Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Percentage Accurate: 97.7% → 97.8%

Time: 8.4s

Alternatives: 14

Speedup: 1.0×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{z - t}{\frac{y}{x}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return t + ((z - t) / (y / 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 + ((z - t) / (y / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. *-commutative 97.9%

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

   2. clear-num 97.6%

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

   3. un-div-inv 98.0%

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

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
6. Add Preprocessing

Alternative 2: 64.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ t_2 := \frac{z \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))) (t_2 (/ (* z x) y)))
   (if (<= (/ x y) -2e+188)
     t_2
     (if (<= (/ x y) -5e+70)
       (/ (* t x) (- y))
       (if (<= (/ x y) -2e-66)
         t_1
         (if (<= (/ x y) 1e-65)
           t
           (if (<= (/ x y) 5e+32)
             t_1
             (if (<= (/ x y) 1e+207) (* t (/ x (- y))) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_2;
	} else if ((x / y) <= -5e+70) {
		tmp = (t * x) / -y;
	} else if ((x / y) <= -2e-66) {
		tmp = t_1;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_1;
	} else if ((x / y) <= 1e+207) {
		tmp = t * (x / -y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x / y)
    t_2 = (z * x) / y
    if ((x / y) <= (-2d+188)) then
        tmp = t_2
    else if ((x / y) <= (-5d+70)) then
        tmp = (t * x) / -y
    else if ((x / y) <= (-2d-66)) then
        tmp = t_1
    else if ((x / y) <= 1d-65) then
        tmp = t
    else if ((x / y) <= 5d+32) then
        tmp = t_1
    else if ((x / y) <= 1d+207) then
        tmp = t * (x / -y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_2;
	} else if ((x / y) <= -5e+70) {
		tmp = (t * x) / -y;
	} else if ((x / y) <= -2e-66) {
		tmp = t_1;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_1;
	} else if ((x / y) <= 1e+207) {
		tmp = t * (x / -y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	t_2 = (z * x) / y
	tmp = 0
	if (x / y) <= -2e+188:
		tmp = t_2
	elif (x / y) <= -5e+70:
		tmp = (t * x) / -y
	elif (x / y) <= -2e-66:
		tmp = t_1
	elif (x / y) <= 1e-65:
		tmp = t
	elif (x / y) <= 5e+32:
		tmp = t_1
	elif (x / y) <= 1e+207:
		tmp = t * (x / -y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	t_2 = Float64(Float64(z * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e+188)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e+70)
		tmp = Float64(Float64(t * x) / Float64(-y));
	elseif (Float64(x / y) <= -2e-66)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-65)
		tmp = t;
	elseif (Float64(x / y) <= 5e+32)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e+207)
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	t_2 = (z * x) / y;
	tmp = 0.0;
	if ((x / y) <= -2e+188)
		tmp = t_2;
	elseif ((x / y) <= -5e+70)
		tmp = (t * x) / -y;
	elseif ((x / y) <= -2e-66)
		tmp = t_1;
	elseif ((x / y) <= 1e-65)
		tmp = t;
	elseif ((x / y) <= 5e+32)
		tmp = t_1;
	elseif ((x / y) <= 1e+207)
		tmp = t * (x / -y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+188], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e+70], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e-66], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-65], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+32], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e+207], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -2e188 or 1e207 < (/.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in x around -inf 98.2%

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

   5. Taylor expanded in z around inf 71.9%

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

   if -2e188 < (/.f64 x y) < -5.0000000000000002e70

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 93.7%

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

   4. Taylor expanded in x around -inf 93.7%

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

   5. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

      3. *-commutative 80.3%

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

   7. Simplified 80.3%

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

   if -5.0000000000000002e70 < (/.f64 x y) < -2e-66 or 9.99999999999999923e-66 < (/.f64 x y) < 4.9999999999999997e32

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in x around -inf 71.7%

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

   5. Taylor expanded in z around inf 54.2%

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

      1. associate-*l/ 66.2%

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

      2. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -2e-66 < (/.f64 x y) < 9.99999999999999923e-66

