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

Percentage Accurate: 97.1% → 97.1%

Time: 9.6s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% 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 98.5%

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

Alternative 2: 70.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+206}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -16:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -5.2e+206)
     t
     (if (<= y -16.0)
       t_1
       (if (<= y 6.5e-279)
         (* x (/ t (- z y)))
         (if (<= y 6.8e+17) (* t (/ (- x y) z)) (if (<= y 6.4e+81) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.2e+206) {
		tmp = t;
	} else if (y <= -16.0) {
		tmp = t_1;
	} else if (y <= 6.5e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.8e+17) {
		tmp = t * ((x - y) / z);
	} else if (y <= 6.4e+81) {
		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 = (y - x) * (t / y)
    if (y <= (-5.2d+206)) then
        tmp = t
    else if (y <= (-16.0d0)) then
        tmp = t_1
    else if (y <= 6.5d-279) then
        tmp = x * (t / (z - y))
    else if (y <= 6.8d+17) then
        tmp = t * ((x - y) / z)
    else if (y <= 6.4d+81) 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 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.2e+206) {
		tmp = t;
	} else if (y <= -16.0) {
		tmp = t_1;
	} else if (y <= 6.5e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 6.8e+17) {
		tmp = t * ((x - y) / z);
	} else if (y <= 6.4e+81) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -5.2e+206:
		tmp = t
	elif y <= -16.0:
		tmp = t_1
	elif y <= 6.5e-279:
		tmp = x * (t / (z - y))
	elif y <= 6.8e+17:
		tmp = t * ((x - y) / z)
	elif y <= 6.4e+81:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -5.2e+206)
		tmp = t;
	elseif (y <= -16.0)
		tmp = t_1;
	elseif (y <= 6.5e-279)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 6.8e+17)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -5.2e+206)
		tmp = t;
	elseif (y <= -16.0)
		tmp = t_1;
	elseif (y <= 6.5e-279)
		tmp = x * (t / (z - y));
	elseif (y <= 6.8e+17)
		tmp = t * ((x - y) / z);
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+206], t, If[LessEqual[y, -16.0], t$95$1, If[LessEqual[y, 6.5e-279], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+17], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+81], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.19999999999999977e206 or 6.4e81 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 80.2%

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

   if -5.19999999999999977e206 < y < -16 or 6.8e17 < y < 6.4e81

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 75.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 75.4%

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

      1. *-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. sub-neg N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

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

      9. associate-*r* N/A

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

      10. div-inv N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y - \color{blue}{x}\right)\right) \]

      18. --lowering--.f64 69.5%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 69.5%

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

   if -16 < y < 6.4999999999999997e-279

   1. Initial program 94.7%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 94.2%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 79.7%

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

      1. associate-/r/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{x}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), x\right) \]

      4. --lowering--.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 79.9%

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

   if 6.4999999999999997e-279 < y < 6.8e17

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x - y}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), t\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), t\right) \]

   5. Simplified 80.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+206}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -16:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+17}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0033:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -5.8e+200)
     t
     (if (<= y -7.5)
       t_1
       (if (<= y 0.0033) (* x (/ t (- z y))) (if (<= y 3.2e+78) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -7.5) {
		tmp = t_1;
	} else if (y <= 0.0033) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.2e+78) {
		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 = (y - x) * (t / y)
    if (y <= (-5.8d+200)) then
        tmp = t
    else if (y <= (-7.5d0)) then
        tmp = t_1
    else if (y <= 0.0033d0) then
        tmp = x * (t / (z - y))
    else if (y <= 3.2d+78) 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 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -7.5) {
		tmp = t_1;
	} else if (y <= 0.0033) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.2e+78) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -5.8e+200:
		tmp = t
	elif y <= -7.5:
		tmp = t_1
	elif y <= 0.0033:
		tmp = x * (t / (z - y))
	elif y <= 3.2e+78:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -7.5)
		tmp = t_1;
	elseif (y <= 0.0033)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 3.2e+78)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -7.5)
		tmp = t_1;
	elseif (y <= 0.0033)
		tmp = x * (t / (z - y));
	elseif (y <= 3.2e+78)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+200], t, If[LessEqual[y, -7.5], t$95$1, If[LessEqual[y, 0.0033], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+78], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999998e200 or 3.19999999999999994e78 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 80.2%

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

   if -5.7999999999999998e200 < y < -7.5 or 0.0033 < y < 3.19999999999999994e78

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 72.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 72.4%

