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

Percentage Accurate: 97.2% → 97.3%

Time: 10.4s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

   1. *-commutative 97.5%

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

   2. clear-num 97.5%

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

   3. un-div-inv 97.6%

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

4. Applied egg-rr 97.6%

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

Alternative 2: 59.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.36:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z x))))
   (if (<= y -3.9e+124)
     t
     (if (<= y -1.92e+74)
       (* t (/ x (- y)))
       (if (<= y -6.6e+41)
         t
         (if (<= y -1.36)
           t_1
           (if (<= y -9.8e-38)
             (* x (/ t (- y)))
             (if (<= y -1.25e-73)
               (/ y (/ z (- t)))
               (if (<= y -7.5e-114)
                 (/ (* t (- x)) y)
                 (if (<= y 6.6e+94) t_1 t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double tmp;
	if (y <= -3.9e+124) {
		tmp = t;
	} else if (y <= -1.92e+74) {
		tmp = t * (x / -y);
	} else if (y <= -6.6e+41) {
		tmp = t;
	} else if (y <= -1.36) {
		tmp = t_1;
	} else if (y <= -9.8e-38) {
		tmp = x * (t / -y);
	} else if (y <= -1.25e-73) {
		tmp = y / (z / -t);
	} else if (y <= -7.5e-114) {
		tmp = (t * -x) / y;
	} else if (y <= 6.6e+94) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (z / x)
    if (y <= (-3.9d+124)) then
        tmp = t
    else if (y <= (-1.92d+74)) then
        tmp = t * (x / -y)
    else if (y <= (-6.6d+41)) then
        tmp = t
    else if (y <= (-1.36d0)) then
        tmp = t_1
    else if (y <= (-9.8d-38)) then
        tmp = x * (t / -y)
    else if (y <= (-1.25d-73)) then
        tmp = y / (z / -t)
    else if (y <= (-7.5d-114)) then
        tmp = (t * -x) / y
    else if (y <= 6.6d+94) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double tmp;
	if (y <= -3.9e+124) {
		tmp = t;
	} else if (y <= -1.92e+74) {
		tmp = t * (x / -y);
	} else if (y <= -6.6e+41) {
		tmp = t;
	} else if (y <= -1.36) {
		tmp = t_1;
	} else if (y <= -9.8e-38) {
		tmp = x * (t / -y);
	} else if (y <= -1.25e-73) {
		tmp = y / (z / -t);
	} else if (y <= -7.5e-114) {
		tmp = (t * -x) / y;
	} else if (y <= 6.6e+94) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / x)
	tmp = 0
	if y <= -3.9e+124:
		tmp = t
	elif y <= -1.92e+74:
		tmp = t * (x / -y)
	elif y <= -6.6e+41:
		tmp = t
	elif y <= -1.36:
		tmp = t_1
	elif y <= -9.8e-38:
		tmp = x * (t / -y)
	elif y <= -1.25e-73:
		tmp = y / (z / -t)
	elif y <= -7.5e-114:
		tmp = (t * -x) / y
	elif y <= 6.6e+94:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / x))
	tmp = 0.0
	if (y <= -3.9e+124)
		tmp = t;
	elseif (y <= -1.92e+74)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (y <= -6.6e+41)
		tmp = t;
	elseif (y <= -1.36)
		tmp = t_1;
	elseif (y <= -9.8e-38)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= -1.25e-73)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif (y <= -7.5e-114)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	elseif (y <= 6.6e+94)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / x);
	tmp = 0.0;
	if (y <= -3.9e+124)
		tmp = t;
	elseif (y <= -1.92e+74)
		tmp = t * (x / -y);
	elseif (y <= -6.6e+41)
		tmp = t;
	elseif (y <= -1.36)
		tmp = t_1;
	elseif (y <= -9.8e-38)
		tmp = x * (t / -y);
	elseif (y <= -1.25e-73)
		tmp = y / (z / -t);
	elseif (y <= -7.5e-114)
		tmp = (t * -x) / y;
	elseif (y <= 6.6e+94)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.9e+124], t, If[LessEqual[y, -1.92e+74], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e+41], t, If[LessEqual[y, -1.36], t$95$1, If[LessEqual[y, -9.8e-38], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-73], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-114], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.6e+94], t$95$1, t]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.9e124 or -1.92000000000000002e74 < y < -6.6000000000000001e41 or 6.6e94 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.7%

