%

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

      6. +-commutative 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in t around inf 70.5%

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

      1. associate-*r/ 77.0%

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

   7. Simplified 77.0%

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

   if -1e7 < z < 1.1e18

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 71.7%

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

   4. Simplified 71.7%

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

   if 1.04999999999999997e192 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 84.8%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 62.9%

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

      3. cancel-sign-sub-inv 62.9%

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

      4. metadata-eval 62.9%

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

      5. *-lft-identity 62.9%

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

      6. +-commutative 62.9%

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

   4. Simplified 62.9%

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

      1. *-commutative 62.9%

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

      2. clear-num 62.8%

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

      3. un-div-inv 62.9%

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

      4. +-commutative 62.9%

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

   6. Applied egg-rr 62.9%

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

      1. associate-/r/ 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around 0 70.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -10000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 4: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))))
   (if (<= z -9.2e+96)
     t_1
     (if (<= z -7000000.0)
       (/ t (/ z x))
       (if (<= z 7e+17)
         (* y (/ x z))
         (if (<= z 1.7e+118)
           (* t (/ x z))
           (if (<= z 4.2e+192) t_1 (* x (/ t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double tmp;
	if (z <= -9.2e+96) {
		tmp = t_1;
	} else if (z <= -7000000.0) {
		tmp = t / (z / x);
	} else if (z <= 7e+17) {
		tmp = y * (x / z);
	} else if (z <= 1.7e+118) {
		tmp = t * (x / z);
	} else if (z <= 4.2e+192) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (z <= (-9.2d+96)) then
        tmp = t_1
    else if (z <= (-7000000.0d0)) then
        tmp = t / (z / x)
    else if (z <= 7d+17) then
        tmp = y * (x / z)
    else if (z <= 1.7d+118) then
        tmp = t * (x / z)
    else if (z <= 4.2d+192) then
        tmp = t_1
    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 t_1 = x * (y / z);
	double tmp;
	if (z <= -9.2e+96) {
		tmp = t_1;
	} else if (z <= -7000000.0) {
		tmp = t / (z / x);
	} else if (z <= 7e+17) {
		tmp = y * (x / z);
	} else if (z <= 1.7e+118) {
		tmp = t * (x / z);
	} else if (z <= 4.2e+192) {
		tmp = t_1;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	tmp = 0
	if z <= -9.2e+96:
		tmp = t_1
	elif z <= -7000000.0:
		tmp = t / (z / x)
	elif z <= 7e+17:
		tmp = y * (x / z)
	elif z <= 1.7e+118:
		tmp = t * (x / z)
	elif z <= 4.2e+192:
		tmp = t_1
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -9.2e+96)
		tmp = t_1;
	elseif (z <= -7000000.0)
		tmp = Float64(t / Float64(z / x));
	elseif (z <= 7e+17)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.7e+118)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 4.2e+192)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (z <= -9.2e+96)
		tmp = t_1;
	elseif (z <= -7000000.0)
		tmp = t / (z / x);
	elseif (z <= 7e+17)
		tmp = y * (x / z);
	elseif (z <= 1.7e+118)
		tmp = t * (x / z);
	elseif (z <= 4.2e+192)
		tmp = t_1;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+96], t$95$1, If[LessEqual[z, -7000000.0], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+17], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+118], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+192], t$95$1, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.2000000000000006e96 or 1.69999999999999993e118 < z < 4.19999999999999989e192

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 74.2%

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

   4. Simplified 74.2%

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

   if -9.2000000000000006e96 < z < -7e6

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 88.1%

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

      1. associate-/l* 93.4%

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

      2. associate-/r/ 88.0%

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

      3. cancel-sign-sub-inv 88.0%

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

      4. metadata-eval 88.0%

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

      5. *-lft-identity 88.0%

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

      6. +-commutative 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

   if -7e6 < z < 7e17

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 71.7%

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

   4. Simplified 71.7%

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

   if 7e17 < z < 1.69999999999999993e118

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 92.4%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. metadata-eval 96.1%

