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

Percentage Accurate: 97.1% → 97.1%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% 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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x - y) / (z - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 2: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := t \cdot \frac{-y}{z - y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-117}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* t (/ (- y) (- z y)))))
   (if (<= y -8.5e+38)
     t_2
     (if (<= y -8.4e-16)
       t_1
       (if (<= y -1.42e-61)
         (/ t (/ z (- x y)))
         (if (<= y -2.1e-117)
           (* (- x y) (/ t z))
           (if (<= y -4.2e-211)
             (* x (/ t (- z y)))
             (if (<= y 9.8e-83)
               (* t (/ (- x y) z))
               (if (<= y 2.9e-5)
                 (* t (/ x (- z y)))
                 (if (<= y 2.5e+150) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = t * (-y / (z - y));
	double tmp;
	if (y <= -8.5e+38) {
		tmp = t_2;
	} else if (y <= -8.4e-16) {
		tmp = t_1;
	} else if (y <= -1.42e-61) {
		tmp = t / (z / (x - y));
	} else if (y <= -2.1e-117) {
		tmp = (x - y) * (t / z);
	} else if (y <= -4.2e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.8e-83) {
		tmp = t * ((x - y) / z);
	} else if (y <= 2.9e-5) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.5e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = t * (-y / (z - y))
    if (y <= (-8.5d+38)) then
        tmp = t_2
    else if (y <= (-8.4d-16)) then
        tmp = t_1
    else if (y <= (-1.42d-61)) then
        tmp = t / (z / (x - y))
    else if (y <= (-2.1d-117)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-4.2d-211)) then
        tmp = x * (t / (z - y))
    else if (y <= 9.8d-83) then
        tmp = t * ((x - y) / z)
    else if (y <= 2.9d-5) then
        tmp = t * (x / (z - y))
    else if (y <= 2.5d+150) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = t * (-y / (z - y));
	double tmp;
	if (y <= -8.5e+38) {
		tmp = t_2;
	} else if (y <= -8.4e-16) {
		tmp = t_1;
	} else if (y <= -1.42e-61) {
		tmp = t / (z / (x - y));
	} else if (y <= -2.1e-117) {
		tmp = (x - y) * (t / z);
	} else if (y <= -4.2e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 9.8e-83) {
		tmp = t * ((x - y) / z);
	} else if (y <= 2.9e-5) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.5e+150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = t * (-y / (z - y))
	tmp = 0
	if y <= -8.5e+38:
		tmp = t_2
	elif y <= -8.4e-16:
		tmp = t_1
	elif y <= -1.42e-61:
		tmp = t / (z / (x - y))
	elif y <= -2.1e-117:
		tmp = (x - y) * (t / z)
	elif y <= -4.2e-211:
		tmp = x * (t / (z - y))
	elif y <= 9.8e-83:
		tmp = t * ((x - y) / z)
	elif y <= 2.9e-5:
		tmp = t * (x / (z - y))
	elif y <= 2.5e+150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(t * Float64(Float64(-y) / Float64(z - y)))
	tmp = 0.0
	if (y <= -8.5e+38)
		tmp = t_2;
	elseif (y <= -8.4e-16)
		tmp = t_1;
	elseif (y <= -1.42e-61)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= -2.1e-117)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -4.2e-211)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 9.8e-83)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 2.9e-5)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 2.5e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = t * (-y / (z - y));
	tmp = 0.0;
	if (y <= -8.5e+38)
		tmp = t_2;
	elseif (y <= -8.4e-16)
		tmp = t_1;
	elseif (y <= -1.42e-61)
		tmp = t / (z / (x - y));
	elseif (y <= -2.1e-117)
		tmp = (x - y) * (t / z);
	elseif (y <= -4.2e-211)
		tmp = x * (t / (z - y));
	elseif (y <= 9.8e-83)
		tmp = t * ((x - y) / z);
	elseif (y <= 2.9e-5)
		tmp = t * (x / (z - y));
	elseif (y <= 2.5e+150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+38], t$95$2, If[LessEqual[y, -8.4e-16], t$95$1, If[LessEqual[y, -1.42e-61], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-117], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-211], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-83], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-5], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+150], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.4999999999999997e38 or 2.50000000000000004e150 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 90.7%

