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

Percentage Accurate: 94.4% → 96.2%

Time: 10.4s

Alternatives: 12

Speedup: 0.5×

• 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: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * x) / 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 / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y * x) / 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[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * x), $MachinePrecision] / z), $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 70.3%

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

   3. Taylor expanded in y around inf 100.0%

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

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

   1. Initial program 96.8%

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

4. Final simplification 97.0%

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

Alternative 2: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-54} \lor \neg \left(y \leq 2.8 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y x) z)) (t_2 (* x (/ t z))))
   (if (<= y -2.25e-91)
     t_1
     (if (<= y 7.1e-168)
       t_2
       (if (<= y 4.2e-104)
         (/ x (/ z y))
         (if (or (<= y 1.3e-54) (and (not (<= y 2.8e+43)) (<= y 1.3e+73)))
           t_2
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * x) / z;
	double t_2 = x * (t / z);
	double tmp;
	if (y <= -2.25e-91) {
		tmp = t_1;
	} else if (y <= 7.1e-168) {
		tmp = t_2;
	} else if (y <= 4.2e-104) {
		tmp = x / (z / y);
	} else if ((y <= 1.3e-54) || (!(y <= 2.8e+43) && (y <= 1.3e+73))) {
		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 = (y * x) / z
    t_2 = x * (t / z)
    if (y <= (-2.25d-91)) then
        tmp = t_1
    else if (y <= 7.1d-168) then
        tmp = t_2
    else if (y <= 4.2d-104) then
        tmp = x / (z / y)
    else if ((y <= 1.3d-54) .or. (.not. (y <= 2.8d+43)) .and. (y <= 1.3d+73)) 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 = (y * x) / z;
	double t_2 = x * (t / z);
	double tmp;
	if (y <= -2.25e-91) {
		tmp = t_1;
	} else if (y <= 7.1e-168) {
		tmp = t_2;
	} else if (y <= 4.2e-104) {
		tmp = x / (z / y);
	} else if ((y <= 1.3e-54) || (!(y <= 2.8e+43) && (y <= 1.3e+73))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * x) / z
	t_2 = x * (t / z)
	tmp = 0
	if y <= -2.25e-91:
		tmp = t_1
	elif y <= 7.1e-168:
		tmp = t_2
	elif y <= 4.2e-104:
		tmp = x / (z / y)
	elif (y <= 1.3e-54) or (not (y <= 2.8e+43) and (y <= 1.3e+73)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * x) / z)
	t_2 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (y <= -2.25e-91)
		tmp = t_1;
	elseif (y <= 7.1e-168)
		tmp = t_2;
	elseif (y <= 4.2e-104)
		tmp = Float64(x / Float64(z / y));
	elseif ((y <= 1.3e-54) || (!(y <= 2.8e+43) && (y <= 1.3e+73)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * x) / z;
	t_2 = x * (t / z);
	tmp = 0.0;
	if (y <= -2.25e-91)
		tmp = t_1;
	elseif (y <= 7.1e-168)
		tmp = t_2;
	elseif (y <= 4.2e-104)
		tmp = x / (z / y);
	elseif ((y <= 1.3e-54) || (~((y <= 2.8e+43)) && (y <= 1.3e+73)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e-91], t$95$1, If[LessEqual[y, 7.1e-168], t$95$2, If[LessEqual[y, 4.2e-104], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.3e-54], And[N[Not[LessEqual[y, 2.8e+43]], $MachinePrecision], LessEqual[y, 1.3e+73]]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.24999999999999988e-91 or 1.30000000000000001e-54 < y < 2.80000000000000019e43 or 1.3e73 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 83.8%

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

   if -2.24999999999999988e-91 < y < 7.10000000000000019e-168 or 4.19999999999999997e-104 < y < 1.30000000000000001e-54 or 2.80000000000000019e43 < y < 1.3e73

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-/l* 87.0%

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

      4. distribute-rgt-neg-out 87.0%

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

      5. distribute-neg-frac2 87.0%

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

      6. neg-sub0 87.0%

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

      7. associate--r- 87.0%

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

      8. metadata-eval 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in z around inf 56.8%