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 84.4%

      \[\leadsto \color{blue}{t} \]

   if 4.9999999999999997e32 < (/.f64 x y) < 1e207

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in z around 0 66.3%

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

      1. associate-*r/ 69.6%

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

      2. associate-*r* 69.6%

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

      3. neg-mul-1 69.6%

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

      4. cancel-sign-sub-inv 69.6%

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

   7. Simplified 69.6%

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

      1. clear-num 69.4%

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

      2. un-div-inv 69.4%

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

   9. Applied egg-rr 69.4%

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

   10. Taylor expanded in y around 0 66.3%

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

       1. mul-1-neg 66.3%

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

       2. associate-*r/ 69.6%

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

       3. distribute-lft-neg-out 69.6%

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

       4. *-commutative 69.6%

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

   12. Simplified 69.6%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{-y}\\ t_2 := z \cdot \frac{x}{y}\\ t_3 := \frac{z \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- y)))) (t_2 (* z (/ x y))) (t_3 (/ (* z x) y)))
   (if (<= (/ x y) -2e+188)
     t_3
     (if (<= (/ x y) -5e+70)
       t_1
       (if (<= (/ x y) -2e-66)
         t_2
         (if (<= (/ x y) 1e-65)
           t
           (if (<= (/ x y) 5e+32) t_2 (if (<= (/ x y) 1e+207) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double t_2 = z * (x / y);
	double t_3 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_3;
	} else if ((x / y) <= -5e+70) {
		tmp = t_1;
	} else if ((x / y) <= -2e-66) {
		tmp = t_2;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_2;
	} else if ((x / y) <= 1e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t * (x / -y)
    t_2 = z * (x / y)
    t_3 = (z * x) / y
    if ((x / y) <= (-2d+188)) then
        tmp = t_3
    else if ((x / y) <= (-5d+70)) then
        tmp = t_1
    else if ((x / y) <= (-2d-66)) then
        tmp = t_2
    else if ((x / y) <= 1d-65) then
        tmp = t
    else if ((x / y) <= 5d+32) then
        tmp = t_2
    else if ((x / y) <= 1d+207) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double t_2 = z * (x / y);
	double t_3 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_3;
	} else if ((x / y) <= -5e+70) {
		tmp = t_1;
	} else if ((x / y) <= -2e-66) {
		tmp = t_2;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_2;
	} else if ((x / y) <= 1e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / -y)
	t_2 = z * (x / y)
	t_3 = (z * x) / y
	tmp = 0
	if (x / y) <= -2e+188:
		tmp = t_3
	elif (x / y) <= -5e+70:
		tmp = t_1
	elif (x / y) <= -2e-66:
		tmp = t_2
	elif (x / y) <= 1e-65:
		tmp = t
	elif (x / y) <= 5e+32:
		tmp = t_2
	elif (x / y) <= 1e+207:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(-y)))
	t_2 = Float64(z * Float64(x / y))
	t_3 = Float64(Float64(z * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e+188)
		tmp = t_3;
	elseif (Float64(x / y) <= -5e+70)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e-66)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e-65)
		tmp = t;
	elseif (Float64(x / y) <= 5e+32)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / -y);
	t_2 = z * (x / y);
	t_3 = (z * x) / y;
	tmp = 0.0;
	if ((x / y) <= -2e+188)
		tmp = t_3;
	elseif ((x / y) <= -5e+70)
		tmp = t_1;
	elseif ((x / y) <= -2e-66)
		tmp = t_2;
	elseif ((x / y) <= 1e-65)
		tmp = t;
	elseif ((x / y) <= 5e+32)
		tmp = t_2;
	elseif ((x / y) <= 1e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+188], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], -5e+70], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e-66], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e-65], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+32], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e+207], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2e188 or 1e207 < (/.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in x around -inf 98.2%

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

   5. Taylor expanded in z around inf 71.9%

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

   if -2e188 < (/.f64 x y) < -5.0000000000000002e70 or 4.9999999999999997e32 < (/.f64 x y) < 1e207

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 71.2%

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

      1. associate-*r/ 73.3%

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

      2. associate-*r* 73.3%

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

      3. neg-mul-1 73.3%

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

      4. cancel-sign-sub-inv 73.3%

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

   7. Simplified 73.3%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.3%

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

   9. Applied egg-rr 73.3%

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

   10. Taylor expanded in y around 0 71.2%

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

       1. mul-1-neg 71.2%

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

       2. associate-*r/ 73.3%

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

       3. distribute-lft-neg-out 73.3%

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

       4. *-commutative 73.3%

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

   12. Simplified 73.3%

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

   if -5.0000000000000002e70 < (/.f64 x y) < -2e-66 or 9.99999999999999923e-66 < (/.f64 x y) < 4.9999999999999997e32

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in x around -inf 71.7%

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

   5. Taylor expanded in z around inf 54.2%

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

      1. associate-*l/ 66.2%

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

      2. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -2e-66 < (/.f64 x y) < 9.99999999999999923e-66

