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

Percentage Accurate: 96.7% → 96.7%

Time: 10.9s

Alternatives: 16

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: 96.7% 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: 96.7% 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 96.7%

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

Alternative 2: 70.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 -5e+216)
     (/ (* x t) z)
     (if (<= t_1 -1e+51)
       (/ (* x t) (- y))
       (if (<= t_1 -4e-73)
         t_2
         (if (<= t_1 0.5)
           (* t (/ y (- z)))
           (if (<= t_1 5e+15)
             (* t 1.0)
             (if (<= t_1 2e+172) t_2 (* x (/ t (- y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= -4e-73) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = t * (y / -z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t_2;
	} else {
		tmp = x * (t / -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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / z)
    if (t_1 <= (-5d+216)) then
        tmp = (x * t) / z
    else if (t_1 <= (-1d+51)) then
        tmp = (x * t) / -y
    else if (t_1 <= (-4d-73)) then
        tmp = t_2
    else if (t_1 <= 0.5d0) then
        tmp = t * (y / -z)
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    else if (t_1 <= 2d+172) then
        tmp = t_2
    else
        tmp = x * (t / -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 t_2 = t * (x / z);
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= -4e-73) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = t * (y / -z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t_2;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / z)
	tmp = 0
	if t_1 <= -5e+216:
		tmp = (x * t) / z
	elif t_1 <= -1e+51:
		tmp = (x * t) / -y
	elif t_1 <= -4e-73:
		tmp = t_2
	elif t_1 <= 0.5:
		tmp = t * (y / -z)
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	elif t_1 <= 2e+172:
		tmp = t_2
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= -5e+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_1 <= -1e+51)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_1 <= -4e-73)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	elseif (t_1 <= 2e+172)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (t_1 <= -5e+216)
		tmp = (x * t) / z;
	elseif (t_1 <= -1e+51)
		tmp = (x * t) / -y;
	elseif (t_1 <= -4e-73)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = t * (y / -z);
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	elseif (t_1 <= 2e+172)
		tmp = t_2;
	else
		tmp = x * (t / -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]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+51], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$1, -4e-73], t$95$2, If[LessEqual[t$95$1, 0.5], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+172], t$95$2, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < -3.99999999999999999e-73 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e172

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

   if -3.99999999999999999e-73 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 5.4%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 71.0

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

   8. Applied rewrites 71.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 68.9%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 94.5%

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

   if 2.0000000000000002e172 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-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. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.5

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

   7. Applied rewrites 99.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 77.2%

       \[\leadsto x \cdot \frac{t}{-y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 -5e+216)
     (/ (* x t) z)
     (if (<= t_1 -1e+51)
       (/ (* x t) (- y))
       (if (<= t_1 -4e-73)
         t_2
         (if (<= t_1 0.5)
           (* (/ t z) (- y))
           (if (<= t_1 5e+15)
             (* t 1.0)
             (if (<= t_1 2e+172) t_2 (* x (/ t (- y)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= -4e-73) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = (t / z) * -y;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t_2;
	} else {
		tmp = x * (t / -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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / z)
    if (t_1 <= (-5d+216)) then
        tmp = (x * t) / z
    else if (t_1 <= (-1d+51)) then
        tmp = (x * t) / -y
    else if (t_1 <= (-4d-73)) then
        tmp = t_2
    else if (t_1 <= 0.5d0) then
        tmp = (t / z) * -y
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    else if (t_1 <= 2d+172) then
        tmp = t_2
    else
        tmp = x * (t / -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 t_2 = t * (x / z);
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= -4e-73) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = (t / z) * -y;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t_2;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / z)
	tmp = 0
	if t_1 <= -5e+216:
		tmp = (x * t) / z
	elif t_1 <= -1e+51:
		tmp = (x * t) / -y
	elif t_1 <= -4e-73:
		tmp = t_2
	elif t_1 <= 0.5:
		tmp = (t / z) * -y
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	elif t_1 <= 2e+172:
		tmp = t_2
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= -5e+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_1 <= -1e+51)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_1 <= -4e-73)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	elseif (t_1 <= 2e+172)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (t_1 <= -5e+216)
		tmp = (x * t) / z;
	elseif (t_1 <= -1e+51)
		tmp = (x * t) / -y;
	elseif (t_1 <= -4e-73)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = (t / z) * -y;
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	elseif (t_1 <= 2e+172)
		tmp = t_2;
	else
		tmp = x * (t / -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]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+51], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$1, -4e-73], t$95$2, If[LessEqual[t$95$1, 0.5], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+172], t$95$2, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < -3.99999999999999999e-73 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e172

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

   if -3.99999999999999999e-73 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 94.5%

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

   if 2.0000000000000002e172 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-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. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.5