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

      5. *-lft-identity 96.1%

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

      6. +-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in t around inf 68.7%

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

      1. associate-*r/ 76.0%

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

   7. Simplified 76.0%

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

   if 4.19999999999999989e192 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 84.8%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 62.9%

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

      3. cancel-sign-sub-inv 62.9%

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

      4. metadata-eval 62.9%

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

      5. *-lft-identity 62.9%

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

      6. +-commutative 62.9%

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

   4. Simplified 62.9%

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

      1. *-commutative 62.9%

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

      2. clear-num 62.8%

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

      3. un-div-inv 62.9%

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

      4. +-commutative 62.9%

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

   6. Applied egg-rr 62.9%

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

      1. associate-/r/ 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{\frac{t}{z}} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -11200000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (/ x (/ z t))))
   (if (<= z -1.9e+98)
     t_1
     (if (<= z -11200000.0)
       t_2
       (if (<= z 1.25e+18)
         (* y (/ x z))
         (if (<= z 2.1e+114) (* t (/ x z)) (if (<= z 8e+191) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = x / (z / t);
	double tmp;
	if (z <= -1.9e+98) {
		tmp = t_1;
	} else if (z <= -11200000.0) {
		tmp = t_2;
	} else if (z <= 1.25e+18) {
		tmp = y * (x / z);
	} else if (z <= 2.1e+114) {
		tmp = t * (x / z);
	} else if (z <= 8e+191) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = x / (z / t)
    if (z <= (-1.9d+98)) then
        tmp = t_1
    else if (z <= (-11200000.0d0)) then
        tmp = t_2
    else if (z <= 1.25d+18) then
        tmp = y * (x / z)
    else if (z <= 2.1d+114) then
        tmp = t * (x / z)
    else if (z <= 8d+191) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = x / (z / t);
	double tmp;
	if (z <= -1.9e+98) {
		tmp = t_1;
	} else if (z <= -11200000.0) {
		tmp = t_2;
	} else if (z <= 1.25e+18) {
		tmp = y * (x / z);
	} else if (z <= 2.1e+114) {
		tmp = t * (x / z);
	} else if (z <= 8e+191) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	t_2 = x / (z / t)
	tmp = 0
	if z <= -1.9e+98:
		tmp = t_1
	elif z <= -11200000.0:
		tmp = t_2
	elif z <= 1.25e+18:
		tmp = y * (x / z)
	elif z <= 2.1e+114:
		tmp = t * (x / z)
	elif z <= 8e+191:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (z <= -1.9e+98)
		tmp = t_1;
	elseif (z <= -11200000.0)
		tmp = t_2;
	elseif (z <= 1.25e+18)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 2.1e+114)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 8e+191)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	t_2 = x / (z / t);
	tmp = 0.0;
	if (z <= -1.9e+98)
		tmp = t_1;
	elseif (z <= -11200000.0)
		tmp = t_2;
	elseif (z <= 1.25e+18)
		tmp = y * (x / z);
	elseif (z <= 2.1e+114)
		tmp = t * (x / z);
	elseif (z <= 8e+191)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+98], t$95$1, If[LessEqual[z, -11200000.0], t$95$2, If[LessEqual[z, 1.25e+18], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+114], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+191], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.89999999999999995e98 or 2.1e114 < z < 8.00000000000000058e191

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 74.2%

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

   4. Simplified 74.2%

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

   if -1.89999999999999995e98 < z < -1.12e7 or 8.00000000000000058e191 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 97.2%

