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

Percentage Accurate: 97.2% → 97.2%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+84} \lor \neg \left(y \leq 1.95 \cdot 10^{-91} \lor \neg \left(y \leq 5.5 \cdot 10^{-71}\right) \land y \leq 9.5 \cdot 10^{-28}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+84)
         (not (or (<= y 1.95e-91) (and (not (<= y 5.5e-71)) (<= y 9.5e-28)))))
   (* t (/ (- y x) y))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+84) || !((y <= 1.95e-91) || (!(y <= 5.5e-71) && (y <= 9.5e-28)))) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (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 <= (-9d+84)) .or. (.not. (y <= 1.95d-91) .or. (.not. (y <= 5.5d-71)) .and. (y <= 9.5d-28))) then
        tmp = t * ((y - x) / y)
    else
        tmp = (x - y) * (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 <= -9e+84) || !((y <= 1.95e-91) || (!(y <= 5.5e-71) && (y <= 9.5e-28)))) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+84) or not ((y <= 1.95e-91) or (not (y <= 5.5e-71) and (y <= 9.5e-28))):
		tmp = t * ((y - x) / y)
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+84) || !((y <= 1.95e-91) || (!(y <= 5.5e-71) && (y <= 9.5e-28))))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+84) || ~(((y <= 1.95e-91) || (~((y <= 5.5e-71)) && (y <= 9.5e-28)))))
		tmp = t * ((y - x) / y);
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+84], N[Not[Or[LessEqual[y, 1.95e-91], And[N[Not[LessEqual[y, 5.5e-71]], $MachinePrecision], LessEqual[y, 9.5e-28]]]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.9999999999999994e84 or 1.94999999999999997e-91 < y < 5.4999999999999997e-71 or 9.50000000000000001e-28 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 74.9%

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

      2. associate-/l* 70.0%

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

   3. Simplified 70.0%

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

      1. associate-*r/ 74.9%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. distribute-neg-frac2 82.7%

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

      3. sub-neg 82.7%

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

      4. distribute-neg-in 82.7%

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

      5. remove-double-neg 82.7%

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

   9. Simplified 82.7%

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

   10. Taylor expanded in t around 0 60.8%

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

       1. associate-/l* 82.7%

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

   12. Simplified 82.7%

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

   if -8.9999999999999994e84 < y < 1.94999999999999997e-91 or 5.4999999999999997e-71 < y < 9.50000000000000001e-28

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.2%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+84} \lor \neg \left(y \leq 1.95 \cdot 10^{-91} \lor \neg \left(y \leq 5.5 \cdot 10^{-71}\right) \land y \leq 9.5 \cdot 10^{-28}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-55} \lor \neg \left(y \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.7e+21)
     t_1
     (if (<= y -2.2e-43)
       (* (- x y) (/ t z))
       (if (or (<= y -5.8e-55) (not (<= y 2.1e+43)))
         t_1
         (/ t (/ (- z y) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+21) {
		tmp = t_1;
	} else if (y <= -2.2e-43) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -5.8e-55) || !(y <= 2.1e+43)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-1.7d+21)) then
        tmp = t_1
    else if (y <= (-2.2d-43)) then
        tmp = (x - y) * (t / z)
    else if ((y <= (-5.8d-55)) .or. (.not. (y <= 2.1d+43))) then
        tmp = t_1
    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 t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.7e+21) {
		tmp = t_1;
	} else if (y <= -2.2e-43) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -5.8e-55) || !(y <= 2.1e+43)) {
		tmp = t_1;
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.7e+21:
		tmp = t_1
	elif y <= -2.2e-43:
		tmp = (x - y) * (t / z)
	elif (y <= -5.8e-55) or not (y <= 2.1e+43):
		tmp = t_1
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.7e+21)
		tmp = t_1;
	elseif (y <= -2.2e-43)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif ((y <= -5.8e-55) || !(y <= 2.1e+43))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.7e+21)
		tmp = t_1;
	elseif (y <= -2.2e-43)
		tmp = (x - y) * (t / z);
	elseif ((y <= -5.8e-55) || ~((y <= 2.1e+43)))
		tmp = t_1;
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+21], t$95$1, If[LessEqual[y, -2.2e-43], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.8e-55], N[Not[LessEqual[y, 2.1e+43]], $MachinePrecision]], t$95$1, N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e21 or -2.19999999999999997e-43 < y < -5.8e-55 or 2.10000000000000002e43 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.6%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