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

   7. Applied rewrites 99.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 77.2%

       \[\leadsto x \cdot \frac{t}{-y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{-y}\\ t_2 := \frac{x - y}{z - y}\\ t_3 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0.5:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) (- y))) (t_2 (/ (- x y) (- z y))) (t_3 (* t (/ x z))))
   (if (<= t_2 -5e+216)
     (/ (* x t) z)
     (if (<= t_2 -1e+51)
       t_1
       (if (<= t_2 -4e-73)
         t_3
         (if (<= t_2 0.5)
           (* (/ t z) (- y))
           (if (<= t_2 5e+15) (* t 1.0) (if (<= t_2 2e+172) t_3 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / -y;
	double t_2 = (x - y) / (z - y);
	double t_3 = t * (x / z);
	double tmp;
	if (t_2 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= -4e-73) {
		tmp = t_3;
	} else if (t_2 <= 0.5) {
		tmp = (t / z) * -y;
	} else if (t_2 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_2 <= 2e+172) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * t) / -y
    t_2 = (x - y) / (z - y)
    t_3 = t * (x / z)
    if (t_2 <= (-5d+216)) then
        tmp = (x * t) / z
    else if (t_2 <= (-1d+51)) then
        tmp = t_1
    else if (t_2 <= (-4d-73)) then
        tmp = t_3
    else if (t_2 <= 0.5d0) then
        tmp = (t / z) * -y
    else if (t_2 <= 5d+15) then
        tmp = t * 1.0d0
    else if (t_2 <= 2d+172) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / -y;
	double t_2 = (x - y) / (z - y);
	double t_3 = t * (x / z);
	double tmp;
	if (t_2 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= -4e-73) {
		tmp = t_3;
	} else if (t_2 <= 0.5) {
		tmp = (t / z) * -y;
	} else if (t_2 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_2 <= 2e+172) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / -y
	t_2 = (x - y) / (z - y)
	t_3 = t * (x / z)
	tmp = 0
	if t_2 <= -5e+216:
		tmp = (x * t) / z
	elif t_2 <= -1e+51:
		tmp = t_1
	elif t_2 <= -4e-73:
		tmp = t_3
	elif t_2 <= 0.5:
		tmp = (t / z) * -y
	elif t_2 <= 5e+15:
		tmp = t * 1.0
	elif t_2 <= 2e+172:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / Float64(-y))
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	t_3 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_2 <= -5e+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= -4e-73)
		tmp = t_3;
	elseif (t_2 <= 0.5)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (t_2 <= 5e+15)
		tmp = Float64(t * 1.0);
	elseif (t_2 <= 2e+172)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * t) / -y;
	t_2 = (x - y) / (z - y);
	t_3 = t * (x / z);
	tmp = 0.0;
	if (t_2 <= -5e+216)
		tmp = (x * t) / z;
	elseif (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= -4e-73)
		tmp = t_3;
	elseif (t_2 <= 0.5)
		tmp = (t / z) * -y;
	elseif (t_2 <= 5e+15)
		tmp = t * 1.0;
	elseif (t_2 <= 2e+172)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, -1e+51], t$95$1, If[LessEqual[t$95$2, -4e-73], t$95$3, If[LessEqual[t$95$2, 0.5], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t$95$2, 5e+15], N[(t * 1.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+172], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51 or 2.0000000000000002e172 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 73.2%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < -3.99999999999999999e-73 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e172

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

   if -3.99999999999999999e-73 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   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. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 65.0%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 94.5%

      \[\leadsto \color{blue}{1} \cdot t \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5e+216)
     (/ (* x t) z)
     (if (<= t_1 -1e+51)
       (/ (* x t) (- y))
       (if (<= t_1 0.5)
         (* (- x y) (/ t z))
         (if (<= t_1 5e+15)
           (* t 1.0)
           (if (<= t_1 2e+172) (* t (/ x z)) (* x (/ t (- y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= 0.5) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t * (x / z);
	} else {
		tmp = x * (t / -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 <= (-5d+216)) then
        tmp = (x * t) / z
    else if (t_1 <= (-1d+51)) then
        tmp = (x * t) / -y
    else if (t_1 <= 0.5d0) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    else if (t_1 <= 2d+172) then
        tmp = t * (x / z)
    else
        tmp = x * (t / -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 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= 0.5) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_1 <= 2e+172) {
		tmp = t * (x / z);
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -5e+216:
		tmp = (x * t) / z
	elif t_1 <= -1e+51:
		tmp = (x * t) / -y
	elif t_1 <= 0.5:
		tmp = (x - y) * (t / z)
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	elif t_1 <= 2e+172:
		tmp = t * (x / z)
	else:
		tmp = x * (t / -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 <= -5e+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_1 <= -1e+51)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	elseif (t_1 <= 2e+172)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = Float64(x * Float64(t / Float64(-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 <= -5e+216)
		tmp = (x * t) / z;
	elseif (t_1 <= -1e+51)
		tmp = (x * t) / -y;
	elseif (t_1 <= 0.5)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	elseif (t_1 <= 2e+172)
		tmp = t * (x / z);
	else
		tmp = x * (t / -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, -5e+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+51], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$1, 0.5], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+172], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.6%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 94.5%

