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

Percentage Accurate: 96.9% → 97.0%

Time: 11.5s

Alternatives: 16

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: 96.9% 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 96.4%

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

   1. associate-*l/ 82.8%

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

   2. associate-*r/ 83.2%

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

3. Simplified 83.2%

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

   1. associate-*r/ 82.8%

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

   2. associate-*l/ 96.4%

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

   3. *-commutative 96.4%

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

   4. clear-num 96.4%

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

   5. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-101} \lor \neg \left(x \leq 6.2 \cdot 10^{-15}\right) \land x \leq 5.1 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -1.55e+81)
     t_2
     (if (<= x -4.8e-48)
       t_1
       (if (<= x -8.5e-94)
         (* x (/ t (- z y)))
         (if (or (<= x 1.12e-101) (and (not (<= x 6.2e-15)) (<= x 5.1e+29)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -1.55e+81) {
		tmp = t_2;
	} else if (x <= -4.8e-48) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = x * (t / (z - y));
	} else if ((x <= 1.12e-101) || (!(x <= 6.2e-15) && (x <= 5.1e+29))) {
		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 * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-1.55d+81)) then
        tmp = t_2
    else if (x <= (-4.8d-48)) then
        tmp = t_1
    else if (x <= (-8.5d-94)) then
        tmp = x * (t / (z - y))
    else if ((x <= 1.12d-101) .or. (.not. (x <= 6.2d-15)) .and. (x <= 5.1d+29)) 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 * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -1.55e+81) {
		tmp = t_2;
	} else if (x <= -4.8e-48) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = x * (t / (z - y));
	} else if ((x <= 1.12e-101) || (!(x <= 6.2e-15) && (x <= 5.1e+29))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -1.55e+81:
		tmp = t_2
	elif x <= -4.8e-48:
		tmp = t_1
	elif x <= -8.5e-94:
		tmp = x * (t / (z - y))
	elif (x <= 1.12e-101) or (not (x <= 6.2e-15) and (x <= 5.1e+29)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -1.55e+81)
		tmp = t_2;
	elseif (x <= -4.8e-48)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif ((x <= 1.12e-101) || (!(x <= 6.2e-15) && (x <= 5.1e+29)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -1.55e+81)
		tmp = t_2;
	elseif (x <= -4.8e-48)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = x * (t / (z - y));
	elseif ((x <= 1.12e-101) || (~((x <= 6.2e-15)) && (x <= 5.1e+29)))
		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[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+81], t$95$2, If[LessEqual[x, -4.8e-48], t$95$1, If[LessEqual[x, -8.5e-94], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.12e-101], And[N[Not[LessEqual[x, 6.2e-15]], $MachinePrecision], LessEqual[x, 5.1e+29]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e81 or 1.12000000000000005e-101 < x < 6.1999999999999998e-15 or 5.1000000000000001e29 < x

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 81.4%

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

   if -1.55e81 < x < -4.8e-48 or -8.50000000000000003e-94 < x < 1.12000000000000005e-101 or 6.1999999999999998e-15 < x < 5.1000000000000001e29

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. distribute-neg-frac 87.8%

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

   4. Simplified 87.8%

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

      1. frac-2neg 87.8%

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

      2. div-inv 87.7%

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

      3. remove-double-neg 87.7%

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

      4. sub-neg 87.7%

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

      5. distribute-neg-in 87.7%

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

      6. remove-double-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. associate-*r/ 87.8%

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

      2. *-rgt-identity 87.8%

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

      3. +-commutative 87.8%

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

      4. unsub-neg 87.8%

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

   8. Simplified 87.8%

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

   if -4.8e-48 < x < -8.50000000000000003e-94

   1. Initial program 86.0%

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

      1. associate-*l/ 92.9%

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

      2. associate-*r/ 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. Taylor expanded in x around inf 75.5%