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

      1. neg-mul-1 90.7%

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

      2. distribute-neg-frac 90.7%

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

   4. Simplified 90.7%

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

   if -8.4999999999999997e38 < y < -8.4000000000000004e-16 or 2.9e-5 < y < 2.50000000000000004e150

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. div-sub 78.6%

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

      3. sub-neg 78.6%

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

      4. *-inverses 78.6%

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

      5. metadata-eval 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in x around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. *-commutative 78.6%

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

      3. neg-mul-1 78.6%

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

      4. distribute-lft-neg-out 78.6%

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

      5. associate-*l/ 78.6%

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

      6. *-lft-identity 78.6%

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

      7. distribute-rgt-in 78.6%

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

      8. distribute-frac-neg 78.6%

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

      9. sub-neg 78.6%

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

   7. Simplified 78.6%

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

   if -8.4000000000000004e-16 < y < -1.42e-61

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

   if -1.42e-61 < y < -2.0999999999999999e-117

   1. Initial program 88.0%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 69.2%

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

   4. Simplified 69.2%

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

   if -2.0999999999999999e-117 < y < -4.20000000000000015e-211

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*r/ 93.0%

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

   4. Simplified 93.0%

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

   if -4.20000000000000015e-211 < y < 9.8e-83

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 89.1%

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

   if 9.8e-83 < y < 2.9e-5

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 82.5%

      \[\leadsto \color{blue}{\frac{x}{z - y}} \cdot t \]
3. Recombined 7 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-117}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 3: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-124}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 0.02:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.9e+42)
     (* t (/ (- y) (- z y)))
     (if (<= y -1.55e-13)
       t_1
       (if (<= y -2.6e-61)
         (/ t (/ z (- x y)))
         (if (<= y -7.5e-124)
           (* (- x y) (/ t z))
           (if (<= y -3.5e-211)
             (* x (/ t (- z y)))
             (if (<= y 4.7e-82)
               (* t (/ (- x y) z))
               (if (<= y 0.02)
                 (* t (/ x (- z y)))
                 (if (<= y 2.45e+150) t_1 (/ (- t) (+ (/ z y) -1.0))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.9e+42) {
		tmp = t * (-y / (z - y));
	} else if (y <= -1.55e-13) {
		tmp = t_1;
	} else if (y <= -2.6e-61) {
		tmp = t / (z / (x - y));
	} else if (y <= -7.5e-124) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.5e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.7e-82) {
		tmp = t * ((x - y) / z);
	} else if (y <= 0.02) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.45e+150) {
		tmp = t_1;
	} else {
		tmp = -t / ((z / y) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.9d+42)) then
        tmp = t * (-y / (z - y))
    else if (y <= (-1.55d-13)) then
        tmp = t_1
    else if (y <= (-2.6d-61)) then
        tmp = t / (z / (x - y))
    else if (y <= (-7.5d-124)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-3.5d-211)) then
        tmp = x * (t / (z - y))
    else if (y <= 4.7d-82) then
        tmp = t * ((x - y) / z)
    else if (y <= 0.02d0) then
        tmp = t * (x / (z - y))
    else if (y <= 2.45d+150) then
        tmp = t_1
    else
        tmp = -t / ((z / y) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.9e+42) {
		tmp = t * (-y / (z - y));
	} else if (y <= -1.55e-13) {
		tmp = t_1;
	} else if (y <= -2.6e-61) {
		tmp = t / (z / (x - y));
	} else if (y <= -7.5e-124) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.5e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.7e-82) {
		tmp = t * ((x - y) / z);
	} else if (y <= 0.02) {
		tmp = t * (x / (z - y));
	} else if (y <= 2.45e+150) {
		tmp = t_1;
	} else {
		tmp = -t / ((z / y) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.9e+42:
		tmp = t * (-y / (z - y))
	elif y <= -1.55e-13:
		tmp = t_1
	elif y <= -2.6e-61:
		tmp = t / (z / (x - y))
	elif y <= -7.5e-124:
		tmp = (x - y) * (t / z)
	elif y <= -3.5e-211:
		tmp = x * (t / (z - y))
	elif y <= 4.7e-82:
		tmp = t * ((x - y) / z)
	elif y <= 0.02:
		tmp = t * (x / (z - y))
	elif y <= 2.45e+150:
		tmp = t_1
	else:
		tmp = -t / ((z / y) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.9e+42)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	elseif (y <= -1.55e-13)
		tmp = t_1;
	elseif (y <= -2.6e-61)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= -7.5e-124)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -3.5e-211)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.7e-82)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 0.02)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 2.45e+150)
		tmp = t_1;
	else
		tmp = Float64(Float64(-t) / Float64(Float64(z / y) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.9e+42)
		tmp = t * (-y / (z - y));
	elseif (y <= -1.55e-13)
		tmp = t_1;
	elseif (y <= -2.6e-61)
		tmp = t / (z / (x - y));
	elseif (y <= -7.5e-124)
		tmp = (x - y) * (t / z);
	elseif (y <= -3.5e-211)
		tmp = x * (t / (z - y));
	elseif (y <= 4.7e-82)
		tmp = t * ((x - y) / z);
	elseif (y <= 0.02)
		tmp = t * (x / (z - y));
	elseif (y <= 2.45e+150)
		tmp = t_1;
	else
		tmp = -t / ((z / y) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+42], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.55e-13], t$95$1, If[LessEqual[y, -2.6e-61], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-124], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-211], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-82], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.02], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+150], t$95$1, N[((-t) / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.8999999999999999e42