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 84.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{-y}\\ t_2 := z \cdot \frac{x}{y}\\ t_3 := \frac{z \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- y)))) (t_2 (* z (/ x y))) (t_3 (/ (* z x) y)))
   (if (<= (/ x y) -2e+188)
     t_3
     (if (<= (/ x y) -5e+70)
       t_1
       (if (<= (/ x y) -2e-66)
         t_2
         (if (<= (/ x y) 1e-65)
           t
           (if (<= (/ x y) 5e+32) t_2 (if (<= (/ x y) 1e+207) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / -y);
	double t_2 = z * (x / y);
	double t_3 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_3;
	} else if ((x / y) <= -5e+70) {
		tmp = t_1;
	} else if ((x / y) <= -2e-66) {
		tmp = t_2;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_2;
	} else if ((x / y) <= 1e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * (t / -y)
    t_2 = z * (x / y)
    t_3 = (z * x) / y
    if ((x / y) <= (-2d+188)) then
        tmp = t_3
    else if ((x / y) <= (-5d+70)) then
        tmp = t_1
    else if ((x / y) <= (-2d-66)) then
        tmp = t_2
    else if ((x / y) <= 1d-65) then
        tmp = t
    else if ((x / y) <= 5d+32) then
        tmp = t_2
    else if ((x / y) <= 1d+207) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / -y);
	double t_2 = z * (x / y);
	double t_3 = (z * x) / y;
	double tmp;
	if ((x / y) <= -2e+188) {
		tmp = t_3;
	} else if ((x / y) <= -5e+70) {
		tmp = t_1;
	} else if ((x / y) <= -2e-66) {
		tmp = t_2;
	} else if ((x / y) <= 1e-65) {
		tmp = t;
	} else if ((x / y) <= 5e+32) {
		tmp = t_2;
	} else if ((x / y) <= 1e+207) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / -y)
	t_2 = z * (x / y)
	t_3 = (z * x) / y
	tmp = 0
	if (x / y) <= -2e+188:
		tmp = t_3
	elif (x / y) <= -5e+70:
		tmp = t_1
	elif (x / y) <= -2e-66:
		tmp = t_2
	elif (x / y) <= 1e-65:
		tmp = t
	elif (x / y) <= 5e+32:
		tmp = t_2
	elif (x / y) <= 1e+207:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(-y)))
	t_2 = Float64(z * Float64(x / y))
	t_3 = Float64(Float64(z * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e+188)
		tmp = t_3;
	elseif (Float64(x / y) <= -5e+70)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e-66)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e-65)
		tmp = t;
	elseif (Float64(x / y) <= 5e+32)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / -y);
	t_2 = z * (x / y);
	t_3 = (z * x) / y;
	tmp = 0.0;
	if ((x / y) <= -2e+188)
		tmp = t_3;
	elseif ((x / y) <= -5e+70)
		tmp = t_1;
	elseif ((x / y) <= -2e-66)
		tmp = t_2;
	elseif ((x / y) <= 1e-65)
		tmp = t;
	elseif ((x / y) <= 5e+32)
		tmp = t_2;
	elseif ((x / y) <= 1e+207)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+188], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], -5e+70], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e-66], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e-65], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+32], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e+207], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2e188 or 1e207 < (/.f64 x y)

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in x around -inf 98.2%

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

   5. Taylor expanded in z around inf 71.9%

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

   if -2e188 < (/.f64 x y) < -5.0000000000000002e70 or 4.9999999999999997e32 < (/.f64 x y) < 1e207

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 71.2%

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

      1. associate-*r/ 73.3%

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

      2. associate-*r* 73.3%

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

      3. neg-mul-1 73.3%

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

      4. cancel-sign-sub-inv 73.3%

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

   7. Simplified 73.3%

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

      1. clear-num 73.1%

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

      2. un-div-inv 73.3%

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

   9. Applied egg-rr 73.3%

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

   10. Taylor expanded in y around 0 71.2%

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

       1. associate-*l/ 64.8%

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

       2. *-commutative 64.8%

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

       3. neg-mul-1 64.8%

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

       4. distribute-rgt-neg-in 64.8%

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

       5. distribute-frac-neg2 64.8%

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

   12. Simplified 64.8%

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

   if -5.0000000000000002e70 < (/.f64 x y) < -2e-66 or 9.99999999999999923e-66 < (/.f64 x y) < 4.9999999999999997e32

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.3%

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

   4. Taylor expanded in x around -inf 71.7%

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

   5. Taylor expanded in z around inf 54.2%

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

      1. associate-*l/ 66.2%

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

      2. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -2e-66 < (/.f64 x y) < 9.99999999999999923e-66