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

   if -3.9e124 < y < -1.92000000000000002e74

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 68.4%

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

   4. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

   6. Simplified 60.4%

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

   if -6.6000000000000001e41 < y < -1.3600000000000001 or -7.5000000000000002e-114 < y < 6.6e94

   1. Initial program 95.1%

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

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around 0 65.3%

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

   if -1.3600000000000001 < y < -9.80000000000000078e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. associate-*l/ 64.2%

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

      2. associate-/l* 64.4%

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

   5. Applied egg-rr 64.4%

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

   6. Taylor expanded in z around 0 57.4%

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

      1. associate-*r/ 57.4%

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

      2. mul-1-neg 57.4%

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

   8. Simplified 57.4%

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

   if -9.80000000000000078e-38 < y < -1.25e-73

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. clear-num 99.4%

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

      3. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   8. Simplified 90.3%

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

      1. associate-/r/ 90.0%

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

      2. distribute-rgt-neg-out 90.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.0%

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

      5. sqr-neg 23.0%

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

      6. sqrt-unprod 23.0%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 23.0%

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

      10. sqrt-unprod 23.0%

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

      11. sqr-neg 23.0%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 90.0%

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

      14. clear-num 90.0%

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

      15. div-inv 90.3%

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

   10. Applied egg-rr 90.3%

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

   if -1.25e-73 < y < -7.5000000000000002e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.4%