      1. associate-*r/ 76.6%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in x around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. div-sub 85.8%

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

      3. sub-neg 85.8%

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

      4. *-inverses 85.8%

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

      5. metadata-eval 85.8%

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

   9. Simplified 85.8%

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

   10. Taylor expanded in t around 0 85.8%

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

   if -1.7e21 < y < -2.19999999999999997e-43

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   if -5.8e-55 < y < 2.10000000000000002e43

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.7%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. associate-*r/ 87.7%

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

      2. associate-*l/ 94.7%

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

      3. *-commutative 94.7%

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

      4. clear-num 94.2%

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

      5. un-div-inv 94.3%

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

   6. Applied egg-rr 94.3%

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

   7. Taylor expanded in x around inf 81.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-43}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-55} \lor \neg \left(y \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-55} \lor \neg \left(y \leq 6.7 \cdot 10^{+49}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.65e+21)
     t_1
     (if (<= y -4.5e-45)
       (* (- x y) (/ t z))
       (if (or (<= y -4.6e-55) (not (<= y 6.7e+49)))
         t_1
         (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.65e+21) {
		tmp = t_1;
	} else if (y <= -4.5e-45) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -4.6e-55) || !(y <= 6.7e+49)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-1.65d+21)) then
        tmp = t_1
    else if (y <= (-4.5d-45)) then
        tmp = (x - y) * (t / z)
    else if ((y <= (-4.6d-55)) .or. (.not. (y <= 6.7d+49))) then
        tmp = t_1
    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 t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.65e+21) {
		tmp = t_1;
	} else if (y <= -4.5e-45) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -4.6e-55) || !(y <= 6.7e+49)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.65e+21:
		tmp = t_1
	elif y <= -4.5e-45:
		tmp = (x - y) * (t / z)
	elif (y <= -4.6e-55) or not (y <= 6.7e+49):
		tmp = t_1
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.65e+21)
		tmp = t_1;
	elseif (y <= -4.5e-45)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif ((y <= -4.6e-55) || !(y <= 6.7e+49))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.65e+21)
		tmp = t_1;
	elseif (y <= -4.5e-45)
		tmp = (x - y) * (t / z);
	elseif ((y <= -4.6e-55) || ~((y <= 6.7e+49)))
		tmp = t_1;
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+21], t$95$1, If[LessEqual[y, -4.5e-45], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.6e-55], N[Not[LessEqual[y, 6.7e+49]], $MachinePrecision]], t$95$1, N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e21 or -4.4999999999999999e-45 < y < -4.60000000000000023e-55 or 6.6999999999999999e49 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.6%

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

      2. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

      1. associate-*r/ 76.6%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in x around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. div-sub 85.8%

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

      3. sub-neg 85.8%

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

      4. *-inverses 85.8%

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

      5. metadata-eval 85.8%

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

   9. Simplified 85.8%

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

   10. Taylor expanded in t around 0 85.8%

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

   if -1.65e21 < y < -4.4999999999999999e-45

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   if -4.60000000000000023e-55 < y < 6.6999999999999999e49