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

      2. associate-/r/ 73.4%

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

      3. cancel-sign-sub-inv 73.4%

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

      4. metadata-eval 73.4%

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

      5. *-lft-identity 73.4%

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

      6. +-commutative 73.4%

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

   4. Simplified 73.4%

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

      1. *-commutative 73.4%

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

      2. clear-num 73.3%

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

      3. un-div-inv 73.4%

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

      4. +-commutative 73.4%

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

   6. Applied egg-rr 73.4%

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

      1. associate-/r/ 97.0%

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

   8. Simplified 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 97.0%

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

      3. un-div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

   11. Taylor expanded in y around 0 73.6%

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

   if -1.12e7 < z < 1.25e18

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 67.2%

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

      1. associate-/l* 66.0%

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

      2. associate-/r/ 71.7%

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

   4. Simplified 71.7%

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

   if 1.25e18 < z < 2.1e114

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 92.4%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. metadata-eval 96.1%

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

      5. *-lft-identity 96.1%

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

      6. +-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in t around inf 68.7%

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

      1. associate-*r/ 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -11200000:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 6: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ t_2 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -2.02 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y z))) (t_2 (/ x (/ z t))))
   (if (<= z -2.02e+96)
     t_1
     (if (<= z -3700000.0)
       t_2
       (if (<= z 2.9e+17)
         (* x (- (/ y z) t))
         (if (<= z 7.6e+113) (* t (/ x z)) (if (<= z 4.2e+192) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = x / (z / t);
	double tmp;
	if (z <= -2.02e+96) {
		tmp = t_1;
	} else if (z <= -3700000.0) {
		tmp = t_2;
	} else if (z <= 2.9e+17) {
		tmp = x * ((y / z) - t);
	} else if (z <= 7.6e+113) {
		tmp = t * (x / z);
	} else if (z <= 4.2e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / z)
    t_2 = x / (z / t)
    if (z <= (-2.02d+96)) then
        tmp = t_1
    else if (z <= (-3700000.0d0)) then
        tmp = t_2
    else if (z <= 2.9d+17) then
        tmp = x * ((y / z) - t)
    else if (z <= 7.6d+113) then
        tmp = t * (x / z)
    else if (z <= 4.2d+192) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / z);
	double t_2 = x / (z / t);
	double tmp;
	if (z <= -2.02e+96) {
		tmp = t_1;
	} else if (z <= -3700000.0) {
		tmp = t_2;
	} else if (z <= 2.9e+17) {
		tmp = x * ((y / z) - t);
	} else if (z <= 7.6e+113) {
		tmp = t * (x / z);
	} else if (z <= 4.2e+192) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / z)
	t_2 = x / (z / t)
	tmp = 0
	if z <= -2.02e+96:
		tmp = t_1
	elif z <= -3700000.0:
		tmp = t_2
	elif z <= 2.9e+17:
		tmp = x * ((y / z) - t)
	elif z <= 7.6e+113:
		tmp = t * (x / z)
	elif z <= 4.2e+192:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / z))
	t_2 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (z <= -2.02e+96)
		tmp = t_1;
	elseif (z <= -3700000.0)
		tmp = t_2;
	elseif (z <= 2.9e+17)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 7.6e+113)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 4.2e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / z);
	t_2 = x / (z / t);
	tmp = 0.0;
	if (z <= -2.02e+96)
		tmp = t_1;
	elseif (z <= -3700000.0)
		tmp = t_2;
	elseif (z <= 2.9e+17)
		tmp = x * ((y / z) - t);
	elseif (z <= 7.6e+113)
		tmp = t * (x / z);
	elseif (z <= 4.2e+192)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.02e+96], t$95$1, If[LessEqual[z, -3700000.0], t$95$2, If[LessEqual[z, 2.9e+17], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+113], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+192], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.02000000000000006e96 or 7.6000000000000007e113 < z < 4.19999999999999989e192