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

   if 5e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e172

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.5

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

   5. Applied rewrites 70.5%

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

   if 2.0000000000000002e172 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-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. lower-/.f64 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 99.5

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

   7. Applied rewrites 99.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 77.2%

       \[\leadsto x \cdot \frac{t}{-y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot t}{-y}\\ t_2 := \frac{x - y}{z - y}\\ t_3 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x t) (- y))) (t_2 (/ (- x y) (- z y))) (t_3 (* t (/ x z))))
   (if (<= t_2 -5e+216)
     (/ (* x t) z)
     (if (<= t_2 -1e+51)
       t_1
       (if (<= t_2 5e-10)
         t_3
         (if (<= t_2 5e+15) (* t 1.0) (if (<= t_2 2e+172) t_3 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / -y;
	double t_2 = (x - y) / (z - y);
	double t_3 = t * (x / z);
	double tmp;
	if (t_2 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= 5e-10) {
		tmp = t_3;
	} else if (t_2 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_2 <= 2e+172) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * t) / -y
    t_2 = (x - y) / (z - y)
    t_3 = t * (x / z)
    if (t_2 <= (-5d+216)) then
        tmp = (x * t) / z
    else if (t_2 <= (-1d+51)) then
        tmp = t_1
    else if (t_2 <= 5d-10) then
        tmp = t_3
    else if (t_2 <= 5d+15) then
        tmp = t * 1.0d0
    else if (t_2 <= 2d+172) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * t) / -y;
	double t_2 = (x - y) / (z - y);
	double t_3 = t * (x / z);
	double tmp;
	if (t_2 <= -5e+216) {
		tmp = (x * t) / z;
	} else if (t_2 <= -1e+51) {
		tmp = t_1;
	} else if (t_2 <= 5e-10) {
		tmp = t_3;
	} else if (t_2 <= 5e+15) {
		tmp = t * 1.0;
	} else if (t_2 <= 2e+172) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * t) / -y
	t_2 = (x - y) / (z - y)
	t_3 = t * (x / z)
	tmp = 0
	if t_2 <= -5e+216:
		tmp = (x * t) / z
	elif t_2 <= -1e+51:
		tmp = t_1
	elif t_2 <= 5e-10:
		tmp = t_3
	elif t_2 <= 5e+15:
		tmp = t * 1.0
	elif t_2 <= 2e+172:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * t) / Float64(-y))
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	t_3 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_2 <= -5e+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= 5e-10)
		tmp = t_3;
	elseif (t_2 <= 5e+15)
		tmp = Float64(t * 1.0);
	elseif (t_2 <= 2e+172)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * t) / -y;
	t_2 = (x - y) / (z - y);
	t_3 = t * (x / z);
	tmp = 0.0;
	if (t_2 <= -5e+216)
		tmp = (x * t) / z;
	elseif (t_2 <= -1e+51)
		tmp = t_1;
	elseif (t_2 <= 5e-10)
		tmp = t_3;
	elseif (t_2 <= 5e+15)
		tmp = t * 1.0;
	elseif (t_2 <= 2e+172)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$2, -1e+51], t$95$1, If[LessEqual[t$95$2, 5e-10], t$95$3, If[LessEqual[t$95$2, 5e+15], N[(t * 1.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+172], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51 or 2.0000000000000002e172 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 73.2%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e172

   1. Initial program 96.2%

      \[\frac{x - y}{z - y} \cdot t \]
   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 60.1

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

   5. Applied rewrites 60.1%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 91.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{+172}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-268}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-268)
     (* (- x y) (/ t (- z y)))
     (if (<= t_1 0.5)
       (* t (/ (- x y) z))
       (if (<= t_1 5e+15) (fma t (/ (- z 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 <= 5e-268) {
		tmp = (x - y) * (t / (z - y));
	} else if (t_1 <= 0.5) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 5e+15) {
		tmp = fma(t, ((z - 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 <= 5e-268)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	elseif (t_1 <= 0.5)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 5e+15)
		tmp = fma(t, Float64(Float64(z - x) / y), t);
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return 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-268], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.5], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.9999999999999999e-268

   1. Initial program 91.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 91.9

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

   4. Applied rewrites 91.9%

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

   if 4.9999999999999999e-268 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 95.0

