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

Percentage Accurate: 94.4% → 94.1%

Time: 8.7s

Alternatives: 10

Speedup: N/A×

• 21.7% 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: 94.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (<= t_1 1e+306) t_1 (* y (/ x z)))))

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 <= 1e+306) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_1 <= 1d+306) then
        tmp = t_1
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_1 <= 1e+306) {
		tmp = t_1;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_1 <= 1e+306:
		tmp = t_1
	else:
		tmp = y * (x / z)
	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 <= 1e+306)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_1 <= 1e+306)
		tmp = t_1;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+306], t$95$1, N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))) < 1.00000000000000002e306

   1. Initial program 96.3%

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

   if 1.00000000000000002e306 < (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

   1. Initial program 80.0%

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

   2. Taylor expanded in y around inf 89.4%

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

      1. associate-/l* 70.0%

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

      2. associate-/r/ 91.9%

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

   4. Simplified 91.9%

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

4. Final simplification 95.7%

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

Alternative 2: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= y -4.4e-69)
     (* y (/ x z))
     (if (<= y -1.8e-203)
       t_1
       (if (<= y -4.2e-296)
         (* x (- t))
         (if (<= y 2.5e-79) t_1 (* x (/ y z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (y <= -4.4e-69) {
		tmp = y * (x / z);
	} else if (y <= -1.8e-203) {
		tmp = t_1;
	} else if (y <= -4.2e-296) {
		tmp = x * -t;
	} else if (y <= 2.5e-79) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (y <= (-4.4d-69)) then
        tmp = y * (x / z)
    else if (y <= (-1.8d-203)) then
        tmp = t_1
    else if (y <= (-4.2d-296)) then
        tmp = x * -t
    else if (y <= 2.5d-79) then
        tmp = t_1
    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 t_1 = x * (t / z);
	double tmp;
	if (y <= -4.4e-69) {
		tmp = y * (x / z);
	} else if (y <= -1.8e-203) {
		tmp = t_1;
	} else if (y <= -4.2e-296) {
		tmp = x * -t;
	} else if (y <= 2.5e-79) {
		tmp = t_1;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if y <= -4.4e-69:
		tmp = y * (x / z)
	elif y <= -1.8e-203:
		tmp = t_1
	elif y <= -4.2e-296:
		tmp = x * -t
	elif y <= 2.5e-79:
		tmp = t_1
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (y <= -4.4e-69)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= -1.8e-203)
		tmp = t_1;
	elseif (y <= -4.2e-296)
		tmp = Float64(x * Float64(-t));
	elseif (y <= 2.5e-79)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (y <= -4.4e-69)
		tmp = y * (x / z);
	elseif (y <= -1.8e-203)
		tmp = t_1;
	elseif (y <= -4.2e-296)
		tmp = x * -t;
	elseif (y <= 2.5e-79)
		tmp = t_1;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e-69], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.8e-203], t$95$1, If[LessEqual[y, -4.2e-296], N[(x * (-t)), $MachinePrecision], If[LessEqual[y, 2.5e-79], t$95$1, N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4e-69

   1. Initial program 92.4%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

   if -4.4e-69 < y < -1.7999999999999999e-203 or -4.1999999999999999e-296 < y < 2.5e-79