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 59.9%

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

      1. associate-*r/ 74.2%

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

   4. Simplified 74.2%

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

   if -2.02000000000000006e96 < z < -3.7e6 or 4.19999999999999989e192 < z

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 97.2%

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

      2. associate-/r/ 73.4%

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

      3. cancel-sign-sub-inv 73.4%

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

      4. metadata-eval 73.4%

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

      5. *-lft-identity 73.4%

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

      6. +-commutative 73.4%

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

   4. Simplified 73.4%

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

      1. *-commutative 73.4%

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

      2. clear-num 73.3%

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

      3. un-div-inv 73.4%

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

      4. +-commutative 73.4%

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

   6. Applied egg-rr 73.4%

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

      1. associate-/r/ 97.0%

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

   8. Simplified 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 97.0%

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

      3. un-div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

   11. Taylor expanded in y around 0 73.6%

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

   if -3.7e6 < z < 2.9e17

   1. Initial program 92.1%

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

   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/ 87.4%

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

      3. *-commutative 87.4%

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

      4. associate-*r* 87.4%

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

      5. neg-mul-1 87.4%

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

      6. distribute-rgt-out 90.4%

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

      7. unsub-neg 90.4%

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

   4. Simplified 90.4%

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

   if 2.9e17 < z < 7.6000000000000007e113

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 92.4%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 96.1%

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

      3. cancel-sign-sub-inv 96.1%

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

      4. metadata-eval 96.1%

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

      5. *-lft-identity 96.1%

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

      6. +-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in t around inf 68.7%

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

      1. associate-*r/ 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.02 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3700000:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+192}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]

Alternative 7: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+160} \lor \neg \left(t \leq -9.6 \cdot 10^{+105}\right) \land \left(t \leq -3.3 \cdot 10^{+51} \lor \neg \left(t \leq 4.8 \cdot 10^{+53}\right)\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.3e+160)
         (and (not (<= t -9.6e+105))
              (or (<= t -3.3e+51) (not (<= t 4.8e+53)))))
   (* x (/ t (+ z -1.0)))
   (/ x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.3e+160) || (!(t <= -9.6e+105) && ((t <= -3.3e+51) || !(t <= 4.8e+53)))) {
		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 <= (-5.3d+160)) .or. (.not. (t <= (-9.6d+105))) .and. (t <= (-3.3d+51)) .or. (.not. (t <= 4.8d+53))) 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 <= -5.3e+160) || (!(t <= -9.6e+105) && ((t <= -3.3e+51) || !(t <= 4.8e+53)))) {
		tmp = x * (t / (z + -1.0));
	} else {
		tmp = x / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.3e+160) or (not (t <= -9.6e+105) and ((t <= -3.3e+51) or not (t <= 4.8e+53))):
		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 <= -5.3e+160) || (!(t <= -9.6e+105) && ((t <= -3.3e+51) || !(t <= 4.8e+53))))
		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 <= -5.3e+160) || (~((t <= -9.6e+105)) && ((t <= -3.3e+51) || ~((t <= 4.8e+53)))))
		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, -5.3e+160], And[N[Not[LessEqual[t, -9.6e+105]], $MachinePrecision], Or[LessEqual[t, -3.3e+51], N[Not[LessEqual[t, 4.8e+53]], $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 < -5.3000000000000001e160 or -9.599999999999999e105 < t < -3.2999999999999997e51 or 4.8e53 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 73.4%

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

      1. associate-*r/ 73.4%

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

      2. mul-1-neg 73.4%

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

      3. *-commutative 73.4%

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

      4. distribute-rgt-neg-in 73.4%

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

      5. associate-*r/ 77.6%

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

      6. distribute-frac-neg 77.6%

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

      7. mul-1-neg 77.6%

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

      8. *-commutative 77.6%

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

      9. associate-*l/ 77.6%

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

      10. associate-*r/ 77.6%

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

      11. metadata-eval 77.6%

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

      12. associate-/r* 77.6%

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

      13. neg-mul-1 77.6%

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

      14. associate-*r/ 77.6%

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

      15. *-rgt-identity 77.6%

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

      16. neg-sub0 77.6%

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

      17. associate--r- 77.6%

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

      18. metadata-eval 77.6%

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

   4. Simplified 77.6%

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

   if -5.3000000000000001e160 < t < -9.599999999999999e105 or -3.2999999999999997e51 < t < 4.8e53