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 87.4%

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

      1. neg-mul-1 87.4%

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

      2. distribute-neg-frac 87.4%

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

   4. Simplified 87.4%

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

   if -1.8999999999999999e42 < y < -1.55e-13 or 0.0200000000000000004 < y < 2.45000000000000003e150

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. div-sub 78.6%

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

      3. sub-neg 78.6%

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

      4. *-inverses 78.6%

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

      5. metadata-eval 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in x around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. *-commutative 78.6%

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

      3. neg-mul-1 78.6%

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

      4. distribute-lft-neg-out 78.6%

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

      5. associate-*l/ 78.6%

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

      6. *-lft-identity 78.6%

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

      7. distribute-rgt-in 78.6%

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

      8. distribute-frac-neg 78.6%

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

      9. sub-neg 78.6%

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

   7. Simplified 78.6%

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

   if -1.55e-13 < y < -2.6000000000000001e-61

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 83.8%

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

      1. associate-/l* 83.8%

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

   4. Simplified 83.8%

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

   if -2.6000000000000001e-61 < y < -7.4999999999999996e-124

   1. Initial program 88.0%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. associate-/l* 57.2%

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

      2. associate-/r/ 69.2%

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

   4. Simplified 69.2%

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

   if -7.4999999999999996e-124 < y < -3.5e-211

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*r/ 93.0%

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

   4. Simplified 93.0%

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

   if -3.5e-211 < y < 4.7000000000000001e-82

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 89.1%

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

   if 4.7000000000000001e-82 < y < 0.0200000000000000004

   1. Initial program 93.2%

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

   2. Taylor expanded in x around inf 82.5%

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

   if 2.45000000000000003e150 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. associate-/l* 95.2%

