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

Percentage Accurate: 96.9% → 96.9%

Time: 6.8s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.8

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

4. Applied rewrites 97.8%

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

Alternative 2: 93.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;t - t \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -2e-8)
     t_2
     (if (<= t_1 0.002)
       (* (/ t (- z y)) (- x y))
       (if (<= t_1 10000000000000.0) (- t (* t (/ (- x z) y))) 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 - y)) * t;
	double tmp;
	if (t_1 <= -2e-8) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = (t / (z - y)) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = t - (t * ((x - z) / y));
	} 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 - y)) * t
    if (t_1 <= (-2d-8)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = (t / (z - y)) * (x - y)
    else if (t_1 <= 10000000000000.0d0) then
        tmp = t - (t * ((x - z) / y))
    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 - y)) * t;
	double tmp;
	if (t_1 <= -2e-8) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = (t / (z - y)) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = t - (t * ((x - z) / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -2e-8:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = (t / (z - y)) * (x - y)
	elif t_1 <= 10000000000000.0:
		tmp = t - (t * ((x - z) / y))
	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 / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -2e-8)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(t / Float64(z - y)) * Float64(x - y));
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(t - Float64(t * Float64(Float64(x - z) / y)));
	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 - y)) * t;
	tmp = 0.0;
	if (t_1 <= -2e-8)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = (t / (z - y)) * (x - y);
	elseif (t_1 <= 10000000000000.0)
		tmp = t - (t * ((x - z) / y));
	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 / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-8], t$95$2, If[LessEqual[t$95$1, 0.002], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(t - N[(t * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e-8 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if -2e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 96.0%

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

      1. lift-*.f64 N/A

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

      2. 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 95.3

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

   4. Applied rewrites 95.3%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-div N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 82.0

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

   6. Applied rewrites 82.0%

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

   7. Taylor expanded in y around inf

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. distribute-lft-out-- N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 100.0

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

   9. Applied rewrites 100.0%

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

Alternative 3: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -5000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;t - t \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -5000000000.0)
     t_2
     (if (<= t_1 0.002)
       (* (/ (- x y) z) t)
       (if (<= t_1 10000000000000.0) (- t (* t (/ (- x z) y))) 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 - y)) * t;
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10000000000000.0) {
		tmp = t - (t * ((x - z) / y));
	} 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 - y)) * t
    if (t_1 <= (-5000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 10000000000000.0d0) then
        tmp = t - (t * ((x - z) / y))
    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 - y)) * t;
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10000000000000.0) {
		tmp = t - (t * ((x - z) / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -5000000000.0:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = ((x - y) / z) * t
	elif t_1 <= 10000000000000.0:
		tmp = t - (t * ((x - z) / y))
	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 / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -5000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(t - Float64(t * Float64(Float64(x - z) / y)));
	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 - y)) * t;
	tmp = 0.0;
	if (t_1 <= -5000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 10000000000000.0)
		tmp = t - (t * ((x - z) / y));
	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 / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000.0], t$95$2, If[LessEqual[t$95$1, 0.002], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(t - N[(t * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e9 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if -5e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.4

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

   5. Applied rewrites 94.4%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. sub-div N/A

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

      5. lift--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. associate-*r/ N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 82.0

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

   6. Applied rewrites 82.0%

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

   7. Taylor expanded in y around inf

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. distribute-lft-out-- N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower--.f64 100.0

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

   9. Applied rewrites 100.0%

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

Alternative 4: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -5000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -5000000000.0)
     t_2
     (if (<= t_1 0.002)
       (* (/ (- x y) z) t)
       (if (<= t_1 10000000000000.0) (* (- 1.0 (/ x y)) 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 - y)) * t;
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * 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 - y)) * t
    if (t_1 <= (-5000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 10000000000000.0d0) then
        tmp = (1.0d0 - (x / y)) * 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 - y)) * t;
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -5000000000.0:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = ((x - y) / z) * t
	elif t_1 <= 10000000000000.0:
		tmp = (1.0 - (x / y)) * 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 / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -5000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * 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 - y)) * t;
	tmp = 0.0;
	if (t_1 <= -5000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 10000000000000.0)
		tmp = (1.0 - (x / y)) * 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 / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000.0], t$95$2, If[LessEqual[t$95$1, 0.002], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e9 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if -5e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.4