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. metadata-eval 71.7%

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

      5. *-lft-identity 71.7%

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

      6. +-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in t around 0 57.9%

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

      1. associate-*l/ 63.1%

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

   10. Simplified 63.1%

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

   if -1.7999999999999999e-203 < y < -4.1999999999999999e-296

   1. Initial program 83.6%

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

   2. Taylor expanded in z around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 68.0%

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

      3. *-commutative 68.0%

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

      4. associate-*r* 68.0%

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

      5. neg-mul-1 68.0%

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

      6. distribute-rgt-out 68.0%

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

      7. unsub-neg 68.0%

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

   4. Simplified 68.0%

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

   5. Taylor expanded in y around 0 61.4%

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

      1. neg-mul-1 61.4%

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

      2. distribute-rgt-neg-in 61.4%

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

   7. Simplified 61.4%

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

   if 2.5e-79 < y

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 76.0%

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

      1. associate-*r/ 75.9%

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

   4. Simplified 75.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= y -6.5e-69)
     (* y (/ x z))
     (if (<= y -1e-203)
       t_1
       (if (<= y -1.7e-296)
         (* x (- t))
         (if (<= y 2e-80) t_1 (/ (* x y) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (y <= -6.5e-69) {
		tmp = y * (x / z);
	} else if (y <= -1e-203) {
		tmp = t_1;
	} else if (y <= -1.7e-296) {
		tmp = x * -t;
	} else if (y <= 2e-80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (t / z)
    if (y <= (-6.5d-69)) then
        tmp = y * (x / z)
    else if (y <= (-1d-203)) then
        tmp = t_1
    else if (y <= (-1.7d-296)) then
        tmp = x * -t
    else if (y <= 2d-80) then
        tmp = t_1
    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 t_1 = x * (t / z);
	double tmp;
	if (y <= -6.5e-69) {
		tmp = y * (x / z);
	} else if (y <= -1e-203) {
		tmp = t_1;
	} else if (y <= -1.7e-296) {
		tmp = x * -t;
	} else if (y <= 2e-80) {
		tmp = t_1;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if y <= -6.5e-69:
		tmp = y * (x / z)
	elif y <= -1e-203:
		tmp = t_1
	elif y <= -1.7e-296:
		tmp = x * -t
	elif y <= 2e-80:
		tmp = t_1
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (y <= -6.5e-69)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= -1e-203)
		tmp = t_1;
	elseif (y <= -1.7e-296)
		tmp = Float64(x * Float64(-t));
	elseif (y <= 2e-80)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	tmp = 0.0;
	if (y <= -6.5e-69)
		tmp = y * (x / z);
	elseif (y <= -1e-203)
		tmp = t_1;
	elseif (y <= -1.7e-296)
		tmp = x * -t;
	elseif (y <= 2e-80)
		tmp = t_1;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-69], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-203], t$95$1, If[LessEqual[y, -1.7e-296], N[(x * (-t)), $MachinePrecision], If[LessEqual[y, 2e-80], t$95$1, N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.49999999999999951e-69

   1. Initial program 92.4%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

   if -6.49999999999999951e-69 < y < -1e-203 or -1.69999999999999998e-296 < y < 1.99999999999999992e-80

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. associate-/l* 72.9%

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

      2. associate-/r/ 71.7%

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

      3. cancel-sign-sub-inv 71.7%

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

      4. metadata-eval 71.7%

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

      5. *-lft-identity 71.7%

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

      6. +-commutative 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in t around 0 57.9%