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

   4. Taylor expanded in z around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. neg-mul-1 39.0%

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

      3. distribute-lft-neg-in 39.0%

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

   6. Simplified 39.0%

      \[\leadsto \color{blue}{\frac{\left(-t\right) \cdot x}{y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+124}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.36:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+94}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0175:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z x))) (t_2 (* t (/ x (- y)))))
   (if (<= y -3.2e+126)
     t
     (if (<= y -1.92e+74)
       t_2
       (if (<= y -5.8e+38)
         t
         (if (<= y -0.0175)
           t_1
           (if (<= y -1.75e-36)
             (* x (/ t (- y)))
             (if (<= y -7e-70)
               (/ y (/ z (- t)))
               (if (<= y -7.5e-114) t_2 (if (<= y 7.8e+95) t_1 t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double t_2 = t * (x / -y);
	double tmp;
	if (y <= -3.2e+126) {
		tmp = t;
	} else if (y <= -1.92e+74) {
		tmp = t_2;
	} else if (y <= -5.8e+38) {
		tmp = t;
	} else if (y <= -0.0175) {
		tmp = t_1;
	} else if (y <= -1.75e-36) {
		tmp = x * (t / -y);
	} else if (y <= -7e-70) {
		tmp = y / (z / -t);
	} else if (y <= -7.5e-114) {
		tmp = t_2;
	} else if (y <= 7.8e+95) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (z / x)
    t_2 = t * (x / -y)
    if (y <= (-3.2d+126)) then
        tmp = t
    else if (y <= (-1.92d+74)) then
        tmp = t_2
    else if (y <= (-5.8d+38)) then
        tmp = t
    else if (y <= (-0.0175d0)) then
        tmp = t_1
    else if (y <= (-1.75d-36)) then
        tmp = x * (t / -y)
    else if (y <= (-7d-70)) then
        tmp = y / (z / -t)
    else if (y <= (-7.5d-114)) then
        tmp = t_2
    else if (y <= 7.8d+95) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double t_2 = t * (x / -y);
	double tmp;
	if (y <= -3.2e+126) {
		tmp = t;
	} else if (y <= -1.92e+74) {
		tmp = t_2;
	} else if (y <= -5.8e+38) {
		tmp = t;
	} else if (y <= -0.0175) {
		tmp = t_1;
	} else if (y <= -1.75e-36) {
		tmp = x * (t / -y);
	} else if (y <= -7e-70) {
		tmp = y / (z / -t);
	} else if (y <= -7.5e-114) {
		tmp = t_2;
	} else if (y <= 7.8e+95) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / x)
	t_2 = t * (x / -y)
	tmp = 0
	if y <= -3.2e+126:
		tmp = t
	elif y <= -1.92e+74:
		tmp = t_2
	elif y <= -5.8e+38:
		tmp = t
	elif y <= -0.0175:
		tmp = t_1
	elif y <= -1.75e-36:
		tmp = x * (t / -y)
	elif y <= -7e-70:
		tmp = y / (z / -t)
	elif y <= -7.5e-114:
		tmp = t_2
	elif y <= 7.8e+95:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / x))
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (y <= -3.2e+126)
		tmp = t;
	elseif (y <= -1.92e+74)
		tmp = t_2;
	elseif (y <= -5.8e+38)
		tmp = t;
	elseif (y <= -0.0175)
		tmp = t_1;
	elseif (y <= -1.75e-36)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= -7e-70)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif (y <= -7.5e-114)
		tmp = t_2;
	elseif (y <= 7.8e+95)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / x);
	t_2 = t * (x / -y);
	tmp = 0.0;
	if (y <= -3.2e+126)
		tmp = t;
	elseif (y <= -1.92e+74)
		tmp = t_2;
	elseif (y <= -5.8e+38)
		tmp = t;
	elseif (y <= -0.0175)
		tmp = t_1;
	elseif (y <= -1.75e-36)
		tmp = x * (t / -y);
	elseif (y <= -7e-70)
		tmp = y / (z / -t);
	elseif (y <= -7.5e-114)
		tmp = t_2;
	elseif (y <= 7.8e+95)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+126], t, If[LessEqual[y, -1.92e+74], t$95$2, If[LessEqual[y, -5.8e+38], t, If[LessEqual[y, -0.0175], t$95$1, If[LessEqual[y, -1.75e-36], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-70], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-114], t$95$2, If[LessEqual[y, 7.8e+95], t$95$1, t]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1999999999999998e126 or -1.92000000000000002e74 < y < -5.80000000000000013e38 or 7.7999999999999994e95 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.7%

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

   if -3.1999999999999998e126 < y < -1.92000000000000002e74 or -6.99999999999999949e-70 < y < -7.5000000000000002e-114

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 63.3%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. mul-1-neg 51.2%

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

   6. Simplified 51.2%

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

   if -5.80000000000000013e38 < y < -0.017500000000000002 or -7.5000000000000002e-114 < y < 7.7999999999999994e95

   1. Initial program 95.1%

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

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.4%

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

   4. Applied egg-rr 95.4%

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

   5. Taylor expanded in y around 0 65.3%

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

   if -0.017500000000000002 < y < -1.75e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 64.4%

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

      1. associate-*l/ 64.2%

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

      2. associate-/l* 64.4%

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

   5. Applied egg-rr 64.4%

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

   6. Taylor expanded in z around 0 57.4%

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

      1. associate-*r/ 57.4%

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

      2. mul-1-neg 57.4%

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

   8. Simplified 57.4%

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

   if -1.75e-36 < y < -6.99999999999999949e-70

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. clear-num 99.4%

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

      3. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   8. Simplified 90.3%

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

      1. associate-/r/ 90.0%

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

      2. distribute-rgt-neg-out 90.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.0%

