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

Percentage Accurate: 97.0% → 97.0%

Time: 8.9s

Alternatives: 17

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: 97.0% 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: 97.0% 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]

Derivation

1. Initial program 97.5%

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

   1. associate-*l/ 86.3%

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

   2. associate-/l* 83.9%

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

3. Simplified 83.9%

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

   1. associate-*r/ 86.3%

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

   2. associate-*l/ 97.5%

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

   3. *-commutative 97.5%

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

   4. clear-num 97.5%

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

   5. un-div-inv 97.7%

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

6. Applied egg-rr 97.7%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 2: 73.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56} \lor \neg \left(y \leq 3.8 \cdot 10^{-25}\right) \land y \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.3e+42)
     t_1
     (if (<= y -2.7e-42)
       (/ t (/ z (- x y)))
       (if (<= y 2.5e-235)
         (* x (/ t (- z y)))
         (if (or (<= y 3.2e-56) (and (not (<= y 3.8e-25)) (<= y 9.2e+53)))
           (* t (/ (- x y) z))
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.3e+42) {
		tmp = t_1;
	} else if (y <= -2.7e-42) {
		tmp = t / (z / (x - y));
	} else if (y <= 2.5e-235) {
		tmp = x * (t / (z - y));
	} else if ((y <= 3.2e-56) || (!(y <= 3.8e-25) && (y <= 9.2e+53))) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-2.3d+42)) then
        tmp = t_1
    else if (y <= (-2.7d-42)) then
        tmp = t / (z / (x - y))
    else if (y <= 2.5d-235) then
        tmp = x * (t / (z - y))
    else if ((y <= 3.2d-56) .or. (.not. (y <= 3.8d-25)) .and. (y <= 9.2d+53)) then
        tmp = t * ((x - y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.3e+42) {
		tmp = t_1;
	} else if (y <= -2.7e-42) {
		tmp = t / (z / (x - y));
	} else if (y <= 2.5e-235) {
		tmp = x * (t / (z - y));
	} else if ((y <= 3.2e-56) || (!(y <= 3.8e-25) && (y <= 9.2e+53))) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.3e+42:
		tmp = t_1
	elif y <= -2.7e-42:
		tmp = t / (z / (x - y))
	elif y <= 2.5e-235:
		tmp = x * (t / (z - y))
	elif (y <= 3.2e-56) or (not (y <= 3.8e-25) and (y <= 9.2e+53)):
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.3e+42)
		tmp = t_1;
	elseif (y <= -2.7e-42)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 2.5e-235)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif ((y <= 3.2e-56) || (!(y <= 3.8e-25) && (y <= 9.2e+53)))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.3e+42)
		tmp = t_1;
	elseif (y <= -2.7e-42)
		tmp = t / (z / (x - y));
	elseif (y <= 2.5e-235)
		tmp = x * (t / (z - y));
	elseif ((y <= 3.2e-56) || (~((y <= 3.8e-25)) && (y <= 9.2e+53)))
		tmp = t * ((x - y) / z);
	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[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+42], t$95$1, If[LessEqual[y, -2.7e-42], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-235], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.2e-56], And[N[Not[LessEqual[y, 3.8e-25]], $MachinePrecision], LessEqual[y, 9.2e+53]]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.3e42 or 3.19999999999999986e-56 < y < 3.7999999999999998e-25 or 9.20000000000000079e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

   5. Simplified 81.0%

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

   6. Taylor expanded in x around 0 75.5%

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

      1. *-lft-identity 75.5%

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

      2. *-commutative 75.5%

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

      3. mul-1-neg 75.5%

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

      4. associate-/l* 81.0%

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

      5. distribute-rgt-neg-in 81.0%

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

      6. distribute-lft-in 81.0%

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

      7. sub-neg 81.0%

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

   8. Simplified 81.0%

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

   if -2.3e42 < y < -2.69999999999999999e-42

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

      1. associate-*r/ 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.6%

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

      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 inf 93.5%

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

   if -2.69999999999999999e-42 < y < 2.4999999999999999e-235

   1. Initial program 92.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-*r/ 95.5%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

      4. clear-num 92.4%

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

      5. un-div-inv 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in x around inf 84.8%

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

      1. associate-/r/ 85.8%

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

   9. Applied egg-rr 85.8%

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

   if 2.4999999999999999e-235 < y < 3.19999999999999986e-56 or 3.7999999999999998e-25 < y < 9.20000000000000079e53

