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

Percentage Accurate: 96.8% → 96.8%

Time: 7.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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

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

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 96.1%

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

Alternative 2: 79.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+167}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -2e+24)
     (* (/ (- t) y) x)
     (if (<= t_1 5e-16)
       (* (/ t z) (- x y))
       (if (<= t_1 2.0)
         (* 1.0 t)
         (if (<= t_1 1e+167) (* (/ x (- y)) 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 5e-16) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else if (t_1 <= 1e+167) {
		tmp = (x / -y) * 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 <= (-2d+24)) then
        tmp = (-t / y) * x
    else if (t_1 <= 5d-16) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else if (t_1 <= 1d+167) then
        tmp = (x / -y) * 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 5e-16) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else if (t_1 <= 1e+167) {
		tmp = (x / -y) * 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 <= -2e+24:
		tmp = (-t / y) * x
	elif t_1 <= 5e-16:
		tmp = (t / z) * (x - y)
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	elif t_1 <= 1e+167:
		tmp = (x / -y) * 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 <= -2e+24)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	elseif (t_1 <= 5e-16)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	elseif (t_1 <= 1e+167)
		tmp = Float64(Float64(x / Float64(-y)) * 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 <= -2e+24)
		tmp = (-t / y) * x;
	elseif (t_1 <= 5e-16)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	elseif (t_1 <= 1e+167)
		tmp = (x / -y) * 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, -2e+24], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e-16], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+167], N[(N[(x / (-y)), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e24

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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. div-inv N/A

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

      7. lift--.f64 N/A

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

      8. flip3-- N/A

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

      9. clear-num N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. clear-num N/A

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

      14. flip3-- N/A

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

      15. lift--.f64 N/A

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

      16. inv-pow N/A

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

      17. lower-pow.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   6. 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 97.5

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

   7. Applied rewrites 97.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 81.2%

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

   if -2e24 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.7

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 94.1%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   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 94.3%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e167

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 63.6%

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

   if 1e167 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 84.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{+167}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{elif}\;t\_1 \leq 10^{+167}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -2e+24)
     (* (/ (- t) y) x)
     (if (<= t_1 0.1)
       (* (/ x z) t)
       (if (<= t_1 2.0)
         (* 1.0 t)
         (if (<= t_1 1e+167) (* (/ x (- y)) 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else if (t_1 <= 1e+167) {
		tmp = (x / -y) * 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 <= (-2d+24)) then
        tmp = (-t / y) * x
    else if (t_1 <= 0.1d0) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else if (t_1 <= 1d+167) then
        tmp = (x / -y) * 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else if (t_1 <= 1e+167) {
		tmp = (x / -y) * 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 <= -2e+24:
		tmp = (-t / y) * x
	elif t_1 <= 0.1:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	elif t_1 <= 1e+167:
		tmp = (x / -y) * 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 <= -2e+24)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	elseif (t_1 <= 0.1)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	elseif (t_1 <= 1e+167)
		tmp = Float64(Float64(x / Float64(-y)) * 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 <= -2e+24)
		tmp = (-t / y) * x;
	elseif (t_1 <= 0.1)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	elseif (t_1 <= 1e+167)
		tmp = (x / -y) * 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, -2e+24], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], If[LessEqual[t$95$1, 1e+167], N[(N[(x / (-y)), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e24

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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. div-inv N/A

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

      7. lift--.f64 N/A

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

      8. flip3-- N/A

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

      9. clear-num N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. clear-num N/A

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

      14. flip3-- N/A

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

      15. lift--.f64 N/A

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

      16. inv-pow N/A

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

      17. lower-pow.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   6. 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 97.5

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

   7. Applied rewrites 97.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 81.2%

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

   if -2e24 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.10000000000000001

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 68.8

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

   5. Applied rewrites 68.8%

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

   if 0.10000000000000001 < (/.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 96.3%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e167

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 63.6%

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

   if 1e167 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 84.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{+167}:\\ \;\;\;\;\frac{x}{-y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -5e-15)
     t_2
     (if (<= t_1 0.1)
       (* (/ (- x y) z) t)
       (if (<= t_1 2e+77) (fma t (/ (- z 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 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -5e-15) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2e+77) {
		tmp = fma(t, ((z - 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(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -5e-15)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2e+77)
		tmp = fma(t, Float64(Float64(z - x) / y), t);
	else
		tmp = t_2;
	end
	return 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, -5e-15], t$95$2, If[LessEqual[t$95$1, 0.1], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+77], N[(t * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999999e-15 or 1.99999999999999997e77 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 97.1

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

   5. Applied rewrites 97.1%

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

   if -4.99999999999999999e-15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.10000000000000001

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 0.10000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999997e77