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-55} \lor \neg \left(y \leq 6.7 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-55} \lor \neg \left(y \leq 1.6 \cdot 10^{-91}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -9e+84)
     t_1
     (if (<= y -1.25e+33)
       (* (/ y z) (- t))
       (if (or (<= y -1.4e-55) (not (<= y 1.6e-91))) t_1 (* t (/ x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -9e+84) {
		tmp = t_1;
	} else if (y <= -1.25e+33) {
		tmp = (y / z) * -t;
	} else if ((y <= -1.4e-55) || !(y <= 1.6e-91)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-9d+84)) then
        tmp = t_1
    else if (y <= (-1.25d+33)) then
        tmp = (y / z) * -t
    else if ((y <= (-1.4d-55)) .or. (.not. (y <= 1.6d-91))) then
        tmp = t_1
    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 t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -9e+84) {
		tmp = t_1;
	} else if (y <= -1.25e+33) {
		tmp = (y / z) * -t;
	} else if ((y <= -1.4e-55) || !(y <= 1.6e-91)) {
		tmp = t_1;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -9e+84:
		tmp = t_1
	elif y <= -1.25e+33:
		tmp = (y / z) * -t
	elif (y <= -1.4e-55) or not (y <= 1.6e-91):
		tmp = t_1
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -9e+84)
		tmp = t_1;
	elseif (y <= -1.25e+33)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif ((y <= -1.4e-55) || !(y <= 1.6e-91))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -9e+84)
		tmp = t_1;
	elseif (y <= -1.25e+33)
		tmp = (y / z) * -t;
	elseif ((y <= -1.4e-55) || ~((y <= 1.6e-91)))
		tmp = t_1;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+84], t$95$1, If[LessEqual[y, -1.25e+33], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[Or[LessEqual[y, -1.4e-55], N[Not[LessEqual[y, 1.6e-91]], $MachinePrecision]], t$95$1, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.9999999999999994e84 or -1.24999999999999993e33 < y < -1.39999999999999992e-55 or 1.59999999999999998e-91 < y

   1. Initial program 99.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.1%

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

      2. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

      1. associate-*r/ 79.1%

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

      2. associate-*l/ 99.2%

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

      3. *-commutative 99.2%

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

      4. clear-num 99.2%

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

      5. un-div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around 0 75.3%

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

      1. neg-mul-1 75.3%

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

      2. distribute-neg-frac2 75.3%

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

      3. sub-neg 75.3%

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

      4. distribute-neg-in 75.3%

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

      5. remove-double-neg 75.3%

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

   9. Simplified 75.3%

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

   10. Taylor expanded in t around 0 57.5%

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

       1. associate-/l* 75.3%

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

   12. Simplified 75.3%

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

   if -8.9999999999999994e84 < y < -1.24999999999999993e33

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in x around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

      4. distribute-neg-frac2 68.1%

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

   10. Simplified 68.1%

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

   if -1.39999999999999992e-55 < y < 1.59999999999999998e-91

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-55} \lor \neg \left(y \leq 1.6 \cdot 10^{-91}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -4.5e+22)
     t_1
     (if (<= y -4.3e-45)
       (* (- x y) (/ t z))
       (if (<= y -3.4e-81)
         (* y (/ t (- y z)))
         (if (<= y 4.3e+39) (/ t (/ (- z y) x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -4.5e+22) {
		tmp = t_1;
	} else if (y <= -4.3e-45) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.4e-81) {
		tmp = y * (t / (y - z));
	} else if (y <= 4.3e+39) {
		tmp = t / ((z - y) / x);
	} 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 = t / (1.0d0 - (z / y))
    if (y <= (-4.5d+22)) then
        tmp = t_1
    else if (y <= (-4.3d-45)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-3.4d-81)) then
        tmp = y * (t / (y - z))
    else if (y <= 4.3d+39) then
        tmp = t / ((z - y) / x)
    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 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -4.5e+22) {
		tmp = t_1;
	} else if (y <= -4.3e-45) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.4e-81) {
		tmp = y * (t / (y - z));
	} else if (y <= 4.3e+39) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -4.5e+22:
		tmp = t_1
	elif y <= -4.3e-45:
		tmp = (x - y) * (t / z)
	elif y <= -3.4e-81:
		tmp = y * (t / (y - z))
	elif y <= 4.3e+39:
		tmp = t / ((z - y) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -4.5e+22)
		tmp = t_1;
	elseif (y <= -4.3e-45)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -3.4e-81)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 4.3e+39)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -4.5e+22)
		tmp = t_1;
	elseif (y <= -4.3e-45)
		tmp = (x - y) * (t / z);
	elseif (y <= -3.4e-81)
		tmp = y * (t / (y - z));
	elseif (y <= 4.3e+39)
		tmp = t / ((z - y) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+22], t$95$1, If[LessEqual[y, -4.3e-45], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-81], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+39], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4999999999999998e22 or 4.3e39 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.2%

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

      2. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

      1. associate-*r/ 75.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. div-sub 85.8%