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 79.3%

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

      1. associate-*r/ 86.2%

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

   4. Simplified 86.2%

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

      1. clear-num 86.1%

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

      2. un-div-inv 87.5%

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

   6. Applied egg-rr 87.5%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+160} \lor \neg \left(t \leq -9.6 \cdot 10^{+105}\right) \land \left(t \leq -3.3 \cdot 10^{+51} \lor \neg \left(t \leq 4.8 \cdot 10^{+53}\right)\right):\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 8: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+263} \lor \neg \left(t \leq -3.45 \cdot 10^{+106}\right) \land \left(t \leq -7.8 \cdot 10^{+51} \lor \neg \left(t \leq 7.5 \cdot 10^{+54}\right)\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e+263)
         (and (not (<= t -3.45e+106))
              (or (<= t -7.8e+51) (not (<= t 7.5e+54)))))
   (* x (/ t z))
   (* x (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+263) || (!(t <= -3.45e+106) && ((t <= -7.8e+51) || !(t <= 7.5e+54)))) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.3d+263)) .or. (.not. (t <= (-3.45d+106))) .and. (t <= (-7.8d+51)) .or. (.not. (t <= 7.5d+54))) then
        tmp = x * (t / z)
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e+263) || (!(t <= -3.45e+106) && ((t <= -7.8e+51) || !(t <= 7.5e+54)))) {
		tmp = x * (t / z);
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e+263) or (not (t <= -3.45e+106) and ((t <= -7.8e+51) or not (t <= 7.5e+54))):
		tmp = x * (t / z)
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e+263) || (!(t <= -3.45e+106) && ((t <= -7.8e+51) || !(t <= 7.5e+54))))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e+263) || (~((t <= -3.45e+106)) && ((t <= -7.8e+51) || ~((t <= 7.5e+54)))))
		tmp = x * (t / z);
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e+263], And[N[Not[LessEqual[t, -3.45e+106]], $MachinePrecision], Or[LessEqual[t, -7.8e+51], N[Not[LessEqual[t, 7.5e+54]], $MachinePrecision]]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3e263 or -3.4499999999999999e106 < t < -7.79999999999999968e51 or 7.50000000000000042e54 < t

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 65.6%

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

      1. associate-/l* 69.6%

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

      2. associate-/r/ 55.7%

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

      3. cancel-sign-sub-inv 55.7%

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

      4. metadata-eval 55.7%

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

      5. *-lft-identity 55.7%

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

      6. +-commutative 55.7%

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

   4. Simplified 55.7%

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

      1. *-commutative 55.7%

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

      2. clear-num 54.9%

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

      3. un-div-inv 54.9%

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

      4. +-commutative 54.9%

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

   6. Applied egg-rr 54.9%

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

      1. associate-/r/ 69.5%

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

   8. Simplified 69.5%

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

   9. Taylor expanded in y around 0 54.8%

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

   if -3.3e263 < t < -3.4499999999999999e106 or -7.79999999999999968e51 < t < 7.50000000000000042e54