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 79.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56} \lor \neg \left(y \leq 3.8 \cdot 10^{-25}\right) \land y \leq 9.2 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 0.21 \lor \neg \left(y \leq 7.6 \cdot 10^{+53}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* t (/ x (- z y)))))
   (if (<= y -2.6e+40)
     t_1
     (if (<= y -3.7e-38)
       (* (- x y) (/ t z))
       (if (<= y 3.4e-73)
         t_2
         (if (<= y 2.7e-58)
           (* t (/ y (- z)))
           (if (or (<= y 0.21) (not (<= y 7.6e+53))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= -3.7e-38) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.4e-73) {
		tmp = t_2;
	} else if (y <= 2.7e-58) {
		tmp = t * (y / -z);
	} else if ((y <= 0.21) || !(y <= 7.6e+53)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = t * (x / (z - y))
    if (y <= (-2.6d+40)) then
        tmp = t_1
    else if (y <= (-3.7d-38)) then
        tmp = (x - y) * (t / z)
    else if (y <= 3.4d-73) then
        tmp = t_2
    else if (y <= 2.7d-58) then
        tmp = t * (y / -z)
    else if ((y <= 0.21d0) .or. (.not. (y <= 7.6d+53))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= -3.7e-38) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.4e-73) {
		tmp = t_2;
	} else if (y <= 2.7e-58) {
		tmp = t * (y / -z);
	} else if ((y <= 0.21) || !(y <= 7.6e+53)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = t * (x / (z - y))
	tmp = 0
	if y <= -2.6e+40:
		tmp = t_1
	elif y <= -3.7e-38:
		tmp = (x - y) * (t / z)
	elif y <= 3.4e-73:
		tmp = t_2
	elif y <= 2.7e-58:
		tmp = t * (y / -z)
	elif (y <= 0.21) or not (y <= 7.6e+53):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= -3.7e-38)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 3.4e-73)
		tmp = t_2;
	elseif (y <= 2.7e-58)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif ((y <= 0.21) || !(y <= 7.6e+53))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= -3.7e-38)
		tmp = (x - y) * (t / z);
	elseif (y <= 3.4e-73)
		tmp = t_2;
	elseif (y <= 2.7e-58)
		tmp = t * (y / -z);
	elseif ((y <= 0.21) || ~((y <= 7.6e+53)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+40], t$95$1, If[LessEqual[y, -3.7e-38], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-73], t$95$2, If[LessEqual[y, 2.7e-58], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 0.21], N[Not[LessEqual[y, 7.6e+53]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6000000000000001e40 or 2.6999999999999999e-58 < y < 0.209999999999999992 or 7.59999999999999995e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. mul-1-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in x around 0 73.8%

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

      1. *-lft-identity 73.8%

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

      2. *-commutative 73.8%

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

      3. mul-1-neg 73.8%

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

      4. associate-/l* 79.0%

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

      5. distribute-rgt-neg-in 79.0%

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

      6. distribute-lft-in 79.0%

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

      7. sub-neg 79.0%

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

   8. Simplified 79.0%

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

   if -2.6000000000000001e40 < y < -3.7e-38

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-/l* 86.2%

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

   7. Simplified 86.2%

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

   if -3.7e-38 < y < 3.40000000000000021e-73 or 0.209999999999999992 < y < 7.59999999999999995e53