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

      3. sub-neg 85.8%

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

      4. *-inverses 85.8%

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

      5. metadata-eval 85.8%

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

   9. Simplified 85.8%

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

   10. Taylor expanded in t around 0 85.8%

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

   if -4.4999999999999998e22 < y < -4.2999999999999999e-45

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 78.1%

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

   7. Simplified 78.1%

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

   if -4.2999999999999999e-45 < y < -3.3999999999999999e-81

   1. Initial program 80.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.3%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*l/ 82.7%

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

      3. distribute-rgt-neg-out 82.7%

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

   7. Simplified 82.7%

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

   if -3.3999999999999999e-81 < y < 4.3e39

   1. Initial program 95.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.0%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. associate-*r/ 88.0%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.7%

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

   6. Applied egg-rr 95.7%

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

   7. Taylor expanded in x around inf 82.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-45}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-81}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-46} \lor \neg \left(y \leq -3.4 \cdot 10^{-55}\right) \land y \leq 2.15 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+89)
   t
   (if (or (<= y -1.45e-46) (and (not (<= y -3.4e-55)) (<= y 2.15e+41)))
     (* x (/ t z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+89) {
		tmp = t;
	} else if ((y <= -1.45e-46) || (!(y <= -3.4e-55) && (y <= 2.15e+41))) {
		tmp = x * (t / z);
	} 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 (y <= (-1.7d+89)) then
        tmp = t
    else if ((y <= (-1.45d-46)) .or. (.not. (y <= (-3.4d-55))) .and. (y <= 2.15d+41)) then
        tmp = x * (t / z)
    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 (y <= -1.7e+89) {
		tmp = t;
	} else if ((y <= -1.45e-46) || (!(y <= -3.4e-55) && (y <= 2.15e+41))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+89:
		tmp = t
	elif (y <= -1.45e-46) or (not (y <= -3.4e-55) and (y <= 2.15e+41)):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+89)
		tmp = t;
	elseif ((y <= -1.45e-46) || (!(y <= -3.4e-55) && (y <= 2.15e+41)))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+89)
		tmp = t;
	elseif ((y <= -1.45e-46) || (~((y <= -3.4e-55)) && (y <= 2.15e+41)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+89], t, If[Or[LessEqual[y, -1.45e-46], And[N[Not[LessEqual[y, -3.4e-55]], $MachinePrecision], LessEqual[y, 2.15e+41]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e89 or -1.45000000000000002e-46 < y < -3.39999999999999973e-55 or 2.15000000000000012e41 < y

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 74.1%

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

      2. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in y around inf 72.9%

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

   if -1.7000000000000001e89 < y < -1.45000000000000002e-46 or -3.39999999999999973e-55 < y < 2.15000000000000012e41

   1. Initial program 95.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 89.2%

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

      2. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around 0 54.7%

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

      1. *-commutative 54.7%

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

      2. associate-/l* 56.9%

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

   7. Simplified 56.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-46} \lor \neg \left(y \leq -3.4 \cdot 10^{-55}\right) \land y \leq 2.15 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+89)
   t
   (if (<= y -2.3e-46)
     (* x (/ t z))
     (if (<= y -4.6e-55) t (if (<= y 1.25e+40) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+89) {
		tmp = t;
	} else if (y <= -2.3e-46) {
		tmp = x * (t / z);
	} else if (y <= -4.6e-55) {
		tmp = t;
	} else if (y <= 1.25e+40) {
		tmp = t * (x / z);
	} 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 (y <= (-1.7d+89)) then
        tmp = t
    else if (y <= (-2.3d-46)) then
        tmp = x * (t / z)
    else if (y <= (-4.6d-55)) then
        tmp = t
    else if (y <= 1.25d+40) then
        tmp = t * (x / z)
    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 (y <= -1.7e+89) {
		tmp = t;
	} else if (y <= -2.3e-46) {
		tmp = x * (t / z);
	} else if (y <= -4.6e-55) {
		tmp = t;
	} else if (y <= 1.25e+40) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+89:
		tmp = t
	elif y <= -2.3e-46:
		tmp = x * (t / z)
	elif y <= -4.6e-55:
		tmp = t
	elif y <= 1.25e+40:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+89)
		tmp = t;
	elseif (y <= -2.3e-46)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= -4.6e-55)
		tmp = t;
	elseif (y <= 1.25e+40)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+89)
		tmp = t;
	elseif (y <= -2.3e-46)
		tmp = x * (t / z);
	elseif (y <= -4.6e-55)
		tmp = t;
	elseif (y <= 1.25e+40)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+89], t, If[LessEqual[y, -2.3e-46], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-55], t, If[LessEqual[y, 1.25e+40], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e89 or -2.2999999999999999e-46 < y < -4.60000000000000023e-55 or 1.25000000000000001e40 < y