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

      3. distribute-neg-frac 95.2%

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

      4. div-sub 95.2%

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

      5. *-inverses 95.2%

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

   4. Simplified 95.2%

      \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y} - 1}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-124}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 0.02:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+150}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -1e-10)
     t_2
     (if (<= y -4.1e-65)
       t_1
       (if (<= y -1.35e-71)
         t_2
         (if (<= y -6.8e-119)
           (* (- x y) (/ t z))
           (if (<= y 7e-8) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1e-10) {
		tmp = t_2;
	} else if (y <= -4.1e-65) {
		tmp = t_1;
	} else if (y <= -1.35e-71) {
		tmp = t_2;
	} else if (y <= -6.8e-119) {
		tmp = (x - y) * (t / z);
	} else if (y <= 7e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-1d-10)) then
        tmp = t_2
    else if (y <= (-4.1d-65)) then
        tmp = t_1
    else if (y <= (-1.35d-71)) then
        tmp = t_2
    else if (y <= (-6.8d-119)) then
        tmp = (x - y) * (t / z)
    else if (y <= 7d-8) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1e-10) {
		tmp = t_2;
	} else if (y <= -4.1e-65) {
		tmp = t_1;
	} else if (y <= -1.35e-71) {
		tmp = t_2;
	} else if (y <= -6.8e-119) {
		tmp = (x - y) * (t / z);
	} else if (y <= 7e-8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1e-10:
		tmp = t_2
	elif y <= -4.1e-65:
		tmp = t_1
	elif y <= -1.35e-71:
		tmp = t_2
	elif y <= -6.8e-119:
		tmp = (x - y) * (t / z)
	elif y <= 7e-8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1e-10)
		tmp = t_2;
	elseif (y <= -4.1e-65)
		tmp = t_1;
	elseif (y <= -1.35e-71)
		tmp = t_2;
	elseif (y <= -6.8e-119)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 7e-8)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1e-10)
		tmp = t_2;
	elseif (y <= -4.1e-65)
		tmp = t_1;
	elseif (y <= -1.35e-71)
		tmp = t_2;
	elseif (y <= -6.8e-119)
		tmp = (x - y) * (t / z);
	elseif (y <= 7e-8)
		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[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-10], t$95$2, If[LessEqual[y, -4.1e-65], t$95$1, If[LessEqual[y, -1.35e-71], t$95$2, If[LessEqual[y, -6.8e-119], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-8], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000004e-10 or -4.09999999999999987e-65 < y < -1.3500000000000001e-71 or 7.00000000000000048e-8 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. div-sub 79.3%

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

      3. sub-neg 79.3%

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

      4. *-inverses 79.3%

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

      5. metadata-eval 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in x around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. *-commutative 73.0%

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

      3. neg-mul-1 73.0%

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

      4. distribute-lft-neg-out 73.0%

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

      5. associate-*l/ 79.3%

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

      6. *-lft-identity 79.3%

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

      7. distribute-rgt-in 79.3%

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

      8. distribute-frac-neg 79.3%

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

      9. sub-neg 79.3%

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

   7. Simplified 79.3%

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

   if -1.00000000000000004e-10 < y < -4.09999999999999987e-65 or -6.80000000000000047e-119 < y < 7.00000000000000048e-8