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

      1. associate-*l/ 63.1%

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

   10. Simplified 63.1%

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

   if -1e-203 < y < -1.69999999999999998e-296

   1. Initial program 83.6%

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

   2. Taylor expanded in z around 0 67.9%

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

      1. +-commutative 67.9%

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

      2. associate-*r/ 68.0%

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

      3. *-commutative 68.0%

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

      4. associate-*r* 68.0%

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

      5. neg-mul-1 68.0%

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

      6. distribute-rgt-out 68.0%

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

      7. unsub-neg 68.0%

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

   4. Simplified 68.0%

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

   5. Taylor expanded in y around 0 61.4%

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

      1. neg-mul-1 61.4%

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

      2. distribute-rgt-neg-in 61.4%

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

   7. Simplified 61.4%

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

   if 1.99999999999999992e-80 < y

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 76.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 96000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.25e+20)
   (* x (/ y z))
   (if (<= z 96000.0)
     (* x (- (/ y z) t))
     (if (<= z 7.8e+66)
       (* t (/ x z))
       (if (<= z 1.05e+214) (/ (* x y) z) (* x (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e+20) {
		tmp = x * (y / z);
	} else if (z <= 96000.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 7.8e+66) {
		tmp = t * (x / z);
	} else if (z <= 1.05e+214) {
		tmp = (x * y) / z;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.25d+20)) then
        tmp = x * (y / z)
    else if (z <= 96000.0d0) then
        tmp = x * ((y / z) - t)
    else if (z <= 7.8d+66) then
        tmp = t * (x / z)
    else if (z <= 1.05d+214) then
        tmp = (x * y) / z
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.25e+20) {
		tmp = x * (y / z);
	} else if (z <= 96000.0) {
		tmp = x * ((y / z) - t);
	} else if (z <= 7.8e+66) {
		tmp = t * (x / z);
	} else if (z <= 1.05e+214) {
		tmp = (x * y) / z;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.25e+20:
		tmp = x * (y / z)
	elif z <= 96000.0:
		tmp = x * ((y / z) - t)
	elif z <= 7.8e+66:
		tmp = t * (x / z)
	elif z <= 1.05e+214:
		tmp = (x * y) / z
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.25e+20)
		tmp = Float64(x * Float64(y / z));
	elseif (z <= 96000.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (z <= 7.8e+66)
		tmp = Float64(t * Float64(x / z));
	elseif (z <= 1.05e+214)
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.25e+20)
		tmp = x * (y / z);
	elseif (z <= 96000.0)
		tmp = x * ((y / z) - t);
	elseif (z <= 7.8e+66)
		tmp = t * (x / z);
	elseif (z <= 1.05e+214)
		tmp = (x * y) / z;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.25e+20], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 96000.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+66], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+214], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.25e20

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 52.5%

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

      1. associate-*r/ 64.1%

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

   4. Simplified 64.1%

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

   if -1.25e20 < z < 96000

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. associate-*r/ 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*r* 81.6%

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

      5. neg-mul-1 81.6%

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

      6. distribute-rgt-out 89.1%

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

      7. unsub-neg 89.1%

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

   4. Simplified 89.1%

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

   if 96000 < z < 7.8000000000000007e66

   1. Initial program 96.1%

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

   2. Taylor expanded in z around inf 91.5%

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

      1. associate-/l* 91.0%

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

      2. associate-/r/ 96.7%

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

      3. cancel-sign-sub-inv 96.7%

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

      4. metadata-eval 96.7%

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

      5. *-lft-identity 96.7%

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

      6. +-commutative 96.7%

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

   4. Simplified 96.7%

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

   5. Taylor expanded in t around inf 73.8%

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

      1. associate-*r/ 73.9%

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

   7. Simplified 73.9%

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

   if 7.8000000000000007e66 < z < 1.05e214

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 65.6%

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

   if 1.05e214 < z

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 66.5%

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

      1. associate-/l* 95.0%

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

      2. associate-/r/ 85.8%

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

      3. cancel-sign-sub-inv 85.8%

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

      4. metadata-eval 85.8%

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

      5. *-lft-identity 85.8%

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

      6. +-commutative 85.8%

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

   4. Simplified 85.8%

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

   5. Taylor expanded in t around inf 51.8%

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

      1. associate-/l* 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in t around 0 51.8%