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

      1. associate-*l/ 61.6%

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

      2. *-commutative 61.6%

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

   8. Simplified 61.6%

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

   if 7.10000000000000019e-168 < y < 4.19999999999999997e-104

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 58.4%

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

      1. associate-*r/ 64.9%

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

   5. Simplified 64.9%

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

      1. clear-num 64.8%

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

      2. un-div-inv 64.9%

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

   7. Applied egg-rr 64.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-168}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-54} \lor \neg \left(y \leq 2.8 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-89} \lor \neg \left(y \leq 7.8 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-89)
         (not (or (<= y 7.8e-168) (and (not (<= y 4e+43)) (<= y 1.3e+73)))))
   (* (/ y z) x)
   (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-89) || !((y <= 7.8e-168) || (!(y <= 4e+43) && (y <= 1.3e+73)))) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.02d-89)) .or. (.not. (y <= 7.8d-168) .or. (.not. (y <= 4d+43)) .and. (y <= 1.3d+73))) then
        tmp = (y / z) * x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-89) || !((y <= 7.8e-168) || (!(y <= 4e+43) && (y <= 1.3e+73)))) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-89) or not ((y <= 7.8e-168) or (not (y <= 4e+43) and (y <= 1.3e+73))):
		tmp = (y / z) * x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-89) || !((y <= 7.8e-168) || (!(y <= 4e+43) && (y <= 1.3e+73))))
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e-89) || ~(((y <= 7.8e-168) || (~((y <= 4e+43)) && (y <= 1.3e+73)))))
		tmp = (y / z) * x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-89], N[Not[Or[LessEqual[y, 7.8e-168], And[N[Not[LessEqual[y, 4e+43]], $MachinePrecision], LessEqual[y, 1.3e+73]]]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0199999999999999e-89 or 7.80000000000000025e-168 < y < 4.00000000000000006e43 or 1.3e73 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-*r/ 73.1%

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

   5. Simplified 73.1%

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

   if -1.0199999999999999e-89 < y < 7.80000000000000025e-168 or 4.00000000000000006e43 < y < 1.3e73

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-/l* 88.3%

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

      4. distribute-rgt-neg-out 88.3%

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

      5. distribute-neg-frac2 88.3%

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

      6. neg-sub0 88.3%

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

      7. associate--r- 88.3%

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

      8. metadata-eval 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 58.3%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   8. Simplified 61.5%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-89} \lor \neg \left(y \leq 7.8 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e-88)
   (* (/ y z) x)
   (if (or (<= y 6.4e-168) (and (not (<= y 4e+43)) (<= y 1.3e+73)))
     (* x (/ t z))
     (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e-88) {
		tmp = (y / z) * x;
	} else if ((y <= 6.4e-168) || (!(y <= 4e+43) && (y <= 1.3e+73))) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7.2d-88)) then
        tmp = (y / z) * x
    else if ((y <= 6.4d-168) .or. (.not. (y <= 4d+43)) .and. (y <= 1.3d+73)) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e-88) {
		tmp = (y / z) * x;
	} else if ((y <= 6.4e-168) || (!(y <= 4e+43) && (y <= 1.3e+73))) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e-88:
		tmp = (y / z) * x
	elif (y <= 6.4e-168) or (not (y <= 4e+43) and (y <= 1.3e+73)):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e-88)
		tmp = Float64(Float64(y / z) * x);
	elseif ((y <= 6.4e-168) || (!(y <= 4e+43) && (y <= 1.3e+73)))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.2e-88)
		tmp = (y / z) * x;
	elseif ((y <= 6.4e-168) || (~((y <= 4e+43)) && (y <= 1.3e+73)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e-88], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[Or[LessEqual[y, 6.4e-168], And[N[Not[LessEqual[y, 4e+43]], $MachinePrecision], LessEqual[y, 1.3e+73]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1999999999999999e-88

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

   if -7.1999999999999999e-88 < y < 6.40000000000000013e-168 or 4.00000000000000006e43 < y < 1.3e73