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 76.1%

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

      1. associate-*r/ 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+263} \lor \neg \left(t \leq -3.45 \cdot 10^{+106}\right) \land \left(t \leq -7.8 \cdot 10^{+51} \lor \neg \left(t \leq 7.5 \cdot 10^{+54}\right)\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 9: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-t\right)\\ t_2 := x \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- t))) (t_2 (* x (/ y z))))
   (if (<= t -2.7e+229)
     t_1
     (if (<= t 9.8e+54)
       t_2
       (if (<= t 3.45e+106) (* t (/ x z)) (if (<= t 1.15e+171) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double t_2 = x * (y / z);
	double tmp;
	if (t <= -2.7e+229) {
		tmp = t_1;
	} else if (t <= 9.8e+54) {
		tmp = t_2;
	} else if (t <= 3.45e+106) {
		tmp = t * (x / z);
	} else if (t <= 1.15e+171) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * -t
    t_2 = x * (y / z)
    if (t <= (-2.7d+229)) then
        tmp = t_1
    else if (t <= 9.8d+54) then
        tmp = t_2
    else if (t <= 3.45d+106) then
        tmp = t * (x / z)
    else if (t <= 1.15d+171) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -t;
	double t_2 = x * (y / z);
	double tmp;
	if (t <= -2.7e+229) {
		tmp = t_1;
	} else if (t <= 9.8e+54) {
		tmp = t_2;
	} else if (t <= 3.45e+106) {
		tmp = t * (x / z);
	} else if (t <= 1.15e+171) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -t
	t_2 = x * (y / z)
	tmp = 0
	if t <= -2.7e+229:
		tmp = t_1
	elif t <= 9.8e+54:
		tmp = t_2
	elif t <= 3.45e+106:
		tmp = t * (x / z)
	elif t <= 1.15e+171:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-t))
	t_2 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (t <= -2.7e+229)
		tmp = t_1;
	elseif (t <= 9.8e+54)
		tmp = t_2;
	elseif (t <= 3.45e+106)
		tmp = Float64(t * Float64(x / z));
	elseif (t <= 1.15e+171)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -t;
	t_2 = x * (y / z);
	tmp = 0.0;
	if (t <= -2.7e+229)
		tmp = t_1;
	elseif (t <= 9.8e+54)
		tmp = t_2;
	elseif (t <= 3.45e+106)
		tmp = t * (x / z);
	elseif (t <= 1.15e+171)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+229], t$95$1, If[LessEqual[t, 9.8e+54], t$95$2, If[LessEqual[t, 3.45e+106], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+171], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e229 or 1.15000000000000009e171 < t

   1. Initial program 93.7%

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

   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/ 48.3%

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

      3. *-commutative 48.3%

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

      4. associate-*r* 48.3%

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

      5. neg-mul-1 48.3%

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

      6. distribute-rgt-out 50.0%

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

      7. unsub-neg 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in y around 0 43.3%

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

      1. associate-*r* 43.3%

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

      2. neg-mul-1 43.3%

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

      3. *-commutative 43.3%

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

   7. Simplified 43.3%

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

   if -2.7e229 < t < 9.80000000000000002e54 or 3.4499999999999999e106 < t < 1.15000000000000009e171

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. associate-*r/ 80.1%

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

   4. Simplified 80.1%

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

   if 9.80000000000000002e54 < t < 3.4499999999999999e106

   1. Initial program 99.5%

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

   2. Taylor expanded in z around inf 84.6%

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

      1. associate-/l* 89.5%

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

      2. associate-/r/ 78.1%

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

      3. cancel-sign-sub-inv 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-lft-identity 78.1%

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

      6. +-commutative 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in t around inf 54.4%

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

      1. associate-*r/ 57.7%

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

   7. Simplified 57.7%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 10: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -440 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -440.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -440.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-440.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -440.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -440.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -440.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -440.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -440.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -440 or 1 < z

   1. Initial program 99.0%

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

   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 -440 < z < 1

   1. Initial program 91.8%

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

   2. Taylor expanded in z around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. associate-*r/ 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*r* 87.6%

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

      5. neg-mul-1 87.6%

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

      6. distribute-rgt-out 90.7%

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

      7. unsub-neg 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -440 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 11: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-27} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e-27) (not (<= z 1.0)))
   (/ x (/ z (+ y t)))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-27) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.8d-27)) .or. (.not. (z <= 1.0d0))) then
        tmp = x / (z / (y + t))
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-27) || !(z <= 1.0)) {
		tmp = x / (z / (y + t));
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e-27) or not (z <= 1.0):
		tmp = x / (z / (y + t))
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e-27) || !(z <= 1.0))
		tmp = Float64(x / Float64(z / Float64(y + t)));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e-27) || ~((z <= 1.0)))
		tmp = x / (z / (y + t));
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e-27], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x / N[(z / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e-27 or 1 < z