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 94.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.1:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -5e-15)
     t_2
     (if (<= t_1 0.1)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* t (/ y (- y z))) 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 <= -5e-15) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} 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 <= (-5d-15)) then
        tmp = t_2
    else if (t_1 <= 0.1d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    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 <= -5e-15) {
		tmp = t_2;
	} else if (t_1 <= 0.1) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} 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 <= -5e-15:
		tmp = t_2
	elif t_1 <= 0.1:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	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 <= -5e-15)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -5e-15)
		tmp = t_2;
	elseif (t_1 <= 0.1)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	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, -5e-15], t$95$2, If[LessEqual[t$95$1, 0.1], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999999e-15 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.2%

      \[\frac{x - y}{z - y} \cdot t \]
   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 91.4

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

   5. Applied rewrites 91.4%

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

   if -4.99999999999999999e-15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.10000000000000001

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 0.10000000000000001 < (/.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 99.9

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

   4. Applied rewrites 99.9%

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

   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. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 99.7

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

   7. Applied rewrites 99.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.1:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -2e+24)
     t_2
     (if (<= t_1 2e-49)
       (* (/ t z) (- x y))
       (if (<= t_1 2.0) (* t (/ y (- y z))) 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 <= -2e+24) {
		tmp = t_2;
	} else if (t_1 <= 2e-49) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} 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 <= (-2d+24)) then
        tmp = t_2
    else if (t_1 <= 2d-49) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    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 <= -2e+24) {
		tmp = t_2;
	} else if (t_1 <= 2e-49) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} 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 <= -2e+24:
		tmp = t_2
	elif t_1 <= 2e-49:
		tmp = (t / z) * (x - y)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	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 <= -2e+24)
		tmp = t_2;
	elseif (t_1 <= 2e-49)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -2e+24)
		tmp = t_2;
	elseif (t_1 <= 2e-49)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	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, -2e+24], t$95$2, If[LessEqual[t$95$1, 2e-49], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e24 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 91.0

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

   5. Applied rewrites 91.0%

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

   if -2e24 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999987e-49

   1. Initial program 94.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

   7. Applied rewrites 95.2%

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

   if 1.99999999999999987e-49 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 99.8

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

   4. Applied rewrites 99.8%

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

   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. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 96.5

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

   7. Applied rewrites 96.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -2e+24)
     t_2
     (if (<= t_1 5e-16) (* (/ t z) (- x y)) (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 <= -2e+24) {
		tmp = t_2;
	} else if (t_1 <= 5e-16) {
		tmp = (t / z) * (x - y);
	} 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 <= (-2d+24)) then
        tmp = t_2
    else if (t_1 <= 5d-16) then
        tmp = (t / z) * (x - y)
    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 <= -2e+24) {
		tmp = t_2;
	} else if (t_1 <= 5e-16) {
		tmp = (t / z) * (x - y);
	} 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 <= -2e+24:
		tmp = t_2
	elif t_1 <= 5e-16:
		tmp = (t / z) * (x - y)
	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 <= -2e+24)
		tmp = t_2;
	elseif (t_1 <= 5e-16)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	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 <= -2e+24)
		tmp = t_2;
	elseif (t_1 <= 5e-16)
		tmp = (t / z) * (x - y);
	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, -2e+24], t$95$2, If[LessEqual[t$95$1, 5e-16], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $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)) < -2e24 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 91.0

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

   5. Applied rewrites 91.0%

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

   if -2e24 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 86.7

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

   5. Applied rewrites 86.7%

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

   7. Applied rewrites 94.1%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   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 94.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -2e+24)
     (* (/ (- t) y) x)
     (if (<= t_1 0.1)
       (* (/ x z) t)
       (if (<= t_1 2e+28) (* 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2e+28) {
		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 <= (-2d+24)) then
        tmp = (-t / y) * x
    else if (t_1 <= 0.1d0) then
        tmp = (x / z) * t
    else if (t_1 <= 2d+28) 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 <= -2e+24) {
		tmp = (-t / y) * x;
	} else if (t_1 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2e+28) {
		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 <= -2e+24:
		tmp = (-t / y) * x
	elif t_1 <= 0.1:
		tmp = (x / z) * t
	elif t_1 <= 2e+28:
		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 <= -2e+24)
		tmp = Float64(Float64(Float64(-t) / y) * x);
	elseif (t_1 <= 0.1)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2e+28)
		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 <= -2e+24)
		tmp = (-t / y) * x;
	elseif (t_1 <= 0.1)
		tmp = (x / z) * t;
	elseif (t_1 <= 2e+28)
		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, -2e+24], N[(N[((-t) / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 0.1], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+28], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e24

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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. div-inv N/A

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

      7. lift--.f64 N/A

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

      8. flip3-- N/A

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

      9. clear-num N/A

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

      10. associate-/r* N/A

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

      11. lower-/.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. clear-num N/A

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

      14. flip3-- N/A

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

      15. lift--.f64 N/A

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

      16. inv-pow N/A

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

      17. lower-pow.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - y}} \]
   6. 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 97.5