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

   5. Applied rewrites 94.4%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 3.8

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

   5. Applied rewrites 3.8%

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

   7. Applied rewrites 3.7%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. distribute-lft-out-- N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. div-add N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. *-inverses N/A

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

      9. +-commutative N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 100.0

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

   10. Applied rewrites 100.0%

       \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right)} \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 92.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1e-42)
     t_2
     (if (<= t_1 0.002)
       (* (/ t z) (- x y))
       (if (<= t_1 10000000000000.0) (* (- 1.0 (/ x y)) 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 - y)) * t;
	double tmp;
	if (t_1 <= -1e-42) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * 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 - y)) * t
    if (t_1 <= (-1d-42)) then
        tmp = t_2
    else if (t_1 <= 0.002d0) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 10000000000000.0d0) then
        tmp = (1.0d0 - (x / y)) * 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 - y)) * t;
	double tmp;
	if (t_1 <= -1e-42) {
		tmp = t_2;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -1e-42:
		tmp = t_2
	elif t_1 <= 0.002:
		tmp = (t / z) * (x - y)
	elif t_1 <= 10000000000000.0:
		tmp = (1.0 - (x / y)) * 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 / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1e-42)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * 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 - y)) * t;
	tmp = 0.0;
	if (t_1 <= -1e-42)
		tmp = t_2;
	elseif (t_1 <= 0.002)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 10000000000000.0)
		tmp = (1.0 - (x / y)) * 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 / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-42], t$95$2, If[LessEqual[t$95$1, 0.002], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000004e-42 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 95.6

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

   5. Applied rewrites 95.6%

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

   if -1.00000000000000004e-42 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 96.2

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

   4. Applied rewrites 96.2%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 94.8

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

   7. Applied rewrites 94.8%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 3.8

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

   5. Applied rewrites 3.8%

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

   7. Applied rewrites 3.7%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. distribute-lft-out-- N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. div-add N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. *-inverses N/A

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

      9. +-commutative N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 100.0

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

   10. Applied rewrites 100.0%

       \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right)} \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5000000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5000000000.0)
     (* (/ t (- z y)) x)
     (if (<= t_1 0.002)
       (* (/ t z) (- x y))
       (if (<= t_1 10000000000000.0)
         (* (- 1.0 (/ x y)) t)
         (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-5000000000.0d0)) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 0.002d0) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 10000000000000.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = (t * x) / (z - y)
    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 tmp;
	if (t_1 <= -5000000000.0) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -5000000000.0:
		tmp = (t / (z - y)) * x
	elif t_1 <= 0.002:
		tmp = (t / z) * (x - y)
	elif t_1 <= 10000000000000.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -5000000000.0)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -5000000000.0)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 0.002)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 10000000000000.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (t * x) / (z - y);
	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]}, If[LessEqual[t$95$1, -5000000000.0], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 0.002], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e9

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   if -5e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.4

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

   4. Applied rewrites 94.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 92.8

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

   7. Applied rewrites 92.8%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 3.8

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

   5. Applied rewrites 3.8%

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

   7. Applied rewrites 3.7%

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

   8. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. distribute-lft-out-- N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. div-add N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. *-lft-identity N/A

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

      8. *-inverses N/A

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

      9. +-commutative N/A

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

      10. fp-cancel-sign-sub-inv N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 100.0