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

      1. *-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. sub-neg N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

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

      9. associate-*r* N/A

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

      10. div-inv N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y - \color{blue}{x}\right)\right) \]

      18. --lowering--.f64 67.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 67.0%

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

   if -7.5 < y < 0.0033

   1. Initial program 97.0%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 96.8%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 82.4%

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

      1. associate-/r/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{x}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), x\right) \]

      4. --lowering--.f64 78.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 78.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 0.0033:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -5.8e+200)
     t
     (if (<= y -2.8e-126)
       t_1
       (if (<= y 1.65e+19) (* (- x y) (/ t z)) (if (<= y 6.4e+81) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -2.8e-126) {
		tmp = t_1;
	} else if (y <= 1.65e+19) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.4e+81) {
		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 = (y - x) * (t / y)
    if (y <= (-5.8d+200)) then
        tmp = t
    else if (y <= (-2.8d-126)) then
        tmp = t_1
    else if (y <= 1.65d+19) then
        tmp = (x - y) * (t / z)
    else if (y <= 6.4d+81) 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 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -2.8e-126) {
		tmp = t_1;
	} else if (y <= 1.65e+19) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.4e+81) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -5.8e+200:
		tmp = t
	elif y <= -2.8e-126:
		tmp = t_1
	elif y <= 1.65e+19:
		tmp = (x - y) * (t / z)
	elif y <= 6.4e+81:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -2.8e-126)
		tmp = t_1;
	elseif (y <= 1.65e+19)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -2.8e-126)
		tmp = t_1;
	elseif (y <= 1.65e+19)
		tmp = (x - y) * (t / z);
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+200], t, If[LessEqual[y, -2.8e-126], t$95$1, If[LessEqual[y, 1.65e+19], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+81], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999998e200 or 6.4e81 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 80.2%

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

   if -5.7999999999999998e200 < y < -2.79999999999999992e-126 or 1.65e19 < y < 6.4e81

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 68.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 68.5%

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

      1. *-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. sub-neg N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

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

      9. associate-*r* N/A

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

      10. div-inv N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y - \color{blue}{x}\right)\right) \]

      18. --lowering--.f64 63.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 63.4%

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

   if -2.79999999999999992e-126 < y < 1.65e19

   1. Initial program 96.5%

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

      1. associate-*l/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(x - y\right) \cdot t\right), \color{blue}{\left(z - y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(x - y\right), t\right), \left(\color{blue}{z} - y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \left(z - y\right)\right) \]

      5. --lowering--.f64 92.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \color{blue}{z}\right) \]
   6. Step-by-step derivation

   7. Simplified 78.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(x - y\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\color{blue}{x} - y\right)\right) \]

      5. --lowering--.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 78.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-126}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+19}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00195:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -5.8e+200)
     t
     (if (<= y -2.75e-126)
       t_1
       (if (<= y 0.00195) (* t (/ x z)) (if (<= y 6.4e+81) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -2.75e-126) {
		tmp = t_1;
	} else if (y <= 0.00195) {
		tmp = t * (x / z);
	} else if (y <= 6.4e+81) {
		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 = (y - x) * (t / y)
    if (y <= (-5.8d+200)) then
        tmp = t
    else if (y <= (-2.75d-126)) then
        tmp = t_1
    else if (y <= 0.00195d0) then
        tmp = t * (x / z)
    else if (y <= 6.4d+81) 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 = (y - x) * (t / y);
	double tmp;
	if (y <= -5.8e+200) {
		tmp = t;
	} else if (y <= -2.75e-126) {
		tmp = t_1;
	} else if (y <= 0.00195) {
		tmp = t * (x / z);
	} else if (y <= 6.4e+81) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -5.8e+200:
		tmp = t
	elif y <= -2.75e-126:
		tmp = t_1
	elif y <= 0.00195:
		tmp = t * (x / z)
	elif y <= 6.4e+81:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -2.75e-126)
		tmp = t_1;
	elseif (y <= 0.00195)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -5.8e+200)
		tmp = t;
	elseif (y <= -2.75e-126)
		tmp = t_1;
	elseif (y <= 0.00195)
		tmp = t * (x / z);
	elseif (y <= 6.4e+81)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+200], t, If[LessEqual[y, -2.75e-126], t$95$1, If[LessEqual[y, 0.00195], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+81], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.7999999999999998e200 or 6.4e81 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 80.2%