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 81.5%

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

   if -1.3500000000000001e-71 < y < -6.80000000000000047e-119

   1. Initial program 81.0%

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

   2. Taylor expanded in z around inf 90.1%

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

      1. associate-/l* 70.9%

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

      2. associate-/r/ 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-71}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -9e-13)
     t_2
     (if (<= y -8.6e-64)
       t_1
       (if (<= y -4.5e-74)
         t_2
         (if (<= y -1e-211)
           (* x (/ t (- z y)))
           (if (<= y 5.5e-23) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -9e-13) {
		tmp = t_2;
	} else if (y <= -8.6e-64) {
		tmp = t_1;
	} else if (y <= -4.5e-74) {
		tmp = t_2;
	} else if (y <= -1e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.5e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-9d-13)) then
        tmp = t_2
    else if (y <= (-8.6d-64)) then
        tmp = t_1
    else if (y <= (-4.5d-74)) then
        tmp = t_2
    else if (y <= (-1d-211)) then
        tmp = x * (t / (z - y))
    else if (y <= 5.5d-23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -9e-13) {
		tmp = t_2;
	} else if (y <= -8.6e-64) {
		tmp = t_1;
	} else if (y <= -4.5e-74) {
		tmp = t_2;
	} else if (y <= -1e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.5e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -9e-13:
		tmp = t_2
	elif y <= -8.6e-64:
		tmp = t_1
	elif y <= -4.5e-74:
		tmp = t_2
	elif y <= -1e-211:
		tmp = x * (t / (z - y))
	elif y <= 5.5e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -9e-13)
		tmp = t_2;
	elseif (y <= -8.6e-64)
		tmp = t_1;
	elseif (y <= -4.5e-74)
		tmp = t_2;
	elseif (y <= -1e-211)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.5e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -9e-13)
		tmp = t_2;
	elseif (y <= -8.6e-64)
		tmp = t_1;
	elseif (y <= -4.5e-74)
		tmp = t_2;
	elseif (y <= -1e-211)
		tmp = x * (t / (z - y));
	elseif (y <= 5.5e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-13], t$95$2, If[LessEqual[y, -8.6e-64], t$95$1, If[LessEqual[y, -4.5e-74], t$95$2, If[LessEqual[y, -1e-211], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-23], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e-13 or -8.59999999999999947e-64 < y < -4.4999999999999999e-74 or 5.5000000000000001e-23 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. div-sub 79.1%

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

      3. sub-neg 79.1%

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

      4. *-inverses 79.1%

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

      5. metadata-eval 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in x around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. *-commutative 72.9%

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

      3. neg-mul-1 72.9%

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

      4. distribute-lft-neg-out 72.9%

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

      5. associate-*l/ 79.1%

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

      6. *-lft-identity 79.1%

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

      7. distribute-rgt-in 79.1%

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

      8. distribute-frac-neg 79.1%

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

      9. sub-neg 79.1%

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

   7. Simplified 79.1%

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

   if -9e-13 < y < -8.59999999999999947e-64 or -1.00000000000000009e-211 < y < 5.5000000000000001e-23

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 86.3%

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

   if -4.4999999999999999e-74 < y < -1.00000000000000009e-211

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r/ 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-13}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-71}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.9e-15)
     t_2
     (if (<= y -1.62e-65)
       t_1
       (if (<= y -2.4e-71)
         (- t (* x (/ t y)))
         (if (<= y -3.2e-211)
           (* x (/ t (- z y)))
           (if (<= y 2.4e-23) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.9e-15) {
		tmp = t_2;
	} else if (y <= -1.62e-65) {
		tmp = t_1;
	} else if (y <= -2.4e-71) {
		tmp = t - (x * (t / y));
	} else if (y <= -3.2e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.4e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-1.9d-15)) then
        tmp = t_2
    else if (y <= (-1.62d-65)) then
        tmp = t_1
    else if (y <= (-2.4d-71)) then
        tmp = t - (x * (t / y))
    else if (y <= (-3.2d-211)) then
        tmp = x * (t / (z - y))
    else if (y <= 2.4d-23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.9e-15) {
		tmp = t_2;
	} else if (y <= -1.62e-65) {
		tmp = t_1;
	} else if (y <= -2.4e-71) {
		tmp = t - (x * (t / y));
	} else if (y <= -3.2e-211) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.4e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.9e-15:
		tmp = t_2
	elif y <= -1.62e-65:
		tmp = t_1
	elif y <= -2.4e-71:
		tmp = t - (x * (t / y))
	elif y <= -3.2e-211:
		tmp = x * (t / (z - y))
	elif y <= 2.4e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.9e-15)
		tmp = t_2;
	elseif (y <= -1.62e-65)
		tmp = t_1;
	elseif (y <= -2.4e-71)
		tmp = Float64(t - Float64(x * Float64(t / y)));
	elseif (y <= -3.2e-211)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 2.4e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.9e-15)
		tmp = t_2;
	elseif (y <= -1.62e-65)
		tmp = t_1;
	elseif (y <= -2.4e-71)
		tmp = t - (x * (t / y));
	elseif (y <= -3.2e-211)
		tmp = x * (t / (z - y));
	elseif (y <= 2.4e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-15], t$95$2, If[LessEqual[y, -1.62e-65], t$95$1, If[LessEqual[y, -2.4e-71], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-211], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-23], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000001e-15 or 2.39999999999999996e-23 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. div-sub 78.5%