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

   10. Applied rewrites 100.0%

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

   if 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   7. Applied rewrites 92.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5000000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.002:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10000000000000:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5000000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5000000000.0)
     (* (/ t (- z y)) x)
     (if (<= t_1 0.002)
       (* (/ t z) (- x y))
       (if (<= t_1 10000000000000.0) (* 1.0 t) (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5000000000.0) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-5000000000.0d0)) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 0.002d0) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 10000000000000.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (t * x) / (z - y)
    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 tmp;
	if (t_1 <= -5000000000.0) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 0.002) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -5000000000.0:
		tmp = (t / (z - y)) * x
	elif t_1 <= 0.002:
		tmp = (t / z) * (x - y)
	elif t_1 <= 10000000000000.0:
		tmp = 1.0 * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -5000000000.0)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 0.002)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -5000000000.0)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 0.002)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 10000000000000.0)
		tmp = 1.0 * t;
	else
		tmp = (t * x) / (z - y);
	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]}, If[LessEqual[t$95$1, -5000000000.0], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 0.002], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e9

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   if -5e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e-3

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.4

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

   4. Applied rewrites 94.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 92.8

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

   7. Applied rewrites 92.8%

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

   if 2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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 96.4%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   7. Applied rewrites 92.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5000000000:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.002:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{-7}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -2e-36)
     (* (/ t (- z y)) x)
     (if (<= t_1 1e-7)
       (/ (* (- x y) t) z)
       (if (<= t_1 10000000000000.0) (* 1.0 t) (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -2e-36) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-2d-36)) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 1d-7) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 10000000000000.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (t * x) / (z - y)
    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 tmp;
	if (t_1 <= -2e-36) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 1e-7) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -2e-36:
		tmp = (t / (z - y)) * x
	elif t_1 <= 1e-7:
		tmp = ((x - y) * t) / z
	elif t_1 <= 10000000000000.0:
		tmp = 1.0 * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -2e-36)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 1e-7)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -2e-36)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 1e-7)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 10000000000000.0)
		tmp = 1.0 * t;
	else
		tmp = (t * x) / (z - y);
	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]}, If[LessEqual[t$95$1, -2e-36], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e-7], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.9999999999999999e-36

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 84.4

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

   5. Applied rewrites 84.4%

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

   if -1.9999999999999999e-36 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999995e-8

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.3

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

   5. Applied rewrites 88.3%

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

   if 9.9999999999999995e-8 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 94.6%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   7. Applied rewrites 92.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{-36}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{-7}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.0001 \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 0.0001) (not (<= t_1 2.0))) (* (/ t (- z y)) x) (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 2.0)) {
		tmp = (t / (z - y)) * x;
	} else {
		tmp = 1.0 * 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 = (x - y) / (z - y)
    if ((t_1 <= 0.0001d0) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = (t / (z - y)) * x
    else
        tmp = 1.0d0 * t
    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 tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 2.0)) {
		tmp = (t / (z - y)) * x;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 0.0001) or not (t_1 <= 2.0):
		tmp = (t / (z - y)) * x
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 0.0001) || !(t_1 <= 2.0))
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 0.0001) || ~((t_1 <= 2.0)))
		tmp = (t / (z - y)) * x;
	else
		tmp = 1.0 * t;
	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]}, If[Or[LessEqual[t$95$1, 0.0001], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000005e-4 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 75.6

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

   5. Applied rewrites 75.6%

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

   if 1.00000000000000005e-4 < (/.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 97.3%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.0001 \lor \neg \left(\frac{x - y}{z - y} \leq 2\right):\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.0001:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 0.0001)
     (* (/ t (- z y)) x)
     (if (<= t_1 10000000000000.0) (* 1.0 t) (/ (* t x) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.0001) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 0.0001d0) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 10000000000000.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (t * x) / (z - y)
    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 tmp;
	if (t_1 <= 0.0001) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 0.0001:
		tmp = (t / (z - y)) * x
	elif t_1 <= 10000000000000.0:
		tmp = 1.0 * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.0001)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 0.0001)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 10000000000000.0)
		tmp = 1.0 * t;
	else
		tmp = (t * x) / (z - y);
	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]}, If[LessEqual[t$95$1, 0.0001], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000005e-4