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

   if -5.7999999999999998e200 < y < -2.74999999999999993e-126 or 0.0019499999999999999 < y < 6.4e81

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 66.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 66.8%

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

      1. *-commutative N/A

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

      2. div-inv N/A

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

      3. *-commutative N/A

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

      4. sub-neg N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto t \cdot \left(\frac{1}{y} \cdot \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      8. sub-neg N/A

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

      9. associate-*r* N/A

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

      10. div-inv N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{y}\right), \color{blue}{\left(\mathsf{neg}\left(\left(x - y\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\color{blue}{\left(x - y\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right) \]

      15. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)}\right)\right) \]

      16. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y + \left(\mathsf{neg}\left(\color{blue}{x}\right)\right)\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \left(y - \color{blue}{x}\right)\right) \]

      18. --lowering--.f64 62.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, y\right), \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 62.0%

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

   if -2.74999999999999993e-126 < y < 0.0019499999999999999

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 77.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), t\right) \]

   5. Simplified 77.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+200}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-126}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 0.00195:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+81}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -31.0)
   (* t (/ (- y x) y))
   (if (<= y 3.9e-263)
     (* x (/ t (- z y)))
     (if (<= y 3.3e+21) (/ t (/ z (- x y))) (- t (/ t (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -31.0) {
		tmp = t * ((y - x) / y);
	} else if (y <= 3.9e-263) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.3e+21) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-31.0d0)) then
        tmp = t * ((y - x) / y)
    else if (y <= 3.9d-263) then
        tmp = x * (t / (z - y))
    else if (y <= 3.3d+21) then
        tmp = t / (z / (x - y))
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -31.0) {
		tmp = t * ((y - x) / y);
	} else if (y <= 3.9e-263) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.3e+21) {
		tmp = t / (z / (x - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -31.0:
		tmp = t * ((y - x) / y)
	elif y <= 3.9e-263:
		tmp = x * (t / (z - y))
	elif y <= 3.3e+21:
		tmp = t / (z / (x - y))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -31.0)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 3.9e-263)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 3.3e+21)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -31.0)
		tmp = t * ((y - x) / y);
	elseif (y <= 3.9e-263)
		tmp = x * (t / (z - y));
	elseif (y <= 3.3e+21)
		tmp = t / (z / (x - y));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -31.0], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-263], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+21], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -31

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 75.7%

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

   if -31 < y < 3.8999999999999997e-263

   1. Initial program 94.9%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 94.5%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 94.5%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 80.6%

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

      1. associate-/r/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{x}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), x\right) \]

      4. --lowering--.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 80.7%

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

   if 3.8999999999999997e-263 < y < 3.3e21

   1. Initial program 99.8%

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

      1. associate-*l/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(x - y\right) \cdot t\right), \color{blue}{\left(z - y\right)}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(x - y\right), t\right), \left(\color{blue}{z} - y\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \left(z - y\right)\right) \]

      5. --lowering--.f64 95.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   3. Simplified 95.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(x, y\right), t\right), \color{blue}{z}\right) \]
   6. Step-by-step derivation

   7. Simplified 75.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

         \[\leadsto \frac{t}{z} \cdot \frac{{x}^{3} - {y}^{3}}{\color{blue}{x \cdot x + \left(y \cdot y + x \cdot y\right)}} \]

      4. clear-num N/A

         \[\leadsto \frac{t}{z} \cdot \frac{1}{\color{blue}{\frac{x \cdot x + \left(y \cdot y + x \cdot y\right)}{{x}^{3} - {y}^{3}}}} \]

      5. frac-times N/A

         \[\leadsto \frac{t \cdot 1}{\color{blue}{z \cdot \frac{x \cdot x + \left(y \cdot y + x \cdot y\right)}{{x}^{3} - {y}^{3}}}} \]

      6. *-rgt-identity N/A

         \[\leadsto \frac{t}{\color{blue}{z} \cdot \frac{x \cdot x + \left(y \cdot y + x \cdot y\right)}{{x}^{3} - {y}^{3}}} \]

      7. clear-num N/A

         \[\leadsto \frac{t}{z \cdot \frac{1}{\color{blue}{\frac{{x}^{3} - {y}^{3}}{x \cdot x + \left(y \cdot y + x \cdot y\right)}}}} \]

      8. flip3-- N/A

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

      9. div-inv N/A

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

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z}{x - y}\right)}\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{\left(x - y\right)}\right)\right) \]