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 82.7%

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

   if 3.40000000000000021e-73 < y < 2.6999999999999999e-58

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

       \[\leadsto \color{blue}{t \cdot \left(-\frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-38}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 0.21 \lor \neg \left(y \leq 7.6 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+15} \lor \neg \left(y \leq 9.2 \cdot 10^{+53}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* x (/ t (- z y)))))
   (if (<= y -5.2e+40)
     t_1
     (if (<= y -7.8e-32)
       (* (- x y) (/ t z))
       (if (<= y 1.1e-71)
         t_2
         (if (<= y 5e-57)
           (* t (/ y (- z)))
           (if (or (<= y 7.5e+15) (not (<= y 9.2e+53))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -5.2e+40) {
		tmp = t_1;
	} else if (y <= -7.8e-32) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.1e-71) {
		tmp = t_2;
	} else if (y <= 5e-57) {
		tmp = t * (y / -z);
	} else if ((y <= 7.5e+15) || !(y <= 9.2e+53)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = x * (t / (z - y))
    if (y <= (-5.2d+40)) then
        tmp = t_1
    else if (y <= (-7.8d-32)) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.1d-71) then
        tmp = t_2
    else if (y <= 5d-57) then
        tmp = t * (y / -z)
    else if ((y <= 7.5d+15) .or. (.not. (y <= 9.2d+53))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (y <= -5.2e+40) {
		tmp = t_1;
	} else if (y <= -7.8e-32) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.1e-71) {
		tmp = t_2;
	} else if (y <= 5e-57) {
		tmp = t * (y / -z);
	} else if ((y <= 7.5e+15) || !(y <= 9.2e+53)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = x * (t / (z - y))
	tmp = 0
	if y <= -5.2e+40:
		tmp = t_1
	elif y <= -7.8e-32:
		tmp = (x - y) * (t / z)
	elif y <= 1.1e-71:
		tmp = t_2
	elif y <= 5e-57:
		tmp = t * (y / -z)
	elif (y <= 7.5e+15) or not (y <= 9.2e+53):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -5.2e+40)
		tmp = t_1;
	elseif (y <= -7.8e-32)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.1e-71)
		tmp = t_2;
	elseif (y <= 5e-57)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif ((y <= 7.5e+15) || !(y <= 9.2e+53))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (y <= -5.2e+40)
		tmp = t_1;
	elseif (y <= -7.8e-32)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.1e-71)
		tmp = t_2;
	elseif (y <= 5e-57)
		tmp = t * (y / -z);
	elseif ((y <= 7.5e+15) || ~((y <= 9.2e+53)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+40], t$95$1, If[LessEqual[y, -7.8e-32], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-71], t$95$2, If[LessEqual[y, 5e-57], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7.5e+15], N[Not[LessEqual[y, 9.2e+53]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000001e40 or 5.0000000000000002e-57 < y < 7.5e15 or 9.20000000000000079e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. mul-1-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in x around 0 72.1%

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

      1. *-lft-identity 72.1%

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

      2. *-commutative 72.1%

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

      3. mul-1-neg 72.1%

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

      4. associate-/l* 77.1%

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

      5. distribute-rgt-neg-in 77.1%

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

      6. distribute-lft-in 77.1%

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

      7. sub-neg 77.1%

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

   8. Simplified 77.1%

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

   if -5.2000000000000001e40 < y < -7.8000000000000003e-32

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   if -7.8000000000000003e-32 < y < 1.09999999999999999e-71 or 7.5e15 < y < 9.20000000000000079e53

   1. Initial program 94.3%

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

      1. associate-*l/ 93.7%

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

      2. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

      1. associate-*r/ 93.7%

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

      2. associate-*l/ 94.3%

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

      3. *-commutative 94.3%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in x around inf 85.0%

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

      1. associate-/r/ 84.6%

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

   9. Applied egg-rr 84.6%

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

   if 1.09999999999999999e-71 < y < 5.0000000000000002e-57

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   10. Simplified 100.0%

       \[\leadsto \color{blue}{t \cdot \left(-\frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+15} \lor \neg \left(y \leq 9.2 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+40} \lor \neg \left(y \leq 3.5 \cdot 10^{-56} \lor \neg \left(y \leq 1.1 \cdot 10^{+17}\right) \land y \leq 9 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e+40)
         (not (or (<= y 3.5e-56) (and (not (<= y 1.1e+17)) (<= y 9e+53)))))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e+40) || !((y <= 3.5e-56) || (!(y <= 1.1e+17) && (y <= 9e+53)))) {
		tmp = t * (1.0 - (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 <= (-3.4d+40)) .or. (.not. (y <= 3.5d-56) .or. (.not. (y <= 1.1d+17)) .and. (y <= 9d+53))) then
        tmp = t * (1.0d0 - (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 <= -3.4e+40) || !((y <= 3.5e-56) || (!(y <= 1.1e+17) && (y <= 9e+53)))) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4e+40) or not ((y <= 3.5e-56) or (not (y <= 1.1e+17) and (y <= 9e+53))):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e+40) || !((y <= 3.5e-56) || (!(y <= 1.1e+17) && (y <= 9e+53))))
		tmp = Float64(t * Float64(1.0 - Float64(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 <= -3.4e+40) || ~(((y <= 3.5e-56) || (~((y <= 1.1e+17)) && (y <= 9e+53)))))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e+40], N[Not[Or[LessEqual[y, 3.5e-56], And[N[Not[LessEqual[y, 1.1e+17]], $MachinePrecision], LessEqual[y, 9e+53]]]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999989e40 or 3.4999999999999998e-56 < y < 1.1e17 or 9.0000000000000004e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in x around 0 72.3%