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

      5. sqr-neg 23.0%

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

      6. sqrt-unprod 23.0%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 23.0%

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

      10. sqrt-unprod 23.0%

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

      11. sqr-neg 23.0%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 90.0%

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

      14. clear-num 90.0%

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

      15. div-inv 90.3%

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

   10. Applied egg-rr 90.3%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.92 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -0.0175:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+95}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -3.95 \cdot 10^{-140} \lor \neg \left(y \leq 1.65 \cdot 10^{-60}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -6.6e-40)
     t_1
     (if (<= y -3e-69)
       (/ y (/ z (- t)))
       (if (or (<= y -3.95e-140) (not (<= y 1.65e-60)))
         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 <= -6.6e-40) {
		tmp = t_1;
	} else if (y <= -3e-69) {
		tmp = y / (z / -t);
	} else if ((y <= -3.95e-140) || !(y <= 1.65e-60)) {
		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 <= (-6.6d-40)) then
        tmp = t_1
    else if (y <= (-3d-69)) then
        tmp = y / (z / -t)
    else if ((y <= (-3.95d-140)) .or. (.not. (y <= 1.65d-60))) 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 <= -6.6e-40) {
		tmp = t_1;
	} else if (y <= -3e-69) {
		tmp = y / (z / -t);
	} else if ((y <= -3.95e-140) || !(y <= 1.65e-60)) {
		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 <= -6.6e-40:
		tmp = t_1
	elif y <= -3e-69:
		tmp = y / (z / -t)
	elif (y <= -3.95e-140) or not (y <= 1.65e-60):
		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 <= -6.6e-40)
		tmp = t_1;
	elseif (y <= -3e-69)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif ((y <= -3.95e-140) || !(y <= 1.65e-60))
		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 <= -6.6e-40)
		tmp = t_1;
	elseif (y <= -3e-69)
		tmp = y / (z / -t);
	elseif ((y <= -3.95e-140) || ~((y <= 1.65e-60)))
		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, -6.6e-40], t$95$1, If[LessEqual[y, -3e-69], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.95e-140], N[Not[LessEqual[y, 1.65e-60]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.59999999999999986e-40 or -2.99999999999999989e-69 < y < -3.94999999999999983e-140 or 1.6499999999999999e-60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. div-sub 77.9%

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

      3. sub-neg 77.9%

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

      4. *-inverses 77.9%

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

      5. metadata-eval 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 77.9%

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

   if -6.59999999999999986e-40 < y < -2.99999999999999989e-69

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. clear-num 99.4%

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

      3. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   8. Simplified 90.3%

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

      1. associate-/r/ 90.0%

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

      2. distribute-rgt-neg-out 90.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.0%