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

      1. associate-*l/ 75.4%

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

      2. *-commutative 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-101} \lor \neg \left(x \leq 6.2 \cdot 10^{-15}\right) \land x \leq 5.1 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (/ t (/ (- z y) x))))
   (if (<= x -1.3e+81)
     t_2
     (if (<= x -3.8e-45)
       t_1
       (if (<= x -8.5e-94)
         (* x (/ t (- z y)))
         (if (<= x 1.12e-101)
           t_1
           (if (<= x 6.2e-15)
             (* t (/ x (- z y)))
             (if (<= x 1.05e+25) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -1.3e+81) {
		tmp = t_2;
	} else if (x <= -3.8e-45) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = x * (t / (z - y));
	} else if (x <= 1.12e-101) {
		tmp = t_1;
	} else if (x <= 6.2e-15) {
		tmp = t * (x / (z - y));
	} else if (x <= 1.05e+25) {
		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 * (y / (y - z))
    t_2 = t / ((z - y) / x)
    if (x <= (-1.3d+81)) then
        tmp = t_2
    else if (x <= (-3.8d-45)) then
        tmp = t_1
    else if (x <= (-8.5d-94)) then
        tmp = x * (t / (z - y))
    else if (x <= 1.12d-101) then
        tmp = t_1
    else if (x <= 6.2d-15) then
        tmp = t * (x / (z - y))
    else if (x <= 1.05d+25) 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 * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -1.3e+81) {
		tmp = t_2;
	} else if (x <= -3.8e-45) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = x * (t / (z - y));
	} else if (x <= 1.12e-101) {
		tmp = t_1;
	} else if (x <= 6.2e-15) {
		tmp = t * (x / (z - y));
	} else if (x <= 1.05e+25) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t / ((z - y) / x)
	tmp = 0
	if x <= -1.3e+81:
		tmp = t_2
	elif x <= -3.8e-45:
		tmp = t_1
	elif x <= -8.5e-94:
		tmp = x * (t / (z - y))
	elif x <= 1.12e-101:
		tmp = t_1
	elif x <= 6.2e-15:
		tmp = t * (x / (z - y))
	elif x <= 1.05e+25:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -1.3e+81)
		tmp = t_2;
	elseif (x <= -3.8e-45)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (x <= 1.12e-101)
		tmp = t_1;
	elseif (x <= 6.2e-15)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 1.05e+25)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -1.3e+81)
		tmp = t_2;
	elseif (x <= -3.8e-45)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = x * (t / (z - y));
	elseif (x <= 1.12e-101)
		tmp = t_1;
	elseif (x <= 6.2e-15)
		tmp = t * (x / (z - y));
	elseif (x <= 1.05e+25)
		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[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.3e+81], t$95$2, If[LessEqual[x, -3.8e-45], t$95$1, If[LessEqual[x, -8.5e-94], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e-101], t$95$1, If[LessEqual[x, 6.2e-15], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+25], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.29999999999999996e81 or 1.05e25 < x

   1. Initial program 96.5%

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

      1. associate-*l/ 80.9%

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

      2. associate-*r/ 82.4%

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

   3. Simplified 82.4%

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

      1. associate-*r/ 80.9%

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

      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 96.5%

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

      5. un-div-inv 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in x around inf 70.8%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -1.29999999999999996e81 < x < -3.79999999999999997e-45 or -8.50000000000000003e-94 < x < 1.12000000000000005e-101 or 6.1999999999999998e-15 < x < 1.05e25

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. distribute-neg-frac 87.8%

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

   4. Simplified 87.8%

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

      1. frac-2neg 87.8%

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

      2. div-inv 87.7%

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

      3. remove-double-neg 87.7%

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

      4. sub-neg 87.7%

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

      5. distribute-neg-in 87.7%

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

      6. remove-double-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. associate-*r/ 87.8%

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

      2. *-rgt-identity 87.8%

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

      3. +-commutative 87.8%

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

      4. unsub-neg 87.8%

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

   8. Simplified 87.8%

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

   if -3.79999999999999997e-45 < x < -8.50000000000000003e-94

   1. Initial program 86.0%

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

      1. associate-*l/ 92.9%

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

      2. associate-*r/ 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. Taylor expanded in x around inf 75.5%

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

      1. associate-*l/ 75.4%

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

      2. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   if 1.12000000000000005e-101 < x < 6.1999999999999998e-15