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

      1. *-lft-identity 72.3%

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

      2. *-commutative 72.3%

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

      3. mul-1-neg 72.3%

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

      4. associate-/l* 77.3%

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

      5. distribute-rgt-neg-in 77.3%

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

      6. distribute-lft-in 77.3%

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

      7. sub-neg 77.3%

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

   8. Simplified 77.3%

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

   if -3.39999999999999989e40 < y < 3.4999999999999998e-56 or 1.1e17 < y < 9.0000000000000004e53

   1. Initial program 95.1%

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

      1. associate-*l/ 94.5%

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

      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 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-/l* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+40} \lor \neg \left(y \leq 3.5 \cdot 10^{-56} \lor \neg \left(y \leq 1.1 \cdot 10^{+17}\right) \land y \leq 9 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-236}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.7e+42)
     t_1
     (if (<= y -1.22e-33)
       (/ t (/ z (- x y)))
       (if (<= y 5e-236)
         (/ (* t x) (- z y))
         (if (<= y 7.6e+53) (* t (/ (- x y) z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t_1;
	} else if (y <= -1.22e-33) {
		tmp = t / (z / (x - y));
	} else if (y <= 5e-236) {
		tmp = (t * x) / (z - y);
	} else if (y <= 7.6e+53) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.7d+42)) then
        tmp = t_1
    else if (y <= (-1.22d-33)) then
        tmp = t / (z / (x - y))
    else if (y <= 5d-236) then
        tmp = (t * x) / (z - y)
    else if (y <= 7.6d+53) then
        tmp = t * ((x - y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t_1;
	} else if (y <= -1.22e-33) {
		tmp = t / (z / (x - y));
	} else if (y <= 5e-236) {
		tmp = (t * x) / (z - y);
	} else if (y <= 7.6e+53) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.7e+42:
		tmp = t_1
	elif y <= -1.22e-33:
		tmp = t / (z / (x - y))
	elif y <= 5e-236:
		tmp = (t * x) / (z - y)
	elif y <= 7.6e+53:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.7e+42)
		tmp = t_1;
	elseif (y <= -1.22e-33)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 5e-236)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 7.6e+53)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.7e+42)
		tmp = t_1;
	elseif (y <= -1.22e-33)
		tmp = t / (z / (x - y));
	elseif (y <= 5e-236)
		tmp = (t * x) / (z - y);
	elseif (y <= 7.6e+53)
		tmp = t * ((x - y) / z);
	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[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+42], t$95$1, If[LessEqual[y, -1.22e-33], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-236], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e+53], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999988e42 or 7.59999999999999995e53 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in x around 0 75.3%

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

      1. *-lft-identity 75.3%

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

      2. *-commutative 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 81.3%

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

      5. distribute-rgt-neg-in 81.3%

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

      6. distribute-lft-in 81.3%

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

      7. sub-neg 81.3%

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

   8. Simplified 81.3%

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

   if -1.69999999999999988e42 < y < -1.22e-33

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*r/ 99.6%

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

      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 99.6%

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

      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 inf 92.5%

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

   if -1.22e-33 < y < 4.9999999999999998e-236

   1. Initial program 92.8%

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

      1. associate-*l/ 95.6%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around inf 87.2%

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

   if 4.9999999999999998e-236 < y < 7.59999999999999995e53

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 70.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-236}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.9e+41)
     t_2
     (if (<= y -7e-70)
       t_1
       (if (<= y 3.9e-233) (* x (/ t (- z y))) (if (<= y 1.3e+54) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.9e+41) {
		tmp = t_2;
	} else if (y <= -7e-70) {
		tmp = t_1;
	} else if (y <= 3.9e-233) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.3e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-2.9d+41)) then
        tmp = t_2
    else if (y <= (-7d-70)) then
        tmp = t_1
    else if (y <= 3.9d-233) then
        tmp = x * (t / (z - y))
    else if (y <= 1.3d+54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.9e+41) {
		tmp = t_2;
	} else if (y <= -7e-70) {
		tmp = t_1;
	} else if (y <= 3.9e-233) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.3e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.9e+41:
		tmp = t_2
	elif y <= -7e-70:
		tmp = t_1
	elif y <= 3.9e-233:
		tmp = x * (t / (z - y))
	elif y <= 1.3e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.9e+41)
		tmp = t_2;
	elseif (y <= -7e-70)
		tmp = t_1;
	elseif (y <= 3.9e-233)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.3e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.9e+41)
		tmp = t_2;
	elseif (y <= -7e-70)
		tmp = t_1;
	elseif (y <= 3.9e-233)
		tmp = x * (t / (z - y));
	elseif (y <= 1.3e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+41], t$95$2, If[LessEqual[y, -7e-70], t$95$1, If[LessEqual[y, 3.9e-233], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999988e41 or 1.30000000000000003e54 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in x around 0 75.3%