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

      5. sqr-neg 23.0%

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

      6. sqrt-unprod 23.0%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 23.0%

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

      10. sqrt-unprod 23.0%

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

      11. sqr-neg 23.0%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 90.0%

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

      14. clear-num 90.0%

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

      15. div-inv 90.3%

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

   10. Applied egg-rr 90.3%

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

   if -3.94999999999999983e-140 < y < 1.6499999999999999e-60

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. associate-*l/ 76.1%

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

      2. associate-/l* 79.3%

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

   5. Applied egg-rr 79.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -3.95 \cdot 10^{-140} \lor \neg \left(y \leq 1.65 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141} \lor \neg \left(y \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.78e-40)
     t_1
     (if (<= y -6.5e-70)
       (/ y (/ z (- t)))
       (if (or (<= y -8.2e-141) (not (<= y 3.1e-59))) t_1 (/ t (/ z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.78e-40) {
		tmp = t_1;
	} else if (y <= -6.5e-70) {
		tmp = y / (z / -t);
	} else if ((y <= -8.2e-141) || !(y <= 3.1e-59)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.78d-40)) then
        tmp = t_1
    else if (y <= (-6.5d-70)) then
        tmp = y / (z / -t)
    else if ((y <= (-8.2d-141)) .or. (.not. (y <= 3.1d-59))) then
        tmp = t_1
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.78e-40) {
		tmp = t_1;
	} else if (y <= -6.5e-70) {
		tmp = y / (z / -t);
	} else if ((y <= -8.2e-141) || !(y <= 3.1e-59)) {
		tmp = t_1;
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.78e-40:
		tmp = t_1
	elif y <= -6.5e-70:
		tmp = y / (z / -t)
	elif (y <= -8.2e-141) or not (y <= 3.1e-59):
		tmp = t_1
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.78e-40)
		tmp = t_1;
	elseif (y <= -6.5e-70)
		tmp = Float64(y / Float64(z / Float64(-t)));
	elseif ((y <= -8.2e-141) || !(y <= 3.1e-59))
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / x));
	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 <= -1.78e-40)
		tmp = t_1;
	elseif (y <= -6.5e-70)
		tmp = y / (z / -t);
	elseif ((y <= -8.2e-141) || ~((y <= 3.1e-59)))
		tmp = t_1;
	else
		tmp = t / (z / x);
	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, -1.78e-40], t$95$1, If[LessEqual[y, -6.5e-70], N[(y / N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.2e-141], N[Not[LessEqual[y, 3.1e-59]], $MachinePrecision]], t$95$1, N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.78000000000000001e-40 or -6.5000000000000005e-70 < y < -8.20000000000000005e-141 or 3.09999999999999999e-59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. div-sub 77.9%

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

      3. sub-neg 77.9%

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

      4. *-inverses 77.9%

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

      5. metadata-eval 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 77.9%

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

   if -1.78000000000000001e-40 < y < -6.5000000000000005e-70

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. clear-num 99.4%

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

      3. un-div-inv 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

   6. Taylor expanded in x around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. distribute-neg-frac2 90.3%

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

   8. Simplified 90.3%

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

      1. associate-/r/ 90.0%

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

      2. distribute-rgt-neg-out 90.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 23.0%

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

      5. sqr-neg 23.0%

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

      6. sqrt-unprod 23.0%

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

      7. add-sqr-sqrt 23.0%

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

      8. *-commutative 23.0%

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

      9. add-sqr-sqrt 23.0%

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

      10. sqrt-unprod 23.0%

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

      11. sqr-neg 23.0%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 90.0%

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

      14. clear-num 90.0%

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

      15. div-inv 90.3%

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

   10. Applied egg-rr 90.3%

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

   if -8.20000000000000005e-141 < y < 3.09999999999999999e-59

   1. Initial program 93.3%

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

      1. *-commutative 93.3%

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

      2. clear-num 93.2%

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

      3. un-div-inv 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in y around 0 75.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.78 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{z}{-t}}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141} \lor \neg \left(y \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-294}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.75e+128)
   t
   (if (<= y -7e-88)
     (* x (/ t (- y)))
     (if (<= y -2.75e-294)
       (/ (* t x) z)
       (if (<= y 9.4e+95) (/ t (/ z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.75e+128) {
		tmp = t;
	} else if (y <= -7e-88) {
		tmp = x * (t / -y);
	} else if (y <= -2.75e-294) {
		tmp = (t * x) / z;
	} else if (y <= 9.4e+95) {
		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 <= (-2.75d+128)) then
        tmp = t
    else if (y <= (-7d-88)) then
        tmp = x * (t / -y)
    else if (y <= (-2.75d-294)) then
        tmp = (t * x) / z
    else if (y <= 9.4d+95) 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 <= -2.75e+128) {
		tmp = t;
	} else if (y <= -7e-88) {
		tmp = x * (t / -y);
	} else if (y <= -2.75e-294) {
		tmp = (t * x) / z;
	} else if (y <= 9.4e+95) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.75e+128:
		tmp = t
	elif y <= -7e-88:
		tmp = x * (t / -y)
	elif y <= -2.75e-294:
		tmp = (t * x) / z
	elif y <= 9.4e+95:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.75e+128)
		tmp = t;
	elseif (y <= -7e-88)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= -2.75e-294)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 9.4e+95)
		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 <= -2.75e+128)
		tmp = t;
	elseif (y <= -7e-88)
		tmp = x * (t / -y);
	elseif (y <= -2.75e-294)
		tmp = (t * x) / z;
	elseif (y <= 9.4e+95)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.75e+128], t, If[LessEqual[y, -7e-88], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.75e-294], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 9.4e+95], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7499999999999999e128 or 9.39999999999999945e95 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.4%