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 74.1%

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

      2. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in y around inf 72.9%

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

   if -1.7000000000000001e89 < y < -2.2999999999999999e-46

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.6%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in y around 0 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-/l* 38.7%

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

   7. Simplified 38.7%

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

   if -4.60000000000000023e-55 < y < 1.25000000000000001e40

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.8%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+89}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -5.7e+85)
     t_1
     (if (<= y -5.2e-81)
       (* (- x y) (/ t z))
       (if (<= y 2.05e+44) (* t (/ x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -5.7e+85) {
		tmp = t_1;
	} else if (y <= -5.2e-81) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.05e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-5.7d+85)) then
        tmp = t_1
    else if (y <= (-5.2d-81)) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.05d+44) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -5.7e+85) {
		tmp = t_1;
	} else if (y <= -5.2e-81) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.05e+44) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -5.7e+85:
		tmp = t_1
	elif y <= -5.2e-81:
		tmp = (x - y) * (t / z)
	elif y <= 2.05e+44:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -5.7e+85)
		tmp = t_1;
	elseif (y <= -5.2e-81)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.05e+44)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -5.7e+85)
		tmp = t_1;
	elseif (y <= -5.2e-81)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.05e+44)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.7e+85], t$95$1, If[LessEqual[y, -5.2e-81], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+44], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7000000000000002e85 or 2.04999999999999982e44 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

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

      2. associate-/l* 64.8%

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

   3. Simplified 64.8%

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

      1. associate-*r/ 72.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 84.2%

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

      1. neg-mul-1 84.2%

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

      2. distribute-neg-frac2 84.2%

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

      3. sub-neg 84.2%

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

      4. distribute-neg-in 84.2%

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

      5. remove-double-neg 84.2%

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

   9. Simplified 84.2%

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

   10. Taylor expanded in t around 0 59.6%

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

       1. associate-/l* 84.2%

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

   12. Simplified 84.2%

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

   if -5.7000000000000002e85 < y < -5.1999999999999998e-81

   1. Initial program 93.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.1%

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

      2. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-/l* 67.6%

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

   7. Simplified 67.6%

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

   if -5.1999999999999998e-81 < y < 2.04999999999999982e44

   1. Initial program 95.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-81}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+106)
   t
   (if (<= y -7.2e-82)
     (* y (/ t (- z)))
     (if (<= y 1.05e+44) (/ t (/ z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+106) {
		tmp = t;
	} else if (y <= -7.2e-82) {
		tmp = y * (t / -z);
	} else if (y <= 1.05e+44) {
		tmp = t / (z / x);
	} 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 (y <= (-1.45d+106)) then
        tmp = t
    else if (y <= (-7.2d-82)) then
        tmp = y * (t / -z)
    else if (y <= 1.05d+44) then
        tmp = t / (z / x)
    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 (y <= -1.45e+106) {
		tmp = t;
	} else if (y <= -7.2e-82) {
		tmp = y * (t / -z);
	} else if (y <= 1.05e+44) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+106:
		tmp = t
	elif y <= -7.2e-82:
		tmp = y * (t / -z)
	elif y <= 1.05e+44:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+106)
		tmp = t;
	elseif (y <= -7.2e-82)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (y <= 1.05e+44)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+106)
		tmp = t;
	elseif (y <= -7.2e-82)
		tmp = y * (t / -z);
	elseif (y <= 1.05e+44)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+106], t, If[LessEqual[y, -7.2e-82], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+44], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e106 or 1.04999999999999993e44 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.0%