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-45}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-101}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+25}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (/ t (/ (- z y) x))))
   (if (<= x -7.5e+80)
     t_2
     (if (<= x -6.2e-49)
       t_1
       (if (<= x -8.5e-94)
         (/ (* t x) (- z y))
         (if (<= x 9e-102)
           t_1
           (if (<= x 6.2e-15)
             (* t (/ x (- z y)))
             (if (<= x 2.05e+27) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -7.5e+80) {
		tmp = t_2;
	} else if (x <= -6.2e-49) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = (t * x) / (z - y);
	} else if (x <= 9e-102) {
		tmp = t_1;
	} else if (x <= 6.2e-15) {
		tmp = t * (x / (z - y));
	} else if (x <= 2.05e+27) {
		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 * (y / (y - z))
    t_2 = t / ((z - y) / x)
    if (x <= (-7.5d+80)) then
        tmp = t_2
    else if (x <= (-6.2d-49)) then
        tmp = t_1
    else if (x <= (-8.5d-94)) then
        tmp = (t * x) / (z - y)
    else if (x <= 9d-102) then
        tmp = t_1
    else if (x <= 6.2d-15) then
        tmp = t * (x / (z - y))
    else if (x <= 2.05d+27) 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 * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -7.5e+80) {
		tmp = t_2;
	} else if (x <= -6.2e-49) {
		tmp = t_1;
	} else if (x <= -8.5e-94) {
		tmp = (t * x) / (z - y);
	} else if (x <= 9e-102) {
		tmp = t_1;
	} else if (x <= 6.2e-15) {
		tmp = t * (x / (z - y));
	} else if (x <= 2.05e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t / ((z - y) / x)
	tmp = 0
	if x <= -7.5e+80:
		tmp = t_2
	elif x <= -6.2e-49:
		tmp = t_1
	elif x <= -8.5e-94:
		tmp = (t * x) / (z - y)
	elif x <= 9e-102:
		tmp = t_1
	elif x <= 6.2e-15:
		tmp = t * (x / (z - y))
	elif x <= 2.05e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -7.5e+80)
		tmp = t_2;
	elseif (x <= -6.2e-49)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (x <= 9e-102)
		tmp = t_1;
	elseif (x <= 6.2e-15)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 2.05e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -7.5e+80)
		tmp = t_2;
	elseif (x <= -6.2e-49)
		tmp = t_1;
	elseif (x <= -8.5e-94)
		tmp = (t * x) / (z - y);
	elseif (x <= 9e-102)
		tmp = t_1;
	elseif (x <= 6.2e-15)
		tmp = t * (x / (z - y));
	elseif (x <= 2.05e+27)
		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[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e+80], t$95$2, If[LessEqual[x, -6.2e-49], t$95$1, If[LessEqual[x, -8.5e-94], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9e-102], t$95$1, If[LessEqual[x, 6.2e-15], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e+27], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.49999999999999994e80 or 2.0500000000000001e27 < x

   1. Initial program 96.5%

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

      1. associate-*l/ 80.9%

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

      2. associate-*r/ 82.4%

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

   3. Simplified 82.4%

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

      1. associate-*r/ 80.9%

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

      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 96.5%

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

      5. un-div-inv 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in x around inf 70.8%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -7.49999999999999994e80 < x < -6.2e-49 or -8.50000000000000003e-94 < x < 8.99999999999999999e-102 or 6.1999999999999998e-15 < x < 2.0500000000000001e27

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. distribute-neg-frac 87.8%

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

   4. Simplified 87.8%

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

      1. frac-2neg 87.8%

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

      2. div-inv 87.7%

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

      3. remove-double-neg 87.7%

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

      4. sub-neg 87.7%

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

      5. distribute-neg-in 87.7%

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

      6. remove-double-neg 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. associate-*r/ 87.8%

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

      2. *-rgt-identity 87.8%

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

      3. +-commutative 87.8%

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

      4. unsub-neg 87.8%

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

   8. Simplified 87.8%

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

   if -6.2e-49 < x < -8.50000000000000003e-94

   1. Initial program 86.0%

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

      1. associate-*l/ 92.9%

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

      2. associate-*r/ 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. Taylor expanded in x around inf 75.5%