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 84.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+188}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-65}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+207}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000000000.0) (not (<= (/ x y) 5e-8)))
   (/ (* (- z t) x) y)
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000.0) || !((x / y) <= 5e-8)) {
		tmp = ((z - t) * x) / y;
	} else {
		tmp = t + (z / (y / 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 (((x / y) <= (-10000000000.0d0)) .or. (.not. ((x / y) <= 5d-8))) then
        tmp = ((z - t) * x) / y
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000.0) || !((x / y) <= 5e-8)) {
		tmp = ((z - t) * x) / y;
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10000000000.0) or not ((x / y) <= 5e-8):
		tmp = ((z - t) * x) / y
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000000000.0) || !(Float64(x / y) <= 5e-8))
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -10000000000.0) || ~(((x / y) <= 5e-8)))
		tmp = ((z - t) * x) / y;
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-8]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e10 or 4.9999999999999998e-8 < (/.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in x around -inf 93.3%

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

   if -1e10 < (/.f64 x y) < 4.9999999999999998e-8

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 94.7%

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

      1. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

      1. *-commutative 95.6%

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

      2. associate-/r/ 98.4%

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

   7. Applied egg-rr 98.4%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 10^{-65}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-66) (not (<= (/ x y) 1e-65))) (* z (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-66) || !((x / y) <= 1e-65)) {
		tmp = z * (x / y);
	} else {
		tmp = 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 (((x / y) <= (-2d-66)) .or. (.not. ((x / y) <= 1d-65))) then
        tmp = z * (x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-66) || !((x / y) <= 1e-65)) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-66) or not ((x / y) <= 1e-65):
		tmp = z * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-66) || !(Float64(x / y) <= 1e-65))
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-66) || ~(((x / y) <= 1e-65)))
		tmp = z * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-65]], $MachinePrecision]], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e-66 or 9.99999999999999923e-66 < (/.f64 x y)

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0 92.3%

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

   4. Taylor expanded in x around -inf 88.1%

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

   5. Taylor expanded in z around inf 52.6%

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

      1. associate-*l/ 56.5%

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

      2. *-commutative 56.5%

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

   7. Simplified 56.5%

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

   if -2e-66 < (/.f64 x y) < 9.99999999999999923e-66

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 84.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 10^{-65}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \lor \neg \left(t \leq 4.9 \cdot 10^{-64}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65) (not (<= t 4.9e-64)))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65) || !(t <= 4.9e-64)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.65d0)) .or. (.not. (t <= 4.9d-64))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65) || !(t <= 4.9e-64)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65) or not (t <= 4.9e-64):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65) || !(t <= 4.9e-64))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65) || ~((t <= 4.9e-64)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65], N[Not[LessEqual[t, 4.9e-64]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6499999999999999 or 4.9000000000000002e-64 < t

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

      3. *-rgt-identity 86.6%

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

      4. associate-/l* 91.6%

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

      5. distribute-lft-out-- 91.6%

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

   5. Simplified 91.6%

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

   if -1.6499999999999999 < t < 4.9000000000000002e-64

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 80.9%

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

      1. associate-/l* 84.9%

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

   5. Simplified 84.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \lor \neg \left(t \leq 4.9 \cdot 10^{-64}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-194} \lor \neg \left(t \leq 1.2 \cdot 10^{-150}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.4e-194) (not (<= t 1.2e-150)))
   (* t (- 1.0 (/ x y)))
   (* z (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e-194) || !(t <= 1.2e-150)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.4d-194)) .or. (.not. (t <= 1.2d-150))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = z * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e-194) || !(t <= 1.2e-150)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.4e-194) or not (t <= 1.2e-150):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.4e-194) || !(t <= 1.2e-150))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(z * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.4e-194) || ~((t <= 1.2e-150)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = z * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.4e-194], N[Not[LessEqual[t, 1.2e-150]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000006e-194 or 1.2e-150 < t

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. *-rgt-identity 77.7%

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

      4. associate-/l* 81.7%

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

      5. distribute-lft-out-- 81.7%

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

   5. Simplified 81.7%

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

   if -1.40000000000000006e-194 < t < 1.2e-150

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 89.1%

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

   4. Taylor expanded in x around -inf 73.2%

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

   5. Taylor expanded in z around inf 68.8%

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

      1. associate-*l/ 75.8%

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

      2. *-commutative 75.8%

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

   7. Simplified 75.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-194} \lor \neg \left(t \leq 1.2 \cdot 10^{-150}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-105}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e-105)
   (+ t (* x (/ z y)))
   (if (<= z 5.5e-44) (- t (/ t (/ y x))) (+ t (/ z (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e-105) {
		tmp = t + (x * (z / y));
	} else if (z <= 5.5e-44) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / 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 <= (-1.9d-105)) then
        tmp = t + (x * (z / y))
    else if (z <= 5.5d-44) then
        tmp = t - (t / (y / x))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e-105) {
		tmp = t + (x * (z / y));
	} else if (z <= 5.5e-44) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.9e-105:
		tmp = t + (x * (z / y))
	elif z <= 5.5e-44:
		tmp = t - (t / (y / x))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e-105)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 5.5e-44)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.9e-105)
		tmp = t + (x * (z / y));
	elseif (z <= 5.5e-44)
		tmp = t - (t / (y / x));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e-105], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-44], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-105