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

      2. associate-/l* 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -1.4500000000000001e106 < y < -7.19999999999999996e-82

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.5%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in x around 0 47.7%

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

      1. associate-*r/ 47.7%

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

      2. mul-1-neg 47.7%

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

      3. distribute-rgt-neg-out 47.7%

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

      4. associate-*l/ 49.7%

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

   10. Simplified 49.7%

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

   if -7.19999999999999996e-82 < y < 1.04999999999999993e44

   1. Initial program 95.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.9%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 87.9%

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

      2. associate-*l/ 95.6%

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

      3. *-commutative 95.6%

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

      4. clear-num 95.5%

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

      5. un-div-inv 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in y around 0 65.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+106)
   t
   (if (<= y -7.5e+14)
     (* (/ y z) (- t))
     (if (<= y 3.35e+45) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+106) {
		tmp = t;
	} else if (y <= -7.5e+14) {
		tmp = (y / z) * -t;
	} else if (y <= 3.35e+45) {
		tmp = t * (x / z);
	} 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 (y <= (-1.45d+106)) then
        tmp = t
    else if (y <= (-7.5d+14)) then
        tmp = (y / z) * -t
    else if (y <= 3.35d+45) then
        tmp = t * (x / z)
    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 (y <= -1.45e+106) {
		tmp = t;
	} else if (y <= -7.5e+14) {
		tmp = (y / z) * -t;
	} else if (y <= 3.35e+45) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+106:
		tmp = t
	elif y <= -7.5e+14:
		tmp = (y / z) * -t
	elif y <= 3.35e+45:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+106)
		tmp = t;
	elseif (y <= -7.5e+14)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= 3.35e+45)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+106)
		tmp = t;
	elseif (y <= -7.5e+14)
		tmp = (y / z) * -t;
	elseif (y <= 3.35e+45)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+106], t, If[LessEqual[y, -7.5e+14], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, 3.35e+45], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e106 or 3.34999999999999994e45 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.0%

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

      2. associate-/l* 64.3%

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

   3. Simplified 64.3%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -1.4500000000000001e106 < y < -7.5e14

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

   8. Taylor expanded in x around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. associate-/l* 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

      4. distribute-neg-frac2 55.0%

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

   10. Simplified 55.0%

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

   if -7.5e14 < y < 3.34999999999999994e45

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 60.3%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+105)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.55e+111) (* (- y x) (/ t (- y z))) (/ t (/ y (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+105) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.55e+111) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t / (y / (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 (y <= (-4d+105)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.55d+111) then
        tmp = (y - x) * (t / (y - z))
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+105) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.55e+111) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+105:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.55e+111:
		tmp = (y - x) * (t / (y - z))
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+105)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.55e+111)
		tmp = Float64(Float64(y - x) * Float64(t / Float64(y - z)));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e+105)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.55e+111)
		tmp = (y - x) * (t / (y - z));
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+105], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+111], N[(N[(y - x), $MachinePrecision] * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999998e105

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 75.6%

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

      2. associate-/l* 60.1%

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

   3. Simplified 60.1%

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

      1. associate-*r/ 75.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 91.1%

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

      1. mul-1-neg 91.1%

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

      2. div-sub 91.1%

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

      3. sub-neg 91.1%

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

      4. *-inverses 91.1%

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

      5. metadata-eval 91.1%

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

   9. Simplified 91.1%

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

   10. Taylor expanded in t around 0 91.1%

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

   if -3.9999999999999998e105 < y < 1.55e111

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.4%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   if 1.55e111 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 59.4%

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

      2. associate-/l* 64.5%

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

   3. Simplified 64.5%

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

      1. associate-*r/ 59.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 89.6%

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

      1. neg-mul-1 89.6%

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

      2. distribute-neg-frac2 89.6%

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

      3. sub-neg 89.6%

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

      4. distribute-neg-in 89.6%

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

      5. remove-double-neg 89.6%

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

   9. Simplified 89.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.3% 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 97.0%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 82.8%

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

   2. associate-/l* 81.3%

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

3. Simplified 81.3%

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

5. Taylor expanded in y around inf 36.8%

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

Developer target: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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