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

   if 8.99999999999999999e-102 < x < 6.1999999999999998e-15

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+80}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 5: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+75}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.28e+45)
   t
   (if (<= y -2e-37)
     (* t (/ (- x) y))
     (if (<= y 6.6e-36)
       (* x (/ t z))
       (if (<= y 1.52e+44)
         (/ (* t y) y)
         (if (<= y 3.35e+75) (* (- t) (/ y z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.28e+45) {
		tmp = t;
	} else if (y <= -2e-37) {
		tmp = t * (-x / y);
	} else if (y <= 6.6e-36) {
		tmp = x * (t / z);
	} else if (y <= 1.52e+44) {
		tmp = (t * y) / y;
	} else if (y <= 3.35e+75) {
		tmp = -t * (y / 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 <= (-1.28d+45)) then
        tmp = t
    else if (y <= (-2d-37)) then
        tmp = t * (-x / y)
    else if (y <= 6.6d-36) then
        tmp = x * (t / z)
    else if (y <= 1.52d+44) then
        tmp = (t * y) / y
    else if (y <= 3.35d+75) then
        tmp = -t * (y / 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 <= -1.28e+45) {
		tmp = t;
	} else if (y <= -2e-37) {
		tmp = t * (-x / y);
	} else if (y <= 6.6e-36) {
		tmp = x * (t / z);
	} else if (y <= 1.52e+44) {
		tmp = (t * y) / y;
	} else if (y <= 3.35e+75) {
		tmp = -t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.28e+45:
		tmp = t
	elif y <= -2e-37:
		tmp = t * (-x / y)
	elif y <= 6.6e-36:
		tmp = x * (t / z)
	elif y <= 1.52e+44:
		tmp = (t * y) / y
	elif y <= 3.35e+75:
		tmp = -t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.28e+45)
		tmp = t;
	elseif (y <= -2e-37)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= 6.6e-36)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.52e+44)
		tmp = Float64(Float64(t * y) / y);
	elseif (y <= 3.35e+75)
		tmp = Float64(Float64(-t) * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.28e+45)
		tmp = t;
	elseif (y <= -2e-37)
		tmp = t * (-x / y);
	elseif (y <= 6.6e-36)
		tmp = x * (t / z);
	elseif (y <= 1.52e+44)
		tmp = (t * y) / y;
	elseif (y <= 3.35e+75)
		tmp = -t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.28e+45], t, If[LessEqual[y, -2e-37], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e+44], N[(N[(t * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.35e+75], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.28000000000000002e45 or 3.35e75 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.5%

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

      2. associate-*r/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in y around inf 57.3%

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

   if -1.28000000000000002e45 < y < -2.00000000000000013e-37

   1. Initial program 99.6%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. associate-*l/ 70.4%

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

      2. *-commutative 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 64.2%

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

      1. associate-*r/ 64.2%

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

      2. mul-1-neg 64.2%

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

      3. distribute-lft-neg-out 64.2%

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

      4. *-commutative 64.2%

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

   9. Simplified 64.2%

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

   10. Taylor expanded in x around 0 64.2%

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

       1. mul-1-neg 64.2%

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

       2. associate-*r/ 64.1%

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

       3. *-commutative 64.1%

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

       4. distribute-rgt-neg-in 64.1%

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

   12. Simplified 64.1%

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

   if -2.00000000000000013e-37 < y < 6.59999999999999981e-36

   1. Initial program 92.2%

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

      1. associate-*l/ 92.2%

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

      2. associate-*r/ 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. Step-by-step derivation

      1. associate-*r/ 92.2%

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

      2. associate-*l/ 92.2%

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

      3. *-commutative 92.2%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if 6.59999999999999981e-36 < y < 1.52000000000000003e44

   1. Initial program 99.7%

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

      1. associate-*l/ 84.1%

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

      2. associate-*r/ 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. Taylor expanded in z around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. neg-mul-1 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around 0 46.3%

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

   if 1.52000000000000003e44 < y < 3.35e75

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-neg-frac 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. distribute-neg-frac 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{+75}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+46}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+75}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+45)
   t
   (if (<= y -1.65e-37)
     (/ (* t (- x)) y)
     (if (<= y 6.6e-36)
       (* x (/ t z))
       (if (<= y 1.85e+46)
         (/ (* t y) y)
         (if (<= y 1.26e+75) (* (- t) (/ y z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+45) {
		tmp = t;
	} else if (y <= -1.65e-37) {
		tmp = (t * -x) / y;
	} else if (y <= 6.6e-36) {
		tmp = x * (t / z);
	} else if (y <= 1.85e+46) {
		tmp = (t * y) / y;
	} else if (y <= 1.26e+75) {
		tmp = -t * (y / 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 <= (-1.15d+45)) then
        tmp = t
    else if (y <= (-1.65d-37)) then
        tmp = (t * -x) / y
    else if (y <= 6.6d-36) then
        tmp = x * (t / z)
    else if (y <= 1.85d+46) then
        tmp = (t * y) / y
    else if (y <= 1.26d+75) then
        tmp = -t * (y / 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 <= -1.15e+45) {
		tmp = t;
	} else if (y <= -1.65e-37) {
		tmp = (t * -x) / y;
	} else if (y <= 6.6e-36) {
		tmp = x * (t / z);
	} else if (y <= 1.85e+46) {
		tmp = (t * y) / y;
	} else if (y <= 1.26e+75) {
		tmp = -t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+45:
		tmp = t
	elif y <= -1.65e-37:
		tmp = (t * -x) / y
	elif y <= 6.6e-36:
		tmp = x * (t / z)
	elif y <= 1.85e+46:
		tmp = (t * y) / y
	elif y <= 1.26e+75:
		tmp = -t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+45)
		tmp = t;
	elseif (y <= -1.65e-37)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	elseif (y <= 6.6e-36)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.85e+46)
		tmp = Float64(Float64(t * y) / y);
	elseif (y <= 1.26e+75)
		tmp = Float64(Float64(-t) * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+45)
		tmp = t;
	elseif (y <= -1.65e-37)
		tmp = (t * -x) / y;
	elseif (y <= 6.6e-36)
		tmp = x * (t / z);
	elseif (y <= 1.85e+46)
		tmp = (t * y) / y;
	elseif (y <= 1.26e+75)
		tmp = -t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+45], t, If[LessEqual[y, -1.65e-37], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.6e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+46], N[(N[(t * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.26e+75], N[((-t) * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.15000000000000006e45 or 1.26000000000000003e75 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.5%