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-/l* 88.3%

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

      4. distribute-rgt-neg-out 88.3%

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

      5. distribute-neg-frac2 88.3%

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

      6. neg-sub0 88.3%

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

      7. associate--r- 88.3%

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

      8. metadata-eval 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 58.3%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if 6.40000000000000013e-168 < y < 4.00000000000000006e43 or 1.3e73 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/l* 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e-91)
   (/ x (/ z y))
   (if (or (<= y 5e-168) (and (not (<= y 4e+43)) (<= y 1.3e+73)))
     (* x (/ t z))
     (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-91) {
		tmp = x / (z / y);
	} else if ((y <= 5e-168) || (!(y <= 4e+43) && (y <= 1.3e+73))) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d-91)) then
        tmp = x / (z / y)
    else if ((y <= 5d-168) .or. (.not. (y <= 4d+43)) .and. (y <= 1.3d+73)) then
        tmp = x * (t / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e-91) {
		tmp = x / (z / y);
	} else if ((y <= 5e-168) || (!(y <= 4e+43) && (y <= 1.3e+73))) {
		tmp = x * (t / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e-91:
		tmp = x / (z / y)
	elif (y <= 5e-168) or (not (y <= 4e+43) and (y <= 1.3e+73)):
		tmp = x * (t / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e-91)
		tmp = Float64(x / Float64(z / y));
	elseif ((y <= 5e-168) || (!(y <= 4e+43) && (y <= 1.3e+73)))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e-91)
		tmp = x / (z / y);
	elseif ((y <= 5e-168) || (~((y <= 4e+43)) && (y <= 1.3e+73)))
		tmp = x * (t / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e-91], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5e-168], And[N[Not[LessEqual[y, 4e+43]], $MachinePrecision], LessEqual[y, 1.3e+73]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.20000000000000028e-91

   1. Initial program 97.1%

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

   3. Taylor expanded in y around inf 80.1%

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

      1. associate-*r/ 78.6%

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

   5. Simplified 78.6%

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

      1. clear-num 78.1%

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

      2. un-div-inv 78.8%

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

   7. Applied egg-rr 78.8%

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

   if -5.20000000000000028e-91 < y < 5.00000000000000001e-168 or 4.00000000000000006e43 < y < 1.3e73

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 85.0%

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

      1. mul-1-neg 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-/l* 88.3%

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

      4. distribute-rgt-neg-out 88.3%

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

      5. distribute-neg-frac2 88.3%

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

      6. neg-sub0 88.3%

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

      7. associate--r- 88.3%

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

      8. metadata-eval 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 58.3%

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

      1. associate-*l/ 61.5%

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

      2. *-commutative 61.5%

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

   8. Simplified 61.5%

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

   if 5.00000000000000001e-168 < y < 4.00000000000000006e43 or 1.3e73 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/l* 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-168} \lor \neg \left(y \leq 4 \cdot 10^{+43}\right) \land y \leq 1.3 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot x}{z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+43} \lor \neg \left(y \leq 1.7 \cdot 10^{+73}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y x) z)))
   (if (<= y -1e-30)
     t_1
     (if (<= y 2.25e-54)
       (* x (/ t (+ z -1.0)))
       (if (or (<= y 4e+43) (not (<= y 1.7e+73))) t_1 (* x (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * x) / z;
	double tmp;
	if (y <= -1e-30) {
		tmp = t_1;
	} else if (y <= 2.25e-54) {
		tmp = x * (t / (z + -1.0));
	} else if ((y <= 4e+43) || !(y <= 1.7e+73)) {
		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 = (y * x) / z
    if (y <= (-1d-30)) then
        tmp = t_1
    else if (y <= 2.25d-54) then
        tmp = x * (t / (z + (-1.0d0)))
    else if ((y <= 4d+43) .or. (.not. (y <= 1.7d+73))) 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 = (y * x) / z;
	double tmp;
	if (y <= -1e-30) {
		tmp = t_1;
	} else if (y <= 2.25e-54) {
		tmp = x * (t / (z + -1.0));
	} else if ((y <= 4e+43) || !(y <= 1.7e+73)) {
		tmp = t_1;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * x) / z
	tmp = 0
	if y <= -1e-30:
		tmp = t_1
	elif y <= 2.25e-54:
		tmp = x * (t / (z + -1.0))
	elif (y <= 4e+43) or not (y <= 1.7e+73):
		tmp = t_1
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * x) / z)
	tmp = 0.0
	if (y <= -1e-30)
		tmp = t_1;
	elseif (y <= 2.25e-54)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	elseif ((y <= 4e+43) || !(y <= 1.7e+73))
		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 = (y * x) / z;
	tmp = 0.0;
	if (y <= -1e-30)
		tmp = t_1;
	elseif (y <= 2.25e-54)
		tmp = x * (t / (z + -1.0));
	elseif ((y <= 4e+43) || ~((y <= 1.7e+73)))
		tmp = t_1;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1e-30], t$95$1, If[LessEqual[y, 2.25e-54], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 4e+43], N[Not[LessEqual[y, 1.7e+73]], $MachinePrecision]], t$95$1, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e-30 or 2.2499999999999999e-54 < y < 4.00000000000000006e43 or 1.7000000000000001e73 < y