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

   if -2.7499999999999999e128 < y < -7.0000000000000002e-88

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 59.7%

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

      1. associate-*l/ 51.6%

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

      2. associate-/l* 53.3%

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

   5. Applied egg-rr 53.3%

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

   6. Taylor expanded in z around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. mul-1-neg 41.5%

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

   8. Simplified 41.5%

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

   if -7.0000000000000002e-88 < y < -2.75e-294

   1. Initial program 90.5%

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

   3. Taylor expanded in y around 0 66.0%

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

   if -2.75e-294 < y < 9.39999999999999945e95

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. clear-num 97.2%

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

      3. un-div-inv 97.7%

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

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in y around 0 63.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-294}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-267}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -7.2e-37)
     t_1
     (if (<= y 2.45e-267)
       (* (- x y) (/ t z))
       (if (<= y 3.1e-59) (* t (/ x (- z y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -7.2e-37) {
		tmp = t_1;
	} else if (y <= 2.45e-267) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.1e-59) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-7.2d-37)) then
        tmp = t_1
    else if (y <= 2.45d-267) then
        tmp = (x - y) * (t / z)
    else if (y <= 3.1d-59) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -7.2e-37) {
		tmp = t_1;
	} else if (y <= 2.45e-267) {
		tmp = (x - y) * (t / z);
	} else if (y <= 3.1e-59) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -7.2e-37:
		tmp = t_1
	elif y <= 2.45e-267:
		tmp = (x - y) * (t / z)
	elif y <= 3.1e-59:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -7.2e-37)
		tmp = t_1;
	elseif (y <= 2.45e-267)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 3.1e-59)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -7.2e-37)
		tmp = t_1;
	elseif (y <= 2.45e-267)
		tmp = (x - y) * (t / z);
	elseif (y <= 3.1e-59)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e-37], t$95$1, If[LessEqual[y, 2.45e-267], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.1e-59], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000014e-37 or 3.09999999999999999e-59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.5%

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

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 79.5%

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

   if -7.20000000000000014e-37 < y < 2.44999999999999988e-267

   1. Initial program 91.7%

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

   3. Taylor expanded in x around 0 92.5%

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

      1. mul-1-neg 92.5%

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

      2. associate-/l* 93.2%

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

      3. distribute-rgt-neg-in 93.2%

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

      4. associate-/l* 91.7%

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

      5. distribute-lft-in 91.7%

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

      6. +-commutative 91.7%

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

      7. sub-neg 91.7%

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

      8. div-sub 91.7%

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

      9. associate-*r/ 92.5%

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

      10. associate-*l/ 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in z around inf 80.1%

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

   if 2.44999999999999988e-267 < y < 3.09999999999999999e-59

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 84.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-267}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+134} \lor \neg \left(y \leq 2.2 \cdot 10^{+96}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e+134) (not (<= y 2.2e+96)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+134) || !(y <= 2.2e+96)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (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 <= (-1.4d+134)) .or. (.not. (y <= 2.2d+96))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (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 <= -1.4e+134) || !(y <= 2.2e+96)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e+134) or not (y <= 2.2e+96):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e+134) || !(y <= 2.2e+96))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e+134) || ~((y <= 2.2e+96)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e+134], N[Not[LessEqual[y, 2.2e+96]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999e134 or 2.1999999999999999e96 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. div-sub 89.2%

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

      3. sub-neg 89.2%

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

      4. *-inverses 89.2%

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

      5. metadata-eval 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in t around 0 89.2%