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

      2. associate-*r/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in y around inf 57.3%

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

   if -1.15000000000000006e45 < y < -1.64999999999999991e-37

   1. Initial program 99.6%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. *-commutative 63.0%

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

      3. neg-mul-1 63.0%

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

      4. distribute-rgt-neg-in 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x around inf 64.2%

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

      1. associate-*r/ 64.2%

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

      2. neg-mul-1 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

   9. Simplified 64.2%

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

   if -1.64999999999999991e-37 < y < 6.59999999999999981e-36

   1. Initial program 92.2%

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

      1. associate-*l/ 92.2%

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

      2. associate-*r/ 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. Step-by-step derivation

      1. associate-*r/ 92.2%

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

      2. associate-*l/ 92.2%

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

      3. *-commutative 92.2%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if 6.59999999999999981e-36 < y < 1.84999999999999995e46

   1. Initial program 99.7%

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

      1. associate-*l/ 84.1%

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

      2. associate-*r/ 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. Taylor expanded in z around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. neg-mul-1 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around 0 46.3%

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

   if 1.84999999999999995e46 < y < 1.26000000000000003e75

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 67.2%

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

      1. neg-mul-1 67.2%

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

      2. distribute-neg-frac 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in y around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. distribute-neg-frac 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+46}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+75}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+75}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+44)
   t
   (if (<= y -1.75e-37)
     (/ (* t (- x)) y)
     (if (<= y 5.4e-40)
       (* x (/ t z))
       (if (<= y 8.2e+49)
         (/ (* t y) y)
         (if (<= y 2.65e+75) (- (/ (* t y) z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+44) {
		tmp = t;
	} else if (y <= -1.75e-37) {
		tmp = (t * -x) / y;
	} else if (y <= 5.4e-40) {
		tmp = x * (t / z);
	} else if (y <= 8.2e+49) {
		tmp = (t * y) / y;
	} else if (y <= 2.65e+75) {
		tmp = -((t * y) / 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 <= (-1.2d+44)) then
        tmp = t
    else if (y <= (-1.75d-37)) then
        tmp = (t * -x) / y
    else if (y <= 5.4d-40) then
        tmp = x * (t / z)
    else if (y <= 8.2d+49) then
        tmp = (t * y) / y
    else if (y <= 2.65d+75) then
        tmp = -((t * y) / 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 <= -1.2e+44) {
		tmp = t;
	} else if (y <= -1.75e-37) {
		tmp = (t * -x) / y;
	} else if (y <= 5.4e-40) {
		tmp = x * (t / z);
	} else if (y <= 8.2e+49) {
		tmp = (t * y) / y;
	} else if (y <= 2.65e+75) {
		tmp = -((t * y) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+44:
		tmp = t
	elif y <= -1.75e-37:
		tmp = (t * -x) / y
	elif y <= 5.4e-40:
		tmp = x * (t / z)
	elif y <= 8.2e+49:
		tmp = (t * y) / y
	elif y <= 2.65e+75:
		tmp = -((t * y) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+44)
		tmp = t;
	elseif (y <= -1.75e-37)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	elseif (y <= 5.4e-40)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 8.2e+49)
		tmp = Float64(Float64(t * y) / y);
	elseif (y <= 2.65e+75)
		tmp = Float64(-Float64(Float64(t * y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e+44)
		tmp = t;
	elseif (y <= -1.75e-37)
		tmp = (t * -x) / y;
	elseif (y <= 5.4e-40)
		tmp = x * (t / z);
	elseif (y <= 8.2e+49)
		tmp = (t * y) / y;
	elseif (y <= 2.65e+75)
		tmp = -((t * y) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+44], t, If[LessEqual[y, -1.75e-37], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 5.4e-40], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+49], N[(N[(t * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.65e+75], (-N[(N[(t * y), $MachinePrecision] / z), $MachinePrecision]), t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.20000000000000007e44 or 2.6499999999999999e75 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.5%