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

   7. Applied rewrites 97.5%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 81.2%

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

   if -2e24 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.10000000000000001

   1. Initial program 94.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 68.8

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

   5. Applied rewrites 68.8%

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

   if 0.10000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999992e28

   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 92.2%

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

   if 1.99999999999999992e28 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\frac{-t}{y} \cdot x\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.9:\\ \;\;\;\;t\_2 \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ t (- z y))))
   (if (<= t_1 0.9)
     (* t_2 (- x y))
     (if (<= t_1 2e+77) (fma t (/ (- z x) y) t) (* t_2 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t / (z - y);
	double tmp;
	if (t_1 <= 0.9) {
		tmp = t_2 * (x - y);
	} else if (t_1 <= 2e+77) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t_2 * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.9)
		tmp = Float64(t_2 * Float64(x - y));
	elseif (t_1 <= 2e+77)
		tmp = fma(t, Float64(Float64(z - x) / y), t);
	else
		tmp = Float64(t_2 * x);
	end
	return 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[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.9], N[(t$95$2 * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+77], N[(t * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], N[(t$95$2 * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.900000000000000022

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 93.9

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

   4. Applied rewrites 93.9%

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

   if 0.900000000000000022 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999997e77

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

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

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

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

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

      7. associate-/l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. lower-fma.f64 N/A

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

   5. Applied rewrites 94.9%

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

   if 1.99999999999999997e77 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 89.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 96.3

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

   5. Applied rewrites 96.3%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.9:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16} \lor \neg \left(t\_1 \leq 200000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 5e-16) (not (<= t_1 200000000.0)))
     (* x (/ t z))
     (* 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 <= 5e-16) || !(t_1 <= 200000000.0)) {
		tmp = x * (t / z);
	} 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 <= 5d-16) .or. (.not. (t_1 <= 200000000.0d0))) then
        tmp = x * (t / z)
    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 <= 5e-16) || !(t_1 <= 200000000.0)) {
		tmp = x * (t / z);
	} 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 <= 5e-16) or not (t_1 <= 200000000.0):
		tmp = x * (t / z)
	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 <= 5e-16) || !(t_1 <= 200000000.0))
		tmp = Float64(x * Float64(t / z));
	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 <= 5e-16) || ~((t_1 <= 200000000.0)))
		tmp = x * (t / z);
	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, 5e-16], N[Not[LessEqual[t$95$1, 200000000.0]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16 or 2e8 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.2%

      \[\frac{x - y}{z - y} \cdot t \]
   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 54.8

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

   5. Applied rewrites 54.8%

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

   7. Applied rewrites 57.5%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e8

   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 93.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-16} \lor \neg \left(\frac{x - y}{z - y} \leq 200000000\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 0.1)
     (* (/ x z) t)
     (if (<= t_1 2e+28) (* 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 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2e+28) {
		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 <= 0.1d0) then
        tmp = (x / z) * t
    else if (t_1 <= 2d+28) 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 <= 0.1) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2e+28) {
		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 <= 0.1:
		tmp = (x / z) * t
	elif t_1 <= 2e+28:
		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 <= 0.1)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2e+28)
		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 <= 0.1)
		tmp = (x / z) * t;
	elseif (t_1 <= 2e+28)
		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, 0.1], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+28], 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)) < 0.10000000000000001

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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 59.2

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

   5. Applied rewrites 59.2%

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

   if 0.10000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999992e28

   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 92.2%

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

   if 1.99999999999999992e28 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.1:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-16)
     (* x (/ t z))
     (if (<= t_1 2e+28) (* 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 <= 5e-16) {
		tmp = x * (t / z);
	} else if (t_1 <= 2e+28) {
		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 <= 5d-16) then
        tmp = x * (t / z)
    else if (t_1 <= 2d+28) 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 <= 5e-16) {
		tmp = x * (t / z);
	} else if (t_1 <= 2e+28) {
		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 <= 5e-16:
		tmp = x * (t / z)
	elif t_1 <= 2e+28:
		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 <= 5e-16)
		tmp = Float64(x * Float64(t / z));
	elseif (t_1 <= 2e+28)
		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 <= 5e-16)
		tmp = x * (t / z);
	elseif (t_1 <= 2e+28)
		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, 5e-16], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+28], 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)) < 5.0000000000000004e-16

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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 53.8

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

   5. Applied rewrites 53.8%

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

   7. Applied rewrites 58.1%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.99999999999999992e28

   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 90.3%

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

   if 1.99999999999999992e28 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 91.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+28}:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.7% 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 96.1%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 32.9%

   \[\leadsto \color{blue}{1} \cdot t \]
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 2024324 
(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))