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

   if -1.3999999999999999e134 < y < 2.1999999999999999e96

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 87.5%

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

      1. mul-1-neg 87.5%

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

      2. associate-/l* 89.8%

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

      3. distribute-rgt-neg-in 89.8%

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

      4. associate-/l* 96.3%

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

      5. distribute-lft-in 96.3%

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

      6. +-commutative 96.3%

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

      7. sub-neg 96.3%

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

      8. div-sub 96.3%

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

      9. associate-*r/ 88.1%

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

      10. associate-*l/ 89.0%

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

   5. Simplified 89.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+134} \lor \neg \left(y \leq 2.2 \cdot 10^{+96}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+36} \lor \neg \left(x \leq 3.2 \cdot 10^{+31}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e+36) (not (<= x 3.2e+31)))
   (* t (/ x (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e+36) || !(x <= 3.2e+31)) {
		tmp = t * (x / (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 ((x <= (-4.3d+36)) .or. (.not. (x <= 3.2d+31))) then
        tmp = t * (x / (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 ((x <= -4.3e+36) || !(x <= 3.2e+31)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e+36) or not (x <= 3.2e+31):
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e+36) || !(x <= 3.2e+31))
		tmp = Float64(t * Float64(x / 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 ((x <= -4.3e+36) || ~((x <= 3.2e+31)))
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e+36], N[Not[LessEqual[x, 3.2e+31]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000005e36 or 3.2000000000000001e31 < x

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -4.30000000000000005e36 < x < 3.2000000000000001e31

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 84.5%

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

      1. neg-mul-1 84.5%

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

      2. distribute-neg-frac 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+36} \lor \neg \left(x \leq 3.2 \cdot 10^{+31}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-35} \lor \neg \left(y \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-35) (not (<= y 3.1e-59)))
   (* t (- 1.0 (/ x y)))
   (/ t (/ z (- x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-35) || !(y <= 3.1e-59)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t / (z / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.4d-35)) .or. (.not. (y <= 3.1d-59))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t / (z / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-35) || !(y <= 3.1e-59)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t / (z / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-35) or not (y <= 3.1e-59):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t / (z / (x - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-35) || !(y <= 3.1e-59))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t / Float64(z / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e-35) || ~((y <= 3.1e-59)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t / (z / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e-35], N[Not[LessEqual[y, 3.1e-59]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-35 or 3.09999999999999999e-59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.5%

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

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 79.5%

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

   if -1.4e-35 < y < 3.09999999999999999e-59

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. clear-num 94.3%

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

      3. un-div-inv 94.7%

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

   4. Applied egg-rr 94.7%

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

   5. Taylor expanded in z around inf 80.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-35} \lor \neg \left(y \leq 3.1 \cdot 10^{-59}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-35} \lor \neg \left(y \leq 3.2 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.12e-35) (not (<= y 3.2e-60)))
   (* t (- 1.0 (/ x y)))
   (* t (/ (- x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.12e-35) || !(y <= 3.2e-60)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * ((x - 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 <= (-1.12d-35)) .or. (.not. (y <= 3.2d-60))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * ((x - 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 <= -1.12e-35) || !(y <= 3.2e-60)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.12e-35) or not (y <= 3.2e-60):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.12e-35) || !(y <= 3.2e-60))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.12e-35) || ~((y <= 3.2e-60)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.12e-35], N[Not[LessEqual[y, 3.2e-60]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.12e-35 or 3.2000000000000001e-60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.5%

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

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 79.5%

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

   if -1.12e-35 < y < 3.2000000000000001e-60

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 80.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-35} \lor \neg \left(y \leq 3.2 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{-35} \lor \neg \left(y \leq 1.65 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.76e-35) (not (<= y 1.65e-60)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.76e-35) || !(y <= 1.65e-60)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.76d-35)) .or. (.not. (y <= 1.65d-60))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.76e-35) || !(y <= 1.65e-60)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.76e-35) or not (y <= 1.65e-60):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.76e-35) || !(y <= 1.65e-60))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.76e-35) || ~((y <= 1.65e-60)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.76e-35], N[Not[LessEqual[y, 1.65e-60]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7599999999999999e-35 or 1.6499999999999999e-60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.5%