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

      3. sub-neg 78.5%

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

      4. *-inverses 78.5%

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

      5. metadata-eval 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in x around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. *-commutative 72.1%

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

      3. neg-mul-1 72.1%

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

      4. distribute-lft-neg-out 72.1%

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

      5. associate-*l/ 78.5%

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

      6. *-lft-identity 78.5%

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

      7. distribute-rgt-in 78.5%

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

      8. distribute-frac-neg 78.5%

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

      9. sub-neg 78.5%

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

   7. Simplified 78.5%

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

   if -1.9000000000000001e-15 < y < -1.6200000000000001e-65 or -3.19999999999999985e-211 < y < 2.39999999999999996e-23

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 86.3%

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

   if -1.6200000000000001e-65 < y < -2.4e-71

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. div-sub 99.6%

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

      3. sub-neg 99.6%

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

      4. *-inverses 99.6%

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

      5. metadata-eval 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-lft-neg-out 100.0%

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

      5. associate-*l/ 100.0%

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

      6. *-lft-identity 100.0%

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

      7. distribute-rgt-in 99.6%

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

      8. distribute-frac-neg 99.6%

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

      9. sub-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

   10. Simplified 100.0%

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

   if -2.4e-71 < y < -3.19999999999999985e-211

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r/ 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-71}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-23}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 7: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.56 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-71} \lor \neg \left(y \leq 9.5 \cdot 10^{-5}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.56e-16)
     t_1
     (if (<= y -8e-65)
       (* t (/ x z))
       (if (or (<= y -1.6e-71) (not (<= y 9.5e-5)))
         t_1
         (* x (/ t (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.56e-16) {
		tmp = t_1;
	} else if (y <= -8e-65) {
		tmp = t * (x / z);
	} else if ((y <= -1.6e-71) || !(y <= 9.5e-5)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.56d-16)) then
        tmp = t_1
    else if (y <= (-8d-65)) then
        tmp = t * (x / z)
    else if ((y <= (-1.6d-71)) .or. (.not. (y <= 9.5d-5))) then
        tmp = t_1
    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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.56e-16) {
		tmp = t_1;
	} else if (y <= -8e-65) {
		tmp = t * (x / z);
	} else if ((y <= -1.6e-71) || !(y <= 9.5e-5)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.56e-16:
		tmp = t_1
	elif y <= -8e-65:
		tmp = t * (x / z)
	elif (y <= -1.6e-71) or not (y <= 9.5e-5):
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.56e-16)
		tmp = t_1;
	elseif (y <= -8e-65)
		tmp = Float64(t * Float64(x / z));
	elseif ((y <= -1.6e-71) || !(y <= 9.5e-5))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.56e-16)
		tmp = t_1;
	elseif (y <= -8e-65)
		tmp = t * (x / z);
	elseif ((y <= -1.6e-71) || ~((y <= 9.5e-5)))
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.56e-16], t$95$1, If[LessEqual[y, -8e-65], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.6e-71], N[Not[LessEqual[y, 9.5e-5]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55999999999999996e-16 or -7.99999999999999939e-65 < y < -1.5999999999999999e-71 or 9.5000000000000005e-5 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. div-sub 79.5%

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

      3. sub-neg 79.5%

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

      4. *-inverses 79.5%

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

      5. metadata-eval 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in x around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. *-commutative 73.2%