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 85.5%

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

      1. associate-/l* 96.7%

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

      2. associate-/r/ 80.6%

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

      3. cancel-sign-sub-inv 80.6%

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

      4. metadata-eval 80.6%

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

      5. *-lft-identity 80.6%

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

      6. +-commutative 80.6%

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

   4. Simplified 80.6%

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

      1. *-commutative 80.6%

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

      2. clear-num 80.0%

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

      3. un-div-inv 80.1%

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

      4. +-commutative 80.1%

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

   6. Applied egg-rr 80.1%

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

      1. associate-/r/ 96.1%

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

   8. Simplified 96.1%

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

      1. *-commutative 96.1%

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

      2. clear-num 96.0%

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

      3. un-div-inv 96.7%

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

   10. Applied egg-rr 96.7%

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

   if -2.8e-27 < z < 1

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-*r/ 88.7%

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

      3. *-commutative 88.7%

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

      4. associate-*r* 88.7%

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

      5. neg-mul-1 88.7%

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

      6. distribute-rgt-out 91.4%

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

      7. unsub-neg 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-27} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 12: 42.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00031 \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00031) (not (<= z 0.001))) (* t (/ x z)) (* x (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00031) || !(z <= 0.001)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.00031d0)) .or. (.not. (z <= 0.001d0))) then
        tmp = t * (x / z)
    else
        tmp = x * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00031) || !(z <= 0.001)) {
		tmp = t * (x / z);
	} else {
		tmp = x * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00031) or not (z <= 0.001):
		tmp = t * (x / z)
	else:
		tmp = x * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00031) || !(z <= 0.001))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00031) || ~((z <= 0.001)))
		tmp = t * (x / z);
	else
		tmp = x * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00031], N[Not[LessEqual[z, 0.001]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e-4 or 1e-3 < z

   1. Initial program 99.0%

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

   2. Taylor expanded in z around inf 85.9%

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

      1. associate-/l* 97.7%

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

      2. associate-/r/ 80.7%

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

      3. cancel-sign-sub-inv 80.7%

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

      4. metadata-eval 80.7%

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

      5. *-lft-identity 80.7%

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

      6. +-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in t around inf 55.1%

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

      1. associate-*r/ 50.3%

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

   7. Simplified 50.3%

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

   if -3.1e-4 < z < 1e-3

   1. Initial program 91.4%

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

   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/ 87.1%

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

      3. *-commutative 87.1%

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

      4. associate-*r* 87.1%

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

      5. neg-mul-1 87.1%

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

      6. distribute-rgt-out 90.5%

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

      7. unsub-neg 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in y around 0 38.4%

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

      1. associate-*r* 38.4%

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

      2. neg-mul-1 38.4%

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

      3. *-commutative 38.4%

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

   7. Simplified 38.4%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00031 \lor \neg \left(z \leq 0.001\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \end{array} \]

Alternative 13: 23.0% 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 95.4%

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

2. Taylor expanded in z around 0 60.5%

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

   1. +-commutative 60.5%

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

   2. associate-*r/ 61.4%

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

   3. *-commutative 61.4%

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

   4. associate-*r* 61.4%

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

   5. neg-mul-1 61.4%

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

   6. distribute-rgt-out 63.0%

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

   7. unsub-neg 63.0%

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

4. Simplified 63.0%

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

5. Taylor expanded in y around 0 26.0%

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

   1. associate-*r* 26.0%

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

   2. neg-mul-1 26.0%

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

   3. *-commutative 26.0%

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

7. Simplified 26.0%

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

8. Final simplification 26.0%

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

Developer target: 94.8% 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 2023275 
(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)))))