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

      2. associate-*r/ 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in y around inf 57.3%

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

   if -1.20000000000000007e44 < y < -1.7500000000000001e-37

   1. Initial program 99.6%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. *-commutative 63.0%

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

      3. neg-mul-1 63.0%

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

      4. distribute-rgt-neg-in 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in x around inf 64.2%

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

      1. associate-*r/ 64.2%

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

      2. neg-mul-1 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

   9. Simplified 64.2%

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

   if -1.7500000000000001e-37 < y < 5.4e-40

   1. Initial program 92.2%

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

      1. associate-*l/ 92.2%

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

      2. associate-*r/ 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. Step-by-step derivation

      1. associate-*r/ 92.2%

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

      2. associate-*l/ 92.2%

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

      3. *-commutative 92.2%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   8. Simplified 70.1%

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

   if 5.4e-40 < y < 8.2e49

   1. Initial program 99.7%

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

      1. associate-*l/ 84.1%

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

      2. associate-*r/ 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. Taylor expanded in z around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. neg-mul-1 72.7%

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

      4. distribute-rgt-neg-in 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around 0 46.3%

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

   if 8.2e49 < y < 2.6499999999999999e75

   1. Initial program 99.0%

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

      1. associate-*l/ 99.2%

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

      2. associate-*r/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 82.6%

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

   5. Taylor expanded in x around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-lft-neg-out 66.3%

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

      3. *-commutative 66.3%

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

   7. Simplified 66.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{t \cdot y}{y}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+75}:\\ \;\;\;\;-\frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 90.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+172}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.9e+165)
   (* t (- 1.0 (/ x y)))
   (if (<= y 3.9e+172) (* (- x y) (/ t (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.9e+165) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.9e+172) {
		tmp = (x - y) * (t / (z - y));
	} 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 (y <= (-3.9d+165)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 3.9d+172) then
        tmp = (x - y) * (t / (z - y))
    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 (y <= -3.9e+165) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 3.9e+172) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.9e+165:
		tmp = t * (1.0 - (x / y))
	elif y <= 3.9e+172:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.9e+165)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 3.9e+172)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	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 (y <= -3.9e+165)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 3.9e+172)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.9e+165], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+172], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.89999999999999975e165

   1. Initial program 99.9%

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

      1. div-sub 99.9%

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

      2. flip-- 42.1%

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

      3. associate-/r/ 42.1%

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

      4. fma-neg 42.1%

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

      5. +-commutative 42.1%

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

   3. Applied egg-rr 42.1%

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

      1. fma-udef 42.1%

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

      2. unsub-neg 42.1%

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

      3. associate-*l/ 33.3%

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

   5. Simplified 33.3%

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

   6. Taylor expanded in z around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. unsub-neg 85.9%

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

   8. Simplified 85.9%

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

   if -3.89999999999999975e165 < y < 3.89999999999999967e172

   1. Initial program 95.4%

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

      1. associate-*l/ 87.2%

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

      2. associate-*r/ 91.2%

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

   3. Simplified 91.2%

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

   if 3.89999999999999967e172 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 87.1%