      12. --lowering--.f64 79.7%

          \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   9. Applied egg-rr 79.7%

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

   if 3.3e21 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 87.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 87.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\frac{t \cdot x}{y}\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{t \cdot x}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(t \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right) \]

   8. Simplified 76.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{t}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      5. /-lowering-/.f64 87.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   10. Applied egg-rr 87.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -60:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -60.0)
   (* t (/ (- y x) y))
   (if (<= y 2.4e-279)
     (* x (/ t (- z y)))
     (if (<= y 2.4e+21) (* t (/ (- x y) z)) (- t (/ t (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -60.0) {
		tmp = t * ((y - x) / y);
	} else if (y <= 2.4e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.4e+21) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-60.0d0)) then
        tmp = t * ((y - x) / y)
    else if (y <= 2.4d-279) then
        tmp = x * (t / (z - y))
    else if (y <= 2.4d+21) then
        tmp = t * ((x - y) / z)
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -60.0) {
		tmp = t * ((y - x) / y);
	} else if (y <= 2.4e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.4e+21) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -60.0:
		tmp = t * ((y - x) / y)
	elif y <= 2.4e-279:
		tmp = x * (t / (z - y))
	elif y <= 2.4e+21:
		tmp = t * ((x - y) / z)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -60.0)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 2.4e-279)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 2.4e+21)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -60.0)
		tmp = t * ((y - x) / y);
	elseif (y <= 2.4e-279)
		tmp = x * (t / (z - y));
	elseif (y <= 2.4e+21)
		tmp = t * ((x - y) / z);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -60.0], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-279], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+21], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -60

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 75.7%

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

   if -60 < y < 2.3999999999999999e-279

   1. Initial program 94.7%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 94.2%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 79.7%

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

      1. associate-/r/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{x}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), x\right) \]

      4. --lowering--.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 79.9%

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

   if 2.3999999999999999e-279 < y < 2.4e21

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x - y}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), t\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), t\right) \]

   5. Simplified 80.6%

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

   if 2.4e21 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 87.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 87.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\frac{t \cdot x}{y}\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{t \cdot x}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(t \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right) \]

   8. Simplified 76.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{t}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      5. /-lowering-/.f64 87.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   10. Applied egg-rr 87.5%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -60:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -6:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= y -6.0)
     t_1
     (if (<= y 4.5e-279)
       (* x (/ t (- z y)))
       (if (<= y 1.3e+18) (* t (/ (- x y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -6.0) {
		tmp = t_1;
	} else if (y <= 4.5e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.3e+18) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (y <= (-6.0d0)) then
        tmp = t_1
    else if (y <= 4.5d-279) then
        tmp = x * (t / (z - y))
    else if (y <= 1.3d+18) then
        tmp = t * ((x - y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (y <= -6.0) {
		tmp = t_1;
	} else if (y <= 4.5e-279) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.3e+18) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if y <= -6.0:
		tmp = t_1
	elif y <= 4.5e-279:
		tmp = x * (t / (z - y))
	elif y <= 1.3e+18:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -6.0)
		tmp = t_1;
	elseif (y <= 4.5e-279)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.3e+18)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -6.0)
		tmp = t_1;
	elseif (y <= 4.5e-279)
		tmp = x * (t / (z - y));
	elseif (y <= 1.3e+18)
		tmp = t * ((x - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.0], t$95$1, If[LessEqual[y, 4.5e-279], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+18], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6 or 1.3e18 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 81.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 81.6%

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

   if -6 < y < 4.49999999999999995e-279

   1. Initial program 94.7%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 94.2%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 94.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 79.7%

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

      1. associate-/r/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{x}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), x\right) \]

      4. --lowering--.f64 79.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 79.9%

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

   if 4.49999999999999995e-279 < y < 1.3e18

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x - y}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), t\right) \]

      2. --lowering--.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), t\right) \]

   5. Simplified 80.6%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.6e+158)
   (* t (/ (- y x) y))
   (if (<= y 1.65e+22) (* (- x y) (/ t (- z y))) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.6e+158) {
		tmp = t * ((y - x) / y);
	} else if (y <= 1.65e+22) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.6d+158)) then
        tmp = t * ((y - x) / y)
    else if (y <= 1.65d+22) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.6e+158) {
		tmp = t * ((y - x) / y);
	} else if (y <= 1.65e+22) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.6e+158:
		tmp = t * ((y - x) / y)
	elif y <= 1.65e+22:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.6e+158)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 1.65e+22)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.6e+158)
		tmp = t * ((y - x) / y);
	elseif (y <= 1.65e+22)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.6e+158], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+22], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.60000000000000033e158