   1. Initial program 97.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 73.1

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

   5. Applied rewrites 73.1%

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

   if 1.00000000000000005e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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 95.5%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.1

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

   5. Applied rewrites 86.1%

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

   7. Applied rewrites 92.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.0001:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.0001 \lor \neg \left(t\_1 \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 0.0001) (not (<= t_1 10000000000000.0)))
     (* (/ x z) t)
     (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0)) {
		tmp = (x / z) * t;
	} else {
		tmp = 1.0 * 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 = (x - y) / (z - y)
    if ((t_1 <= 0.0001d0) .or. (.not. (t_1 <= 10000000000000.0d0))) then
        tmp = (x / z) * t
    else
        tmp = 1.0d0 * t
    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 tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0)) {
		tmp = (x / z) * t;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 0.0001) or not (t_1 <= 10000000000000.0):
		tmp = (x / z) * t
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0))
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 0.0001) || ~((t_1 <= 10000000000000.0)))
		tmp = (x / z) * t;
	else
		tmp = 1.0 * t;
	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]}, If[Or[LessEqual[t$95$1, 0.0001], N[Not[LessEqual[t$95$1, 10000000000000.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000005e-4 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 63.5

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

   5. Applied rewrites 63.5%

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

   if 1.00000000000000005e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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 95.5%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.0001 \lor \neg \left(\frac{x - y}{z - y} \leq 10000000000000\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.0001 \lor \neg \left(t\_1 \leq 10000000000000\right):\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 0.0001) (not (<= t_1 10000000000000.0)))
     (* (/ t z) x)
     (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0)) {
		tmp = (t / z) * x;
	} else {
		tmp = 1.0 * 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 = (x - y) / (z - y)
    if ((t_1 <= 0.0001d0) .or. (.not. (t_1 <= 10000000000000.0d0))) then
        tmp = (t / z) * x
    else
        tmp = 1.0d0 * t
    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 tmp;
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0)) {
		tmp = (t / z) * x;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 0.0001) or not (t_1 <= 10000000000000.0):
		tmp = (t / z) * x
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 0.0001) || !(t_1 <= 10000000000000.0))
		tmp = Float64(Float64(t / z) * x);
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 0.0001) || ~((t_1 <= 10000000000000.0)))
		tmp = (t / z) * x;
	else
		tmp = 1.0 * t;
	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]}, If[Or[LessEqual[t$95$1, 0.0001], N[Not[LessEqual[t$95$1, 10000000000000.0]], $MachinePrecision]], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000005e-4 or 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 75.9

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

   5. Applied rewrites 75.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.1%

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

   if 1.00000000000000005e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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 95.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.0001 \lor \neg \left(\frac{x - y}{z - y} \leq 10000000000000\right):\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.0001:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 0.0001)
     (* (/ t z) x)
     (if (<= t_1 10000000000000.0) (* 1.0 t) (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.0001) {
		tmp = (t / z) * x;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 0.0001d0) then
        tmp = (t / z) * x
    else if (t_1 <= 10000000000000.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.0001) {
		tmp = (t / z) * x;
	} else if (t_1 <= 10000000000000.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 0.0001:
		tmp = (t / z) * x
	elif t_1 <= 10000000000000.0:
		tmp = 1.0 * t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.0001)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 10000000000000.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 0.0001)
		tmp = (t / z) * x;
	elseif (t_1 <= 10000000000000.0)
		tmp = 1.0 * t;
	else
		tmp = (t * x) / z;
	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]}, If[LessEqual[t$95$1, 0.0001], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 10000000000000.0], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000005e-4

   1. Initial program 97.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 63.1%

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

   if 1.00000000000000005e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e13

   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 95.5%

      \[\leadsto \color{blue}{1} \cdot t \]

   if 1e13 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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. lower-*.f64 59.3

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

   5. Applied rewrites 59.3%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.0001:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10000000000000:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

Alternative 15: 35.0% 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 97.8%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 38.1%

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

Developer Target 1: 96.9% 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 2024320 
(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))