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

      1. associate-*l/ 75.8%

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

   10. Simplified 75.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 96000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+214}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e-69)
   (* y (/ x z))
   (if (<= y 1.3e-78)
     (* x (/ t (+ z -1.0)))
     (if (<= y 4.8e-12)
       (* x (- (/ y z) t))
       (if (<= y 4.9e-12) (* t (/ x z)) (/ (* x y) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e-69) {
		tmp = y * (x / z);
	} else if (y <= 1.3e-78) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 4.8e-12) {
		tmp = x * ((y / z) - t);
	} else if (y <= 4.9e-12) {
		tmp = t * (x / 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 (y <= (-7.8d-69)) then
        tmp = y * (x / z)
    else if (y <= 1.3d-78) then
        tmp = x * (t / (z + (-1.0d0)))
    else if (y <= 4.8d-12) then
        tmp = x * ((y / z) - t)
    else if (y <= 4.9d-12) then
        tmp = t * (x / 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 (y <= -7.8e-69) {
		tmp = y * (x / z);
	} else if (y <= 1.3e-78) {
		tmp = x * (t / (z + -1.0));
	} else if (y <= 4.8e-12) {
		tmp = x * ((y / z) - t);
	} else if (y <= 4.9e-12) {
		tmp = t * (x / z);
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e-69:
		tmp = y * (x / z)
	elif y <= 1.3e-78:
		tmp = x * (t / (z + -1.0))
	elif y <= 4.8e-12:
		tmp = x * ((y / z) - t)
	elif y <= 4.9e-12:
		tmp = t * (x / z)
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e-69)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 1.3e-78)
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	elseif (y <= 4.8e-12)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	elseif (y <= 4.9e-12)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.8e-69)
		tmp = y * (x / z);
	elseif (y <= 1.3e-78)
		tmp = x * (t / (z + -1.0));
	elseif (y <= 4.8e-12)
		tmp = x * ((y / z) - t);
	elseif (y <= 4.9e-12)
		tmp = t * (x / z);
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e-69], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-78], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-12], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-12], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.79999999999999961e-69

   1. Initial program 92.4%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 77.4%

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

   4. Simplified 77.4%

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

   if -7.79999999999999961e-69 < y < 1.3000000000000001e-78

   1. Initial program 94.9%

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

   2. Taylor expanded in y around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. mul-1-neg 73.2%

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

      3. *-commutative 73.2%

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

      4. distribute-rgt-neg-in 73.2%

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

      5. associate-*r/ 76.8%

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

      6. distribute-frac-neg 76.8%

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

      7. mul-1-neg 76.8%

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

      8. *-commutative 76.8%

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

      9. associate-*l/ 76.8%

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

      10. associate-*r/ 76.7%

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

      11. metadata-eval 76.7%

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

      12. associate-/r* 76.7%

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

      13. neg-mul-1 76.7%

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

      14. associate-*r/ 76.8%

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

      15. *-rgt-identity 76.8%

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

      16. neg-sub0 76.8%

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

      17. associate--r- 76.8%

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

      18. metadata-eval 76.8%

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

   4. Simplified 76.8%

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

   if 1.3000000000000001e-78 < y < 4.79999999999999974e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*r/ 77.1%

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

      3. *-commutative 77.1%

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

      4. associate-*r* 77.1%

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

      5. neg-mul-1 77.1%

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

      6. distribute-rgt-out 77.2%

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

      7. unsub-neg 77.2%

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

   4. Simplified 77.2%

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

   if 4.79999999999999974e-12 < y < 4.89999999999999972e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-lft-identity 100.0%

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

      6. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   if 4.89999999999999972e-12 < y

   1. Initial program 93.4%

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

   2. Taylor expanded in y around inf 81.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 6: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6.8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 6.8e-7)))
   (* x (/ (+ y t) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 6.8e-7)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 6.8d-7))) 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 <= -1.0) || !(z <= 6.8e-7)) {
		tmp = x * ((y + t) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 6.8e-7):
		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 <= -1.0) || !(z <= 6.8e-7))
		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 <= -1.0) || ~((z <= 6.8e-7)))
		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, -1.0], N[Not[LessEqual[z, 6.8e-7]], $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 < -1 or 6.79999999999999948e-7 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 95.8%

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

      1. cancel-sign-sub-inv 95.8%

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

      2. metadata-eval 95.8%

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

      3. *-lft-identity 95.8%

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

      4. +-commutative 95.8%

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

   4. Simplified 95.8%

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

   if -1 < z < 6.79999999999999948e-7

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-*r/ 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*r* 81.7%

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

      5. neg-mul-1 81.7%

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

      6. distribute-rgt-out 89.5%

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

      7. unsub-neg 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6.8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \frac{y + t}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]