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -1.8999999999999999e-105 < z < 5.49999999999999993e-44

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

      4. cancel-sign-sub-inv 89.7%

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

   7. Simplified 89.7%

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

      1. clear-num 89.6%

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

      2. un-div-inv 89.9%

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

   9. Applied egg-rr 89.9%

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

   if 5.49999999999999993e-44 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-105}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-44}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-103}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-103)
   (+ t (* x (/ z y)))
   (if (<= z 8.2e-45) (- t (* t (/ x y))) (+ t (/ z (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-103) {
		tmp = t + (x * (z / y));
	} else if (z <= 8.2e-45) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z / (y / 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 <= (-4.8d-103)) then
        tmp = t + (x * (z / y))
    else if (z <= 8.2d-45) then
        tmp = t - (t * (x / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-103) {
		tmp = t + (x * (z / y));
	} else if (z <= 8.2e-45) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-103:
		tmp = t + (x * (z / y))
	elif z <= 8.2e-45:
		tmp = t - (t * (x / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-103)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 8.2e-45)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-103)
		tmp = t + (x * (z / y));
	elseif (z <= 8.2e-45)
		tmp = t - (t * (x / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-103], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-45], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000004e-103

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -4.8000000000000004e-103 < z < 8.1999999999999998e-45

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 89.7%

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

      2. associate-*r* 89.7%

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

      3. neg-mul-1 89.7%

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

      4. cancel-sign-sub-inv 89.7%

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

   7. Simplified 89.7%

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

   if 8.1999999999999998e-45 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-103}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-45}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-105}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-105)
   (+ t (* x (/ z y)))
   (if (<= z 1.1e-44) (* t (- 1.0 (/ x y))) (+ t (/ z (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-105) {
		tmp = t + (x * (z / y));
	} else if (z <= 1.1e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / 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 <= (-2.1d-105)) then
        tmp = t + (x * (z / y))
    else if (z <= 1.1d-44) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-105) {
		tmp = t + (x * (z / y));
	} else if (z <= 1.1e-44) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-105:
		tmp = t + (x * (z / y))
	elif z <= 1.1e-44:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-105)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 1.1e-44)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-105)
		tmp = t + (x * (z / y));
	elseif (z <= 1.1e-44)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-105], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-44], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e-105

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -2.1e-105 < z < 1.10000000000000006e-44

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. unsub-neg 87.0%

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

      3. *-rgt-identity 87.0%

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

      4. associate-/l* 89.7%

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

      5. distribute-lft-out-- 89.6%

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

   5. Simplified 89.6%

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

   if 1.10000000000000006e-44 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 78.3%

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

   5. Simplified 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-105}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.4 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= t -8.4e+65) (* y (/ t y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.4e+65) {
		tmp = y * (t / y);
	} else {
		tmp = 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 (t <= (-8.4d+65)) then
        tmp = y * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.4e+65) {
		tmp = y * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.4e+65:
		tmp = y * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.4e+65)
		tmp = Float64(y * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.4e+65)
		tmp = y * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.4e+65], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if t < -8.39999999999999965e65

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 82.8%

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

      1. mul-1-neg 82.8%

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

      2. *-commutative 82.8%

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

      3. associate-/l* 82.7%

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

      4. distribute-rgt-neg-in 82.7%

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

      5. distribute-neg-frac2 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in y around 0 59.5%

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

      1. neg-mul-1 59.5%

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

      2. +-commutative 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. distribute-lft-out 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in y around inf 28.5%

      \[\leadsto \frac{\color{blue}{t \cdot y}}{y} \]
   10. Step-by-step derivation

       1. *-commutative 28.5%

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

       2. associate-/l* 60.6%

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

   11. Applied egg-rr 60.6%

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

   if -8.39999999999999965e65 < t

   1. Initial program 97.5%

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

   3. Taylor expanded in x around 0 36.7%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) * (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Final simplification 97.9%

   \[\leadsto t + \left(z - t\right) \cdot \frac{x}{y} \]
4. Add Preprocessing

Alternative 14: 37.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in x around 0 38.7%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer target: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))