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

      1. neg-mul-1 87.1%

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

      2. distribute-neg-frac 87.1%

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

   4. Simplified 87.1%

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

      1. frac-2neg 87.1%

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

      2. div-inv 87.0%

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

      3. remove-double-neg 87.0%

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

      4. sub-neg 87.0%

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

      5. distribute-neg-in 87.0%

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

      6. remove-double-neg 87.0%

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

   6. Applied egg-rr 87.0%

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

      1. associate-*r/ 87.1%

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

      2. *-rgt-identity 87.1%

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

      3. +-commutative 87.1%

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

      4. unsub-neg 87.1%

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

   8. Simplified 87.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+172}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 9: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.9e+44)
   t
   (if (<= y -1.8e-37) (* t (/ (- x) y)) (if (<= y 8.5e-36) (* x (/ t z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.9e+44) {
		tmp = t;
	} else if (y <= -1.8e-37) {
		tmp = t * (-x / y);
	} else if (y <= 8.5e-36) {
		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 <= (-5.9d+44)) then
        tmp = t
    else if (y <= (-1.8d-37)) then
        tmp = t * (-x / y)
    else if (y <= 8.5d-36) 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 <= -5.9e+44) {
		tmp = t;
	} else if (y <= -1.8e-37) {
		tmp = t * (-x / y);
	} else if (y <= 8.5e-36) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.9e+44:
		tmp = t
	elif y <= -1.8e-37:
		tmp = t * (-x / y)
	elif y <= 8.5e-36:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.9e+44)
		tmp = t;
	elseif (y <= -1.8e-37)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= 8.5e-36)
		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 <= -5.9e+44)
		tmp = t;
	elseif (y <= -1.8e-37)
		tmp = t * (-x / y);
	elseif (y <= 8.5e-36)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.9e+44], t, If[LessEqual[y, -1.8e-37], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.89999999999999965e44 or 8.5000000000000007e-36 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 74.5%

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

      2. associate-*r/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around inf 52.7%

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

   if -5.89999999999999965e44 < y < -1.80000000000000004e-37

   1. Initial program 99.6%

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

      1. associate-*l/ 84.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.2%

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

      1. associate-*l/ 70.4%

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

      2. *-commutative 70.4%

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

   6. Simplified 70.4%

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

   7. Taylor expanded in z around 0 64.2%

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

      1. associate-*r/ 64.2%

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

      2. mul-1-neg 64.2%

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

      3. distribute-lft-neg-out 64.2%

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

      4. *-commutative 64.2%

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

   9. Simplified 64.2%

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

   10. Taylor expanded in x around 0 64.2%

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

       1. mul-1-neg 64.2%

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

       2. associate-*r/ 64.1%

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

       3. *-commutative 64.1%

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

       4. distribute-rgt-neg-in 64.1%

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

   12. Simplified 64.1%

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

   if -1.80000000000000004e-37 < y < 8.5000000000000007e-36

   1. Initial program 92.2%

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

      1. associate-*l/ 92.2%

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

      2. associate-*r/ 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. Step-by-step derivation

      1. associate-*r/ 92.2%

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

      2. associate-*l/ 92.2%

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

      3. *-commutative 92.2%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-37} \lor \neg \left(y \leq 4.8 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.75e-37) (not (<= y 4.8e-38)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e-37) || !(y <= 4.8e-38)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.75d-37)) .or. (.not. (y <= 4.8d-38))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e-37) || !(y <= 4.8e-38)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.75e-37) or not (y <= 4.8e-38):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.75e-37) || !(y <= 4.8e-38))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.75e-37) || ~((y <= 4.8e-38)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.75e-37], N[Not[LessEqual[y, 4.8e-38]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e-37 or 4.80000000000000044e-38 < y

   1. Initial program 99.7%

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

      1. div-sub 99.7%

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

      2. flip-- 72.7%

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

      3. associate-/r/ 72.7%

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

      4. fma-neg 72.7%

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

      5. +-commutative 72.7%

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

   3. Applied egg-rr 72.7%

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

      1. fma-udef 72.7%

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

      2. unsub-neg 72.7%

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

      3. associate-*l/ 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. unsub-neg 72.5%

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

   8. Simplified 72.5%

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

   if -1.7500000000000001e-37 < y < 4.80000000000000044e-38

   1. Initial program 92.2%

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

      1. associate-*l/ 92.2%

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

      2. associate-*r/ 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. Step-by-step derivation

      1. associate-*r/ 92.2%

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

      2. associate-*l/ 92.2%

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

      3. *-commutative 92.2%

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

      4. clear-num 92.2%

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

      5. un-div-inv 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around 0 65.1%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-37} \lor \neg \left(y \leq 4.8 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]

Alternative 11: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.125 \lor \neg \left(y \leq 2.85 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.125) (not (<= y 2.85e+20)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.125) || !(y <= 2.85e+20)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (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 <= (-0.125d0)) .or. (.not. (y <= 2.85d+20))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / (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 <= -0.125) || !(y <= 2.85e+20)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.125) or not (y <= 2.85e+20):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.125) || !(y <= 2.85e+20))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.125) || ~((y <= 2.85e+20)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.125], N[Not[LessEqual[y, 2.85e+20]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.125 or 2.85e20 < y