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

      3. neg-mul-1 73.2%

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

      4. distribute-lft-neg-out 73.2%

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

      5. associate-*l/ 79.5%

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

      6. *-lft-identity 79.5%

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

      7. distribute-rgt-in 79.5%

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

      8. distribute-frac-neg 79.5%

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

      9. sub-neg 79.5%

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

   7. Simplified 79.5%

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

   if -1.55999999999999996e-16 < y < -7.99999999999999939e-65

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 70.1%

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

   if -1.5999999999999999e-71 < y < 9.5000000000000005e-5

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*r/ 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-65}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-71} \lor \neg \left(y \leq 9.5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 8: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-72} \lor \neg \left(y \leq 1.85 \cdot 10^{-21}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.4e-18)
     t_1
     (if (<= y -1.06e-64)
       (* t (/ x z))
       (if (or (<= y -1.9e-72) (not (<= y 1.85e-21)))
         t_1
         (* (- x y) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.4e-18) {
		tmp = t_1;
	} else if (y <= -1.06e-64) {
		tmp = t * (x / z);
	} else if ((y <= -1.9e-72) || !(y <= 1.85e-21)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-2.4d-18)) then
        tmp = t_1
    else if (y <= (-1.06d-64)) then
        tmp = t * (x / z)
    else if ((y <= (-1.9d-72)) .or. (.not. (y <= 1.85d-21))) then
        tmp = t_1
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.4e-18) {
		tmp = t_1;
	} else if (y <= -1.06e-64) {
		tmp = t * (x / z);
	} else if ((y <= -1.9e-72) || !(y <= 1.85e-21)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.4e-18:
		tmp = t_1
	elif y <= -1.06e-64:
		tmp = t * (x / z)
	elif (y <= -1.9e-72) or not (y <= 1.85e-21):
		tmp = t_1
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.4e-18)
		tmp = t_1;
	elseif (y <= -1.06e-64)
		tmp = Float64(t * Float64(x / z));
	elseif ((y <= -1.9e-72) || !(y <= 1.85e-21))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.4e-18)
		tmp = t_1;
	elseif (y <= -1.06e-64)
		tmp = t * (x / z);
	elseif ((y <= -1.9e-72) || ~((y <= 1.85e-21)))
		tmp = t_1;
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-18], t$95$1, If[LessEqual[y, -1.06e-64], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.9e-72], N[Not[LessEqual[y, 1.85e-21]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999994e-18 or -1.06000000000000007e-64 < y < -1.90000000000000001e-72 or 1.8500000000000001e-21 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. div-sub 79.1%

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

      3. sub-neg 79.1%

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

      4. *-inverses 79.1%

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

      5. metadata-eval 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in x around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. *-commutative 72.9%