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

      1. *-lft-identity 75.3%

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

      2. *-commutative 75.3%

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

      3. mul-1-neg 75.3%

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

      4. associate-/l* 81.3%

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

      5. distribute-rgt-neg-in 81.3%

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

      6. distribute-lft-in 81.3%

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

      7. sub-neg 81.3%

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

   8. Simplified 81.3%

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

   if -2.89999999999999988e41 < y < -6.99999999999999949e-70 or 3.9000000000000001e-233 < y < 1.30000000000000003e54

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 75.8%

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

   if -6.99999999999999949e-70 < y < 3.9000000000000001e-233

   1. Initial program 92.4%

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

      1. associate-*l/ 95.4%

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

      2. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

      1. associate-*r/ 95.4%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in x around inf 84.4%

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

      1. associate-/r/ 85.4%

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

   9. Applied egg-rr 85.4%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-233}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.6e+40)
     t_1
     (if (<= y -9.5e-30)
       (/ t (/ z (- y)))
       (if (<= y -9.5e-238)
         (/ x (/ z t))
         (if (<= y 1.5e-86) (/ t (/ z x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= -9.5e-30) {
		tmp = t / (z / -y);
	} else if (y <= -9.5e-238) {
		tmp = x / (z / t);
	} else if (y <= 1.5e-86) {
		tmp = t / (z / 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 - (x / y))
    if (y <= (-2.6d+40)) then
        tmp = t_1
    else if (y <= (-9.5d-30)) then
        tmp = t / (z / -y)
    else if (y <= (-9.5d-238)) then
        tmp = x / (z / t)
    else if (y <= 1.5d-86) then
        tmp = t / (z / 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 - (x / y));
	double tmp;
	if (y <= -2.6e+40) {
		tmp = t_1;
	} else if (y <= -9.5e-30) {
		tmp = t / (z / -y);
	} else if (y <= -9.5e-238) {
		tmp = x / (z / t);
	} else if (y <= 1.5e-86) {
		tmp = t / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.6e+40:
		tmp = t_1
	elif y <= -9.5e-30:
		tmp = t / (z / -y)
	elif y <= -9.5e-238:
		tmp = x / (z / t)
	elif y <= 1.5e-86:
		tmp = t / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= -9.5e-30)
		tmp = Float64(t / Float64(z / Float64(-y)));
	elseif (y <= -9.5e-238)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 1.5e-86)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.6e+40)
		tmp = t_1;
	elseif (y <= -9.5e-30)
		tmp = t / (z / -y);
	elseif (y <= -9.5e-238)
		tmp = x / (z / t);
	elseif (y <= 1.5e-86)
		tmp = t / (z / 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[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+40], t$95$1, If[LessEqual[y, -9.5e-30], N[(t / N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-238], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-86], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6000000000000001e40 or 1.5e-86 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 72.1%

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

      1. mul-1-neg 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in x around 0 68.3%

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

      1. *-lft-identity 68.3%

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

      2. *-commutative 68.3%

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

      3. mul-1-neg 68.3%

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

      4. associate-/l* 72.1%

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

      5. distribute-rgt-neg-in 72.1%

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

      6. distribute-lft-in 72.1%

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

      7. sub-neg 72.1%

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

   8. Simplified 72.1%

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

   if -2.6000000000000001e40 < y < -9.49999999999999939e-30

   1. Initial program 99.8%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*r/ 99.6%

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

      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 99.6%

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

      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 inf 92.5%

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

   8. Taylor expanded in x around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. neg-mul-1 68.5%

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

   10. Simplified 68.5%

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

   if -9.49999999999999939e-30 < y < -9.50000000000000059e-238

   1. Initial program 91.8%

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

      1. associate-*l/ 97.0%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-/l* 73.9%