   1. Initial program 99.7%

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

      1. div-sub 99.8%

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

      2. flip-- 70.6%

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

      3. associate-/r/ 70.7%

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

      4. fma-neg 70.7%

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

      5. +-commutative 70.7%

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

   3. Applied egg-rr 70.7%

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

      1. fma-udef 70.7%

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

      2. unsub-neg 70.7%

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

      3. associate-*l/ 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in z around 0 73.5%

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

      1. mul-1-neg 73.5%

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

      2. unsub-neg 73.5%

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

   8. Simplified 73.5%

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

   if -0.125 < y < 2.85e20

   1. Initial program 93.1%

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

      1. associate-*l/ 91.8%

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

      2. associate-*r/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 76.2%

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

      1. associate-*l/ 80.5%

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

      2. *-commutative 80.5%

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

   6. Simplified 80.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.125 \lor \neg \left(y \leq 2.85 \cdot 10^{+20}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 12: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+43) t (if (<= y 8.5e-36) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+43) {
		tmp = t;
	} else if (y <= 8.5e-36) {
		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 <= (-9d+43)) then
        tmp = t
    else if (y <= 8.5d-36) 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 <= -9e+43) {
		tmp = t;
	} else if (y <= 8.5e-36) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+43:
		tmp = t
	elif y <= 8.5e-36:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+43)
		tmp = t;
	elseif (y <= 8.5e-36)
		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 <= -9e+43)
		tmp = t;
	elseif (y <= 8.5e-36)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+43], t, If[LessEqual[y, 8.5e-36], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -9e43 or 8.5000000000000007e-36 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 74.5%

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

      2. associate-*r/ 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around inf 52.7%

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

   if -9e43 < y < 8.5000000000000007e-36

   1. Initial program 92.9%

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

      1. associate-*l/ 91.4%

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

      2. associate-*r/ 95.2%

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

   3. Simplified 95.2%

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

      1. associate-*r/ 91.4%

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

      2. associate-*l/ 92.9%

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

      3. *-commutative 92.9%

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

      4. clear-num 93.0%

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

      5. un-div-inv 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in y around 0 60.3%

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

      1. associate-*l/ 64.8%

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

      2. *-commutative 64.8%

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

   8. Simplified 64.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 59.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e+124) t (if (<= y 6.7e-38) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e+124) {
		tmp = t;
	} else if (y <= 6.7e-38) {
		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 <= (-8.2d+124)) then
        tmp = t
    else if (y <= 6.7d-38) 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 <= -8.2e+124) {
		tmp = t;
	} else if (y <= 6.7e-38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e+124:
		tmp = t
	elif y <= 6.7e-38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e+124)
		tmp = t;
	elseif (y <= 6.7e-38)
		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 <= -8.2e+124)
		tmp = t;
	elseif (y <= 6.7e-38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e+124], t, If[LessEqual[y, 6.7e-38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.20000000000000002e124 or 6.7000000000000004e-38 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 74.0%

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

      2. associate-*r/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in y around inf 57.2%

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

   if -8.20000000000000002e124 < y < 6.7000000000000004e-38

   1. Initial program 93.9%

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

   2. Taylor expanded in y around 0 60.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e+124) t (if (<= y 8.2e-36) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e+124) {
		tmp = t;
	} else if (y <= 8.2e-36) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.95d+124)) then
        tmp = t
    else if (y <= 8.2d-36) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e+124) {
		tmp = t;
	} else if (y <= 8.2e-36) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.95e+124:
		tmp = t
	elif y <= 8.2e-36:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.95e+124)
		tmp = t;
	elseif (y <= 8.2e-36)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.95e+124)
		tmp = t;
	elseif (y <= 8.2e-36)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.95e+124], t, If[LessEqual[y, 8.2e-36], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e124 or 8.20000000000000025e-36 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 74.0%

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

      2. associate-*r/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in y around inf 57.2%

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

   if -1.95e124 < y < 8.20000000000000025e-36

   1. Initial program 93.9%

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

      1. associate-*l/ 89.4%

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

      2. associate-*r/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 55.6%

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

      1. associate-/l* 60.1%

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

   6. Simplified 60.1%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 96.9% 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 96.4%

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

2. Final simplification 96.4%

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

Alternative 16: 34.4% 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 96.4%

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

   1. associate-*l/ 82.8%

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

   2. associate-*r/ 83.2%

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

3. Simplified 83.2%

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

4. Taylor expanded in y around inf 32.8%

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

5. Final simplification 32.8%

   \[\leadsto t \]

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 2023240 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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