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

Percentage Accurate: 96.8% → 96.8%

Time: 7.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% 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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 2: 94.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{if}\;t\_1 \leq -0.001:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) (- x y))))
   (if (<= t_1 -0.001)
     t_2
     (if (<= t_1 2e-12)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * (x - y);
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * (x - y)
    if (t_1 <= (-0.001d0)) then
        tmp = t_2
    else if (t_1 <= 2d-12) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * (x - y);
	double tmp;
	if (t_1 <= -0.001) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * (x - y)
	tmp = 0
	if t_1 <= -0.001:
		tmp = t_2
	elif t_1 <= 2e-12:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * Float64(x - y))
	tmp = 0.0
	if (t_1 <= -0.001)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * (x - y);
	tmp = 0.0;
	if (t_1 <= -0.001)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.001], t$95$2, If[LessEqual[t$95$1, 2e-12], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e-3 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 85.3

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

   4. Applied rewrites 85.3%

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

   if -1e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999996e-12

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if 1.99999999999999996e-12 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      11. sub-neg N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(y\right)\right)\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      12. +-commutative N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + z\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      13. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - z}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{0 - \left(x - y\right)}}} \]

      18. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x - y\right)}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}}} \]

      20. +-commutative N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}}} \]

      21. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}}} \]

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.5

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

   7. Applied rewrites 99.5%

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

Alternative 3: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -1e+52)
     t_2
     (if (<= t_1 2e-12)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e+52) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-1d+52)) then
        tmp = t_2
    else if (t_1 <= 2d-12) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e+52) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -1e+52:
		tmp = t_2
	elif t_1 <= 2e-12:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -1e+52)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -1e+52)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+52], t$95$2, If[LessEqual[t$95$1, 2e-12], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.9999999999999999e51 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -9.9999999999999999e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999996e-12

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.0

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

   5. Applied rewrites 96.0%

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

   if 1.99999999999999996e-12 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      11. sub-neg N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(y\right)\right)\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      12. +-commutative N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + z\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      13. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - z}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{0 - \left(x - y\right)}}} \]

      18. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x - y\right)}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}}} \]

      20. +-commutative N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}}} \]

      21. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}}} \]

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.5

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

   7. Applied rewrites 99.5%

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

Alternative 4: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -100000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-34}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -100000000.0)
     t_2
     (if (<= t_1 1e-34)
       (/ (* t (- x y)) z)
       (if (<= t_1 2.0) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -100000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-34) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-100000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 1d-34) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -100000000.0) {
		tmp = t_2;
	} else if (t_1 <= 1e-34) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -100000000.0:
		tmp = t_2
	elif t_1 <= 1e-34:
		tmp = (t * (x - y)) / z
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -100000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e-34)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -100000000.0)
		tmp = t_2;
	elseif (t_1 <= 1e-34)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -100000000.0], t$95$2, If[LessEqual[t$95$1, 1e-34], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e8 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -1e8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.99999999999999928e-35

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 90.1

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

   5. Applied rewrites 90.1%

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

   if 9.99999999999999928e-35 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \frac{t}{\frac{\color{blue}{0 - \left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      10. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z - y\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      11. sub-neg N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(z + \left(\mathsf{neg}\left(y\right)\right)\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      12. +-commutative N/A

          \[\leadsto \frac{t}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + z\right)}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      13. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - z}}{\mathsf{neg}\left(\left(x - y\right)\right)}} \]

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{0 - \left(x - y\right)}}} \]

      18. lift--.f64 N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x - y\right)}}} \]

      19. sub-neg N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)}}} \]

      20. +-commutative N/A

          \[\leadsto \frac{t}{\frac{y - z}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)}}} \]

      21. associate--r+ N/A

          \[\leadsto \frac{t}{\frac{y - z}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(y\right)\right)\right) - x}}} \]

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 97.5

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

   7. Applied rewrites 97.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -100000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{-34}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -100000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -100000000.0)
     t_2
     (if (<= t_1 2e-7) (/ (* t (- x y)) z) (if (<= t_1 2.0) (* 1.0 t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -100000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-100000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 2d-7) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -100000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -100000000.0:
		tmp = t_2
	elif t_1 <= 2e-7:
		tmp = (t * (x - y)) / z
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -100000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -100000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -100000000.0], t$95$2, If[LessEqual[t$95$1, 2e-7], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e8 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   if -1e8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -100000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -1e+52)
     t_2
     (if (<= t_1 2e-12) (* (/ x z) t) (if (<= t_1 2.0) (* 1.0 t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e+52) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-1d+52)) then
        tmp = t_2
    else if (t_1 <= 2d-12) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -1e+52) {
		tmp = t_2;
	} else if (t_1 <= 2e-12) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -1e+52:
		tmp = t_2
	elif t_1 <= 2e-12:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -1e+52)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -1e+52)
		tmp = t_2;
	elseif (t_1 <= 2e-12)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+52], t$95$2, If[LessEqual[t$95$1, 2e-12], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.9999999999999999e51 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 85.4

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

   5. Applied rewrites 85.4%

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

   if -9.9999999999999999e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999996e-12

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 66.7

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

   5. Applied rewrites 66.7%

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

   if 1.99999999999999996e-12 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.7%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
   (if (<= t_1 2e-12) t_2 (if (<= t_1 2.0) (* 1.0 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 2e-12) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / z) * t
    if (t_1 <= 2d-12) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 2e-12) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= 2e-12:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= 2e-12)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= 2e-12)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-12], t$95$2, If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999996e-12 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

   if 1.99999999999999996e-12 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.7%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t \cdot x}{z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* t x) z)))
   (if (<= t_1 2e-37) t_2 (if (<= t_1 2.0) (* 1.0 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 2e-37) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t * x) / z
    if (t_1 <= 2d-37) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 2e-37) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t * x) / z
	tmp = 0
	if t_1 <= 2e-37:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t * x) / z)
	tmp = 0.0
	if (t_1 <= 2e-37)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t * x) / z;
	tmp = 0.0;
	if (t_1 <= 2e-37)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-37], t$95$2, If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.00000000000000013e-37 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 61.4

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

   5. Applied rewrites 61.4%

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

   if 2.00000000000000013e-37 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 92.8%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z} \cdot x\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t z) x)))
   (if (<= t_1 2e-12) t_2 (if (<= t_1 2.0) (* 1.0 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 2e-12) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / z) * x
    if (t_1 <= 2d-12) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 2e-12) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / z) * x
	tmp = 0
	if t_1 <= 2e-12:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / z) * x)
	tmp = 0.0
	if (t_1 <= 2e-12)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / z) * x;
	tmp = 0.0;
	if (t_1 <= 2e-12)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-12], t$95$2, If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999996e-12 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 71.6

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

   5. Applied rewrites 71.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 58.1%

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

   if 1.99999999999999996e-12 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1} \cdot t \]
   4. Step-by-step derivation

   5. Applied rewrites 96.7%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 35.3% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 t))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * t;
}

Python

def code(x, y, z, t):
	return 1.0 * t

Julia

function code(x, y, z, t)
	return Float64(1.0 * t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * t;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * t), $MachinePrecision]

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{1} \cdot t \]
4. Step-by-step derivation

5. Applied rewrites 35.6%

   \[\leadsto \color{blue}{1} \cdot t \]
6. Add Preprocessing

Developer Target 1: 96.8% accurate, 0.8× 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 2024270 
(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))