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

   7. Simplified 73.9%

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

      1. clear-num 73.8%

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

      2. un-div-inv 74.0%

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

   9. Applied egg-rr 74.0%

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

   if -9.50000000000000059e-238 < y < 1.5e-86

   1. Initial program 96.5%

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

      1. associate-*l/ 92.0%

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

      2. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

      1. associate-*r/ 92.0%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.4%

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

      5. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in y around 0 82.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;\frac{t}{\frac{z}{-y}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-40} \lor \neg \left(y \leq 0.38\right) \land y \leq 2.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+43)
   t
   (if (or (<= y 2.7e-40) (and (not (<= y 0.38)) (<= y 2.05e+54)))
     (/ t (/ z x))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+43) {
		tmp = t;
	} else if ((y <= 2.7e-40) || (!(y <= 0.38) && (y <= 2.05e+54))) {
		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 <= (-5.5d+43)) then
        tmp = t
    else if ((y <= 2.7d-40) .or. (.not. (y <= 0.38d0)) .and. (y <= 2.05d+54)) 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 <= -5.5e+43) {
		tmp = t;
	} else if ((y <= 2.7e-40) || (!(y <= 0.38) && (y <= 2.05e+54))) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e+43:
		tmp = t
	elif (y <= 2.7e-40) or (not (y <= 0.38) and (y <= 2.05e+54)):
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+43)
		tmp = t;
	elseif ((y <= 2.7e-40) || (!(y <= 0.38) && (y <= 2.05e+54)))
		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 <= -5.5e+43)
		tmp = t;
	elseif ((y <= 2.7e-40) || (~((y <= 0.38)) && (y <= 2.05e+54)))
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+43], t, If[Or[LessEqual[y, 2.7e-40], And[N[Not[LessEqual[y, 0.38]], $MachinePrecision], LessEqual[y, 2.05e+54]]], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999989e43 or 2.7e-40 < y < 0.38 or 2.04999999999999984e54 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around inf 62.4%

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

   if -5.49999999999999989e43 < y < 2.7e-40 or 0.38 < y < 2.04999999999999984e54

   1. Initial program 95.5%

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

      1. associate-*l/ 95.0%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

      1. associate-*r/ 95.0%

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

      2. associate-*l/ 95.5%

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

      3. *-commutative 95.5%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in y around 0 66.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-40} \lor \neg \left(y \leq 0.38\right) \land y \leq 2.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40} \lor \neg \left(y \leq 0.042\right) \land y \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e+43)
   t
   (if (or (<= y 9e-40) (and (not (<= y 0.042)) (<= y 1.15e+54)))
     (* t (/ x z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e+43) {
		tmp = t;
	} else if ((y <= 9e-40) || (!(y <= 0.042) && (y <= 1.15e+54))) {
		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 <= (-3.9d+43)) then
        tmp = t
    else if ((y <= 9d-40) .or. (.not. (y <= 0.042d0)) .and. (y <= 1.15d+54)) 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 <= -3.9e+43) {
		tmp = t;
	} else if ((y <= 9e-40) || (!(y <= 0.042) && (y <= 1.15e+54))) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e+43:
		tmp = t
	elif (y <= 9e-40) or (not (y <= 0.042) and (y <= 1.15e+54)):
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e+43)
		tmp = t;
	elseif ((y <= 9e-40) || (!(y <= 0.042) && (y <= 1.15e+54)))
		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 <= -3.9e+43)
		tmp = t;
	elseif ((y <= 9e-40) || (~((y <= 0.042)) && (y <= 1.15e+54)))
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e+43], t, If[Or[LessEqual[y, 9e-40], And[N[Not[LessEqual[y, 0.042]], $MachinePrecision], LessEqual[y, 1.15e+54]]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9000000000000001e43 or 9.0000000000000002e-40 < y < 0.0420000000000000026 or 1.14999999999999997e54 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around inf 62.4%

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

   if -3.9000000000000001e43 < y < 9.0000000000000002e-40 or 0.0420000000000000026 < y < 1.14999999999999997e54