   1. Initial program 92.0%

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

   3. Taylor expanded in y around inf 88.0%

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

   if -1e-30 < y < 2.2499999999999999e-54

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. *-commutative 73.2%

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

      3. associate-/l* 77.9%

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

      4. distribute-rgt-neg-out 77.9%

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

      5. distribute-neg-frac2 77.9%

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

      6. neg-sub0 77.9%

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

      7. associate--r- 77.9%

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

      8. metadata-eval 77.9%

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

   5. Simplified 77.9%

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

   if 4.00000000000000006e43 < y < 1.7000000000000001e73

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-out 100.0%

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

      5. distribute-neg-frac2 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-30}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+43} \lor \neg \left(y \leq 1.7 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -26000.0) (not (<= z 1.0)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) (+ t (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - (t + (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 <= (-26000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((y + t) / z)
    else
        tmp = x * ((y / z) - (t + (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 <= -26000.0) || !(z <= 1.0)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - (t + (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -26000.0) or not (z <= 1.0):
		tmp = x * ((y + t) / z)
	else:
		tmp = x * ((y / z) - (t + (z * t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -26000.0) || !(z <= 1.0))
		tmp = Float64(x * Float64(Float64(y + t) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - Float64(t + Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -26000.0) || ~((z <= 1.0)))
		tmp = x * ((y + t) / z);
	else
		tmp = x * ((y / z) - (t + (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -26000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - N[(t + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -26000 or 1 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. *-commutative 93.1%

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

      2. remove-double-neg 93.1%

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

      3. cancel-sign-sub-inv 93.1%

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

      4. metadata-eval 93.1%

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

      5. *-lft-identity 93.1%

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

      6. distribute-neg-out 93.1%

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

      7. neg-mul-1 93.1%

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

      8. sub-neg 93.1%

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

      9. mul-1-neg 93.1%

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

      10. associate-*r* 93.1%

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

      11. *-commutative 93.1%

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

      12. associate-*r/ 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 97.1%

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

      15. associate-*l* 97.1%

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

      16. *-commutative 97.1%

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

      17. associate-*r/ 97.1%

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

   5. Simplified 97.1%

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

   if -26000 < z < 1

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 92.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - \left(t + z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+161} \lor \neg \left(z \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e+161) (not (<= z 6.5e+18)))
   (* x (/ t z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e+161) || !(z <= 6.5e+18)) {
		tmp = x * (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 <= (-2.4d+161)) .or. (.not. (z <= 6.5d+18))) then
        tmp = x * (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 <= -2.4e+161) || !(z <= 6.5e+18)) {
		tmp = x * (t / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e+161) or not (z <= 6.5e+18):
		tmp = x * (t / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e+161) || !(z <= 6.5e+18))
		tmp = Float64(x * Float64(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 <= -2.4e+161) || ~((z <= 6.5e+18)))
		tmp = x * (t / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e+161], N[Not[LessEqual[z, 6.5e+18]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3999999999999999e161 or 6.5e18 < z

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. *-commutative 61.9%

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

      3. associate-/l* 65.7%

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

      4. distribute-rgt-neg-out 65.7%

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

      5. distribute-neg-frac2 65.7%

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

      6. neg-sub0 65.7%

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

      7. associate--r- 65.7%

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

      8. metadata-eval 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in z around inf 61.9%

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

      1. associate-*l/ 65.7%

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

      2. *-commutative 65.7%

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

   8. Simplified 65.7%

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

   if -2.3999999999999999e161 < z < 6.5e18

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-*r/ 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*r* 78.0%