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 87.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 87.4%

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

   if -9.60000000000000033e158 < y < 1.6499999999999999e22

   1. Initial program 97.7%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{\left(x - y\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), \left(\color{blue}{x} - y\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), \left(x - y\right)\right) \]

      7. --lowering--.f64 90.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 90.8%

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

   if 1.6499999999999999e22 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 87.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 87.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\frac{t \cdot x}{y}\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{t \cdot x}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(t \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 76.9%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right) \]

   8. Simplified 76.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{t}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      5. /-lowering-/.f64 87.5%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   10. Applied egg-rr 87.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+102)
   (* t (/ (- y x) y))
   (if (<= y 0.0026) (/ t (/ (- z y) x)) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+102) {
		tmp = t * ((y - x) / y);
	} else if (y <= 0.0026) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.8d+102)) then
        tmp = t * ((y - x) / y)
    else if (y <= 0.0026d0) then
        tmp = t / ((z - y) / x)
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+102) {
		tmp = t * ((y - x) / y);
	} else if (y <= 0.0026) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.8e+102:
		tmp = t * ((y - x) / y)
	elif y <= 0.0026:
		tmp = t / ((z - y) / x)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.8e+102)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 0.0026)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.8e+102)
		tmp = t * ((y - x) / y);
	elseif (y <= 0.0026)
		tmp = t / ((z - y) / x);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.8e+102], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0026], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8000000000000003e102

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 86.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 86.8%

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

   if -8.8000000000000003e102 < y < 0.0025999999999999999

   1. Initial program 97.4%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x - y}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{\left(x - y\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \left(\color{blue}{x} - y\right)\right)\right) \]

      7. --lowering--.f64 97.2%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{z - y}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\left(z - y\right), \color{blue}{x}\right)\right) \]

      2. --lowering--.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, y\right), x\right)\right) \]

   7. Simplified 79.0%

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

   if 0.0025999999999999999 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 83.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 83.5%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto t + \left(\mathsf{neg}\left(\frac{t \cdot x}{y}\right)\right) \]

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \color{blue}{\left(\frac{t \cdot x}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\left(t \cdot x\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 73.9%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, x\right), y\right)\right) \]

   8. Simplified 73.9%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \color{blue}{\frac{x}{y}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(t \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \left(\frac{t}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      5. /-lowering-/.f64 83.6%

         \[\leadsto \mathsf{\_.f64}\left(t, \mathsf{/.f64}\left(t, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   10. Applied egg-rr 83.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 0.0026:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+102) t (if (<= y 0.0042) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+102) {
		tmp = t;
	} else if (y <= 0.0042) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.8d+102)) then
        tmp = t
    else if (y <= 0.0042d0) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.8e+102) {
		tmp = t;
	} else if (y <= 0.0042) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.8e+102:
		tmp = t
	elif y <= 0.0042:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.8e+102)
		tmp = t;
	elseif (y <= 0.0042)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.8e+102)
		tmp = t;
	elseif (y <= 0.0042)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.8e+102], t, If[LessEqual[y, 0.0042], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000003e102 or 0.00419999999999999974 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 69.3%

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

   if -8.8000000000000003e102 < y < 0.00419999999999999974

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 66.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), t\right) \]

   5. Simplified 66.5%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.0042:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -350:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.005:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -350.0) t (if (<= y 0.005) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -350.0) {
		tmp = t;
	} else if (y <= 0.005) {
		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 <= (-350.0d0)) then
        tmp = t
    else if (y <= 0.005d0) 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 <= -350.0) {
		tmp = t;
	} else if (y <= 0.005) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -350.0:
		tmp = t
	elif y <= 0.005:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -350.0)
		tmp = t;
	elseif (y <= 0.005)
		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 <= -350.0)
		tmp = t;
	elseif (y <= 0.005)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -350.0], t, If[LessEqual[y, 0.005], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -350 or 0.0050000000000000001 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 64.5%

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

   if -350 < y < 0.0050000000000000001

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      4. /-lowering-/.f64 65.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 65.6%

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

Alternative 13: 35.0% 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 98.5%

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

3. Taylor expanded in y around inf

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

5. Simplified 37.7%

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

Developer Target 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

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