Alternative 7: 62.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-69} \lor \neg \left(y \leq 4.9 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-69) (not (<= y 4.9e-12))) (* x (/ y z)) (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-69) || !(y <= 4.9e-12)) {
		tmp = x * (y / z);
	} else {
		tmp = t * (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 <= (-3.5d-69)) .or. (.not. (y <= 4.9d-12))) then
        tmp = x * (y / z)
    else
        tmp = t * (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 <= -3.5e-69) || !(y <= 4.9e-12)) {
		tmp = x * (y / z);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-69) or not (y <= 4.9e-12):
		tmp = x * (y / z)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-69) || !(y <= 4.9e-12))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-69) || ~((y <= 4.9e-12)))
		tmp = x * (y / z);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-69], N[Not[LessEqual[y, 4.9e-12]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000001e-69 or 4.89999999999999972e-12 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 77.3%

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

   4. Simplified 77.3%

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

   if -3.5000000000000001e-69 < y < 4.89999999999999972e-12

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf 62.7%

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

      1. associate-/l* 64.5%

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

      2. associate-/r/ 65.5%

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

      3. cancel-sign-sub-inv 65.5%

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

      4. metadata-eval 65.5%

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

      5. *-lft-identity 65.5%

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

      6. +-commutative 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in t around inf 49.2%

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

      1. associate-*r/ 53.8%

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

   7. Simplified 53.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-69} \lor \neg \left(y \leq 4.9 \cdot 10^{-12}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 64.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-69} \lor \neg \left(y \leq 4.6 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-69) (not (<= y 4.6e-81))) (* x (/ y z)) (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-69) || !(y <= 4.6e-81)) {
		tmp = x * (y / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5d-69)) .or. (.not. (y <= 4.6d-81))) then
        tmp = x * (y / z)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-69) || !(y <= 4.6e-81)) {
		tmp = x * (y / z);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e-69) or not (y <= 4.6e-81):
		tmp = x * (y / z)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-69) || !(y <= 4.6e-81))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e-69) || ~((y <= 4.6e-81)))
		tmp = x * (y / z);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-69], N[Not[LessEqual[y, 4.6e-81]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000033e-69 or 4.59999999999999982e-81 < y

   1. Initial program 93.5%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. associate-*r/ 75.0%

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

   4. Simplified 75.0%

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

   if -5.00000000000000033e-69 < y < 4.59999999999999982e-81

   1. Initial program 94.9%

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

   2. Taylor expanded in z around inf 62.4%

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

      1. associate-/l* 63.5%

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

      2. associate-/r/ 64.6%

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

      3. cancel-sign-sub-inv 64.6%

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

      4. metadata-eval 64.6%

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

      5. *-lft-identity 64.6%

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

      6. +-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in t around 0 52.1%

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

      1. associate-*l/ 55.6%

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

   10. Simplified 55.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-69} \lor \neg \left(y \leq 4.6 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 33.7% accurate, 2.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t * (x / 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 = t * (x / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

2. Taylor expanded in z around inf 71.0%

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

   1. associate-/l* 75.7%

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

   2. associate-/r/ 73.9%

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

   3. cancel-sign-sub-inv 73.9%

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

   4. metadata-eval 73.9%

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

   5. *-lft-identity 73.9%

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

   6. +-commutative 73.9%

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

4. Simplified 73.9%

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

5. Taylor expanded in t around inf 34.3%

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

   1. associate-*r/ 38.4%

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

7. Simplified 38.4%

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

8. Final simplification 38.4%

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

Alternative 10: 22.9% 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 93.9%

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

2. Taylor expanded in z around 0 57.0%

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

   1. +-commutative 57.0%

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

   2. associate-*r/ 56.9%

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

   3. *-commutative 56.9%

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

   4. associate-*r* 56.9%

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

   5. neg-mul-1 56.9%

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

   6. distribute-rgt-out 60.8%

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

   7. unsub-neg 60.8%

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

4. Simplified 60.8%

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

5. Taylor expanded in y around 0 19.7%

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

   1. neg-mul-1 19.7%

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

   2. distribute-rgt-neg-in 19.7%

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

7. Simplified 19.7%

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

8. Final simplification 19.7%

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

Developer target: 95.1% 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 2023279 
(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)))))