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 65.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40} \lor \neg \left(y \leq 0.042\right) \land y \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40} \lor \neg \left(y \leq 4.2 \cdot 10^{+16}\right) \land y \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+43)
   t
   (if (or (<= y 9e-40) (and (not (<= y 4.2e+16)) (<= y 7.6e+53)))
     (* x (/ t z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+43) {
		tmp = t;
	} else if ((y <= 9e-40) || (!(y <= 4.2e+16) && (y <= 7.6e+53))) {
		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 <= (-1.9d+43)) then
        tmp = t
    else if ((y <= 9d-40) .or. (.not. (y <= 4.2d+16)) .and. (y <= 7.6d+53)) 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 <= -1.9e+43) {
		tmp = t;
	} else if ((y <= 9e-40) || (!(y <= 4.2e+16) && (y <= 7.6e+53))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+43:
		tmp = t
	elif (y <= 9e-40) or (not (y <= 4.2e+16) and (y <= 7.6e+53)):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+43)
		tmp = t;
	elseif ((y <= 9e-40) || (!(y <= 4.2e+16) && (y <= 7.6e+53)))
		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 <= -1.9e+43)
		tmp = t;
	elseif ((y <= 9e-40) || (~((y <= 4.2e+16)) && (y <= 7.6e+53)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+43], t, If[Or[LessEqual[y, 9e-40], And[N[Not[LessEqual[y, 4.2e+16]], $MachinePrecision], LessEqual[y, 7.6e+53]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000004e43 or 9.0000000000000002e-40 < y < 4.2e16 or 7.59999999999999995e53 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.9%

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

      2. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in y around inf 60.8%

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

   if -1.90000000000000004e43 < y < 9.0000000000000002e-40 or 4.2e16 < y < 7.59999999999999995e53

   1. Initial program 95.3%

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

      1. associate-*l/ 94.8%

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

      2. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around 0 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-/l* 65.0%

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

   7. Simplified 65.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40} \lor \neg \left(y \leq 4.2 \cdot 10^{+16}\right) \land y \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z x))))
   (if (<= y -1.4e+45)
     t
     (if (<= y 9.5e-85)
       t_1
       (if (<= y 10000.0) (* t (/ y (- z))) (if (<= y 9.5e+53) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double tmp;
	if (y <= -1.4e+45) {
		tmp = t;
	} else if (y <= 9.5e-85) {
		tmp = t_1;
	} else if (y <= 10000.0) {
		tmp = t * (y / -z);
	} else if (y <= 9.5e+53) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t / (z / x)
    if (y <= (-1.4d+45)) then
        tmp = t
    else if (y <= 9.5d-85) then
        tmp = t_1
    else if (y <= 10000.0d0) then
        tmp = t * (y / -z)
    else if (y <= 9.5d+53) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double tmp;
	if (y <= -1.4e+45) {
		tmp = t;
	} else if (y <= 9.5e-85) {
		tmp = t_1;
	} else if (y <= 10000.0) {
		tmp = t * (y / -z);
	} else if (y <= 9.5e+53) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / x)
	tmp = 0
	if y <= -1.4e+45:
		tmp = t
	elif y <= 9.5e-85:
		tmp = t_1
	elif y <= 10000.0:
		tmp = t * (y / -z)
	elif y <= 9.5e+53:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / x))
	tmp = 0.0
	if (y <= -1.4e+45)
		tmp = t;
	elseif (y <= 9.5e-85)
		tmp = t_1;
	elseif (y <= 10000.0)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= 9.5e+53)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / x);
	tmp = 0.0;
	if (y <= -1.4e+45)
		tmp = t;
	elseif (y <= 9.5e-85)
		tmp = t_1;
	elseif (y <= 10000.0)
		tmp = t * (y / -z);
	elseif (y <= 9.5e+53)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+45], t, If[LessEqual[y, 9.5e-85], t$95$1, If[LessEqual[y, 10000.0], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+53], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e45 or 9.5000000000000006e53 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in y around inf 63.5%

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

   if -1.4e45 < y < 9.49999999999999964e-85 or 1e4 < y < 9.5000000000000006e53

   1. Initial program 95.8%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

      1. associate-*r/ 94.5%

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

      2. associate-*l/ 95.8%

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

      3. *-commutative 95.8%

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

      4. clear-num 95.7%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around 0 71.7%

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

   if 9.49999999999999964e-85 < y < 1e4

   1. Initial program 96.1%

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

      1. associate-*l/ 99.5%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 47.6%

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

      1. *-commutative 47.6%

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

      2. associate-/l* 47.6%

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

   7. Simplified 47.6%

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

   8. Taylor expanded in x around 0 44.9%

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

      1. mul-1-neg 44.9%

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

      2. associate-/l* 45.2%

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

      3. distribute-rgt-neg-in 45.2%

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

   10. Simplified 45.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 10000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+138}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e+111)
   (* t (- 1.0 (/ x y)))
   (if (<= y 3.1e+138) (* (- x y) (/ t (- z y))) (/ t (- 1.0 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e+111) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.1e+138) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (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 (y <= (-2.25d+111)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 3.1d+138) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e+111) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.1e+138) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e+111:
		tmp = t * (1.0 - (x / y))
	elif y <= 3.1e+138:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e+111)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 3.1e+138)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e+111)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 3.1e+138)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e+111], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e+138], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e111