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

      3. neg-mul-1 72.9%

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

      4. distribute-lft-neg-out 72.9%

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

      5. associate-*l/ 79.1%

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

      6. *-lft-identity 79.1%

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

      7. distribute-rgt-in 79.1%

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

      8. distribute-frac-neg 79.1%

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

      9. sub-neg 79.1%

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

   7. Simplified 79.1%

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

   if -2.39999999999999994e-18 < y < -1.06000000000000007e-64

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 70.1%

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

   if -1.90000000000000001e-72 < y < 1.8500000000000001e-21

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 77.2%

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

      1. associate-/l* 81.9%

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

      2. associate-/r/ 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-18}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.06 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-72} \lor \neg \left(y \leq 1.85 \cdot 10^{-21}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-17}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.4:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+118)
   t
   (if (<= y -1.02e+36)
     (* y (/ (- t) z))
     (if (<= y -3.9e-17) t (if (<= y 0.4) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+118) {
		tmp = t;
	} else if (y <= -1.02e+36) {
		tmp = y * (-t / z);
	} else if (y <= -3.9e-17) {
		tmp = t;
	} else if (y <= 0.4) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.7d+118)) then
        tmp = t
    else if (y <= (-1.02d+36)) then
        tmp = y * (-t / z)
    else if (y <= (-3.9d-17)) then
        tmp = t
    else if (y <= 0.4d0) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+118) {
		tmp = t;
	} else if (y <= -1.02e+36) {
		tmp = y * (-t / z);
	} else if (y <= -3.9e-17) {
		tmp = t;
	} else if (y <= 0.4) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+118:
		tmp = t
	elif y <= -1.02e+36:
		tmp = y * (-t / z)
	elif y <= -3.9e-17:
		tmp = t
	elif y <= 0.4:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+118)
		tmp = t;
	elseif (y <= -1.02e+36)
		tmp = Float64(y * Float64(Float64(-t) / z));
	elseif (y <= -3.9e-17)
		tmp = t;
	elseif (y <= 0.4)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+118)
		tmp = t;
	elseif (y <= -1.02e+36)
		tmp = y * (-t / z);
	elseif (y <= -3.9e-17)
		tmp = t;
	elseif (y <= 0.4)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+118], t, If[LessEqual[y, -1.02e+36], N[(y * N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.9e-17], t, If[LessEqual[y, 0.4], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999993e118 or -1.02000000000000003e36 < y < -3.89999999999999989e-17 or 0.40000000000000002 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 69.8%

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

   if -1.69999999999999993e118 < y < -1.02000000000000003e36

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 74.2%

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

      1. neg-mul-1 74.2%

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

      2. distribute-neg-frac 74.2%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in y around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. associate-*r/ 50.5%

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

      4. distribute-rgt-neg-in 50.5%

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

      5. distribute-neg-frac 50.5%

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

   7. Simplified 50.5%

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

   if -3.89999999999999989e-17 < y < 0.40000000000000002

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 68.9%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{-t}{z}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-17}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.4:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 70.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-17} \lor \neg \left(y \leq 8.8 \cdot 10^{-24}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e-17) (not (<= y 8.8e-24)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-17) || !(y <= 8.8e-24)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1d-17)) .or. (.not. (y <= 8.8d-24))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-17) || !(y <= 8.8e-24)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e-17) or not (y <= 8.8e-24):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e-17) || !(y <= 8.8e-24))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e-17) || ~((y <= 8.8e-24)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e-17], N[Not[LessEqual[y, 8.8e-24]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000007e-17 or 8.80000000000000006e-24 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. div-sub 78.5%

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

      3. sub-neg 78.5%

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

      4. *-inverses 78.5%

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

      5. metadata-eval 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in x around 0 72.1%

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

      1. associate-*r/ 72.1%

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

      2. *-commutative 72.1%

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

      3. neg-mul-1 72.1%

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

      4. distribute-lft-neg-out 72.1%

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

      5. associate-*l/ 78.5%

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

      6. *-lft-identity 78.5%

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

      7. distribute-rgt-in 78.5%

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

      8. distribute-frac-neg 78.5%

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

      9. sub-neg 78.5%

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

   7. Simplified 78.5%

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

   if -1.00000000000000007e-17 < y < 8.80000000000000006e-24

   1. Initial program 95.8%

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

   2. Taylor expanded in y around 0 69.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-17} \lor \neg \left(y \leq 8.8 \cdot 10^{-24}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e-16) t (if (<= y 7e-5) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-16) {
		tmp = t;
	} else if (y <= 7e-5) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d-16)) then
        tmp = t
    else if (y <= 7d-5) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-16) {
		tmp = t;
	} else if (y <= 7e-5) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e-16:
		tmp = t
	elif y <= 7e-5:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e-16)
		tmp = t;
	elseif (y <= 7e-5)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e-16)
		tmp = t;
	elseif (y <= 7e-5)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e-16], t, If[LessEqual[y, 7e-5], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e-16 or 6.9999999999999994e-5 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.5%

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

   if -1.2500000000000001e-16 < y < 6.9999999999999994e-5

   1. Initial program 95.9%

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

   2. Taylor expanded in y around 0 68.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 35.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in y around inf 38.3%

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

3. Final simplification 38.3%

   \[\leadsto t \]

Developer target: 97.1% 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 2023322 
(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))