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

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 79.5%

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

   if -1.7599999999999999e-35 < y < 1.6499999999999999e-60

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. associate-/l* 90.1%

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

      3. distribute-rgt-neg-in 90.1%

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

      4. associate-/l* 94.4%

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

      5. distribute-lft-in 94.4%

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

      6. +-commutative 94.4%

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

      7. sub-neg 94.4%

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

      8. div-sub 94.4%

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

      9. associate-*r/ 89.9%

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

      10. associate-*l/ 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in z around inf 78.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{-35} \lor \neg \left(y \leq 1.65 \cdot 10^{-60}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46} \lor \neg \left(y \leq 6.2 \cdot 10^{+94}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+46) (not (<= y 6.2e+94))) t (* t (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+46) || !(y <= 6.2e+94)) {
		tmp = t;
	} 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 <= (-1.8d+46)) .or. (.not. (y <= 6.2d+94))) then
        tmp = t
    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 <= -1.8e+46) || !(y <= 6.2e+94)) {
		tmp = t;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e+46) or not (y <= 6.2e+94):
		tmp = t
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+46) || !(y <= 6.2e+94))
		tmp = t;
	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 <= -1.8e+46) || ~((y <= 6.2e+94)))
		tmp = t;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+46], N[Not[LessEqual[y, 6.2e+94]], $MachinePrecision]], t, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e46 or 6.19999999999999983e94 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 66.8%

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

   if -1.7999999999999999e46 < y < 6.19999999999999983e94

   1. Initial program 95.8%

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

   3. Taylor expanded in y around 0 57.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+46} \lor \neg \left(y \leq 6.2 \cdot 10^{+94}\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+44) t (if (<= y 2e+95) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+44) {
		tmp = t;
	} else if (y <= 2e+95) {
		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 <= (-2.6d+44)) then
        tmp = t
    else if (y <= 2d+95) 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 <= -2.6e+44) {
		tmp = t;
	} else if (y <= 2e+95) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+44:
		tmp = t
	elif y <= 2e+95:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+44)
		tmp = t;
	elseif (y <= 2e+95)
		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 <= -2.6e+44)
		tmp = t;
	elseif (y <= 2e+95)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+44], t, If[LessEqual[y, 2e+95], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5999999999999999e44 or 2.00000000000000004e95 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 66.8%

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

   if -2.5999999999999999e44 < y < 2.00000000000000004e95

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. un-div-inv 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around 0 58.1%

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

Alternative 15: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.8e+39) t (if (<= y 3.1e-59) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.8e+39) {
		tmp = t;
	} else if (y <= 3.1e-59) {
		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 <= (-9.8d+39)) then
        tmp = t
    else if (y <= 3.1d-59) 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 <= -9.8e+39) {
		tmp = t;
	} else if (y <= 3.1e-59) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.8e+39:
		tmp = t
	elif y <= 3.1e-59:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.8e+39)
		tmp = t;
	elseif (y <= 3.1e-59)
		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 <= -9.8e+39)
		tmp = t;
	elseif (y <= 3.1e-59)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.8e+39], t, If[LessEqual[y, 3.1e-59], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999974e39 or 3.09999999999999999e-59 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.3%

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

   if -9.79999999999999974e39 < y < 3.09999999999999999e-59

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 62.4%

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

      1. associate-*l/ 57.6%

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

      2. associate-/l* 58.3%

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

   5. Applied egg-rr 58.3%

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

Alternative 16: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Final simplification 97.5%

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

Alternative 17: 35.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

3. Taylor expanded in y around inf 35.5%

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

Developer target: 97.3% 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 2024097 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

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

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