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

      5. neg-mul-1 78.0%

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

      6. distribute-rgt-out 85.9%

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

      7. unsub-neg 85.9%

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

   5. Simplified 85.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+161} \lor \neg \left(z \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -26000.0) (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 <= -26000.0) || !(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 <= (-26000.0d0)) .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 <= -26000.0) || !(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 <= -26000.0) 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 <= -26000.0) || !(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 <= -26000.0) || ~((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, -26000.0], 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 < -26000 or 1 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. *-commutative 93.1%

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

      2. remove-double-neg 93.1%

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

      3. cancel-sign-sub-inv 93.1%

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

      4. metadata-eval 93.1%

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

      5. *-lft-identity 93.1%

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

      6. distribute-neg-out 93.1%

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

      7. neg-mul-1 93.1%

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

      8. sub-neg 93.1%

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

      9. mul-1-neg 93.1%

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

      10. associate-*r* 93.1%

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

      11. *-commutative 93.1%

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

      12. associate-*r/ 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 97.1%

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

      15. associate-*l* 97.1%

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

      16. *-commutative 97.1%

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

      17. associate-*r/ 97.1%

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

   5. Simplified 97.1%

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

   if -26000 < z < 1

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. associate-*r/ 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*r* 82.5%

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

      5. neg-mul-1 82.5%

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

      6. distribute-rgt-out 91.9%

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

      7. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -26000.0) (not (<= z 1.0))) (* t (/ x z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-26000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = t * (x / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.0)) {
		tmp = t * (x / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -26000.0) or not (z <= 1.0):
		tmp = t * (x / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -26000.0) || !(z <= 1.0))
		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 <= -26000.0) || ~((z <= 1.0)))
		tmp = t * (x / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -26000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -26000 or 1 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/l* 83.3%

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

      3. cancel-sign-sub-inv 83.3%

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

      4. metadata-eval 83.3%

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

      5. *-lft-identity 83.3%

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

      6. +-commutative 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around inf 58.2%

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

      1. associate-*r/ 54.5%

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

   8. Simplified 54.5%

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

   if -26000 < z < 1

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. associate-*r/ 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*r* 82.5%

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

      5. neg-mul-1 82.5%

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

      6. distribute-rgt-out 91.9%

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

      7. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

      3. distribute-rgt-neg-in 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -26000.0) (not (<= z 1.0))) (* x (/ t z)) (* t (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-26000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * (t / z)
    else
        tmp = t * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -26000.0) || !(z <= 1.0)) {
		tmp = x * (t / z);
	} else {
		tmp = t * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -26000.0) or not (z <= 1.0):
		tmp = x * (t / z)
	else:
		tmp = t * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -26000.0) || !(z <= 1.0))
		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 <= -26000.0) || ~((z <= 1.0)))
		tmp = x * (t / z);
	else
		tmp = t * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -26000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -26000 or 1 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. associate-/l* 61.2%

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

      4. distribute-rgt-neg-out 61.2%

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

      5. distribute-neg-frac2 61.2%

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

      6. neg-sub0 61.2%

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

      7. associate--r- 61.2%

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

      8. metadata-eval 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around inf 58.2%

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

      1. associate-*l/ 61.2%

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

      2. *-commutative 61.2%

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

   8. Simplified 61.2%

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

   if -26000 < z < 1

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. associate-*r/ 82.5%

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

      3. *-commutative 82.5%

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

      4. associate-*r* 82.5%

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

      5. neg-mul-1 82.5%

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

      6. distribute-rgt-out 91.9%

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

      7. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. *-commutative 36.3%

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

      3. distribute-rgt-neg-in 36.3%

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

   8. Simplified 36.3%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.2% 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 95.2%

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

3. Taylor expanded in z around 0 60.1%

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

   1. +-commutative 60.1%

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

   2. associate-*r/ 59.2%

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

   3. *-commutative 59.2%

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

   4. associate-*r* 59.2%

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

   5. neg-mul-1 59.2%

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

   6. distribute-rgt-out 64.3%

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

   7. unsub-neg 64.3%

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

5. Simplified 64.3%

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

6. Taylor expanded in y around 0 26.4%

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

   1. mul-1-neg 26.4%

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

   2. *-commutative 26.4%

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

   3. distribute-rgt-neg-in 26.4%

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

8. Simplified 26.4%

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

9. Final simplification 26.4%

   \[\leadsto t \cdot \left(-x\right) \]
10. Add Preprocessing

Developer target: 95.2% accurate, 0.2× 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 2024039 
(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)))))