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in x around 0 74.4%

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

      1. *-lft-identity 74.4%

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

      2. *-commutative 74.4%

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

      3. mul-1-neg 74.4%

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

      4. associate-/l* 85.2%

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

      5. distribute-rgt-neg-in 85.2%

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

      6. distribute-lft-in 85.2%

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

      7. sub-neg 85.2%

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

   8. Simplified 85.2%

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

   if -2.25e111 < y < 3.0999999999999998e138

   1. Initial program 96.7%

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

      1. associate-*l/ 92.9%

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

      2. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   if 3.0999999999999998e138 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 66.6%

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

      2. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

      1. associate-*r/ 66.6%

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

      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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. div-sub 93.8%

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

      3. sub-neg 93.8%

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

      4. *-inverses 93.8%

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

      5. metadata-eval 93.8%

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

   9. Simplified 93.8%

      \[\leadsto \frac{t}{\color{blue}{-\left(\frac{z}{y} + -1\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+111}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+138}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+64} \lor \neg \left(x \leq 8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e+64) (not (<= x 8e-13)))
   (/ t (/ (- z y) x))
   (/ t (- 1.0 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+64) || !(x <= 8e-13)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t / (1.0 - (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 ((x <= (-4d+64)) .or. (.not. (x <= 8d-13))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e+64) || !(x <= 8e-13)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e+64) or not (x <= 8e-13):
		tmp = t / ((z - y) / x)
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e+64) || !(x <= 8e-13))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4e+64) || ~((x <= 8e-13)))
		tmp = t / ((z - y) / x);
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e+64], N[Not[LessEqual[x, 8e-13]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000009e64 or 8.0000000000000002e-13 < x

   1. Initial program 97.4%

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

      1. associate-*l/ 85.1%

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

      2. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

      1. associate-*r/ 85.1%

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

      2. associate-*l/ 97.4%

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

      3. *-commutative 97.4%

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

      4. clear-num 97.3%

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

      5. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in x around inf 82.2%

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

   if -4.00000000000000009e64 < x < 8.0000000000000002e-13

   1. Initial program 97.7%

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

      1. associate-*l/ 87.3%

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

      2. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

      1. associate-*r/ 87.3%

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

      2. associate-*l/ 97.7%

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

      3. *-commutative 97.7%

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

      4. clear-num 97.7%

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

      5. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in x around 0 80.1%

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

      1. mul-1-neg 80.1%

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

      2. div-sub 80.1%

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

      3. sub-neg 80.1%

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

      4. *-inverses 80.1%

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

      5. metadata-eval 80.1%

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

   9. Simplified 80.1%

      \[\leadsto \frac{t}{\color{blue}{-\left(\frac{z}{y} + -1\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+64} \lor \neg \left(x \leq 8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+64} \lor \neg \left(x \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+64) (not (<= x 1.25e-8)))
   (/ t (/ (- z y) x))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+64) || !(x <= 1.25e-8)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.2d+64)) .or. (.not. (x <= 1.25d-8))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+64) || !(x <= 1.25e-8)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+64) or not (x <= 1.25e-8):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+64) || !(x <= 1.25e-8))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e+64) || ~((x <= 1.25e-8)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+64], N[Not[LessEqual[x, 1.25e-8]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2000000000000001e64 or 1.2499999999999999e-8 < x

   1. Initial program 97.4%

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

      1. associate-*l/ 85.1%

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

      2. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

      1. associate-*r/ 85.1%

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

      2. associate-*l/ 97.4%

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

      3. *-commutative 97.4%

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

      4. clear-num 97.3%

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

      5. un-div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in x around inf 82.2%

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

   if -4.2000000000000001e64 < x < 1.2499999999999999e-8

   1. Initial program 97.7%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac2 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+64} \lor \neg \left(x \leq 1.25 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Final simplification 97.5%

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

Alternative 17: 34.7% 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 97.5%

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

   1. associate-*l/ 86.3%

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

   2. associate-/l* 83.9%

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

3. Simplified 83.9%

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

5. Taylor expanded in y around inf 34.3%

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

Developer target: 97.0% 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 2024091 
(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))