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

   5. Applied rewrites 95.0%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 100.0%

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

   if 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-268}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -4e+20)
     t_2
     (if (<= t_1 0.5)
       (* t (/ (- x y) z))
       (if (<= t_1 5e+15) (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 * (x / (z - y));
	double tmp;
	if (t_1 <= -4e+20) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 5e+15) {
		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(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -4e+20)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 5e+15)
		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[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+20], t$95$2, If[LessEqual[t$95$1, 0.5], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], 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)) < -4e20 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.9

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

   5. Applied rewrites 94.9%

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

   if -4e20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 92.4

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

   5. Applied rewrites 92.4%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 100.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -4e+20)
     t_2
     (if (<= t_1 0.5)
       (* t (/ (- x y) z))
       (if (<= t_1 5e+15) (fma t (- (/ 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 * (x / (z - y));
	double tmp;
	if (t_1 <= -4e+20) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 5e+15) {
		tmp = fma(t, -(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(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -4e+20)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 5e+15)
		tmp = fma(t, Float64(-Float64(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[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+20], t$95$2, If[LessEqual[t$95$1, 0.5], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * (-N[(x / y), $MachinePrecision]) + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4e20 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.9

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

   5. Applied rewrites 94.9%

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

   if -4e20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 92.4

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

   5. Applied rewrites 92.4%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -4e+20)
     t_2
     (if (<= t_1 0.5)
       (* (- x y) (/ t z))
       (if (<= t_1 5e+15) (fma t (- (/ 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 * (x / (z - y));
	double tmp;
	if (t_1 <= -4e+20) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = fma(t, -(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(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -4e+20)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 5e+15)
		tmp = fma(t, Float64(-Float64(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[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+20], t$95$2, If[LessEqual[t$95$1, 0.5], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * (-N[(x / y), $MachinePrecision]) + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4e20 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 94.9

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

   5. Applied rewrites 94.9%

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

   if -4e20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.1%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 -4e+20)
     t_2
     (if (<= t_1 0.5)
       (* (- x y) (/ t z))
       (if (<= t_1 5e+15) (fma t (- (/ 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 * (t / (z - y));
	double tmp;
	if (t_1 <= -4e+20) {
		tmp = t_2;
	} else if (t_1 <= 0.5) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = fma(t, -(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(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -4e+20)
		tmp = t_2;
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 5e+15)
		tmp = fma(t, Float64(-Float64(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[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+20], t$95$2, If[LessEqual[t$95$1, 0.5], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * (-N[(x / y), $MachinePrecision]) + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4e20 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   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. *-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. lower-/.f64 94.8

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

   4. Applied rewrites 94.8%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 88.9

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

   7. Applied rewrites 88.9%

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

   if -4e20 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.1%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 87.6

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

   5. Applied rewrites 87.6%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;t\_1 \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5e+216)
     (/ (* x t) z)
     (if (<= t_1 -1e+51)
       (/ (* x t) (- y))
       (if (<= t_1 0.5) (* (- x y) (/ t z)) (fma t (- (/ x y)) 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+216) {
		tmp = (x * t) / z;
	} else if (t_1 <= -1e+51) {
		tmp = (x * t) / -y;
	} else if (t_1 <= 0.5) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = fma(t, -(x / y), 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+216)
		tmp = Float64(Float64(x * t) / z);
	elseif (t_1 <= -1e+51)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (t_1 <= 0.5)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = fma(t, Float64(-Float64(x / y)), t);
	end
	return 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+216], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+51], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[t$95$1, 0.5], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * (-N[(x / y), $MachinePrecision]) + t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.9999999999999998e216

   1. Initial program 70.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.5

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

   5. Applied rewrites 88.5%

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

   if -4.9999999999999998e216 < (/.f64 (-.f64 x y) (-.f64 z y)) < -1e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 71.4

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

   5. Applied rewrites 71.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 71.6%

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

   if -1e51 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.5

   1. Initial program 95.6%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if 0.5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

      9. distribute-lft-neg-in N/A

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

      14. distribute-lft-neg-in N/A

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 86.6

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

   5. Applied rewrites 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{x}{-y}, t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+216}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.5:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, -\frac{x}{y}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 5e-10) t_2 (if (<= t_1 5e+15) (* t 1.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = t_2;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / z)
    if (t_1 <= 5d-10) then
        tmp = t_2
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = t_2;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / z)
	tmp = 0
	if t_1 <= 5e-10:
		tmp = t_2
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	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(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= 5e-10)
		tmp = t_2;
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (t_1 <= 5e-10)
		tmp = t_2;
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	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[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-10], t$95$2, If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 55.5

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

   5. Applied rewrites 55.5%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 91.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-10)
     (* x (/ t z))
     (if (<= t_1 5e+15) (* t 1.0) (/ (* x t) 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-10) {
		tmp = x * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else {
		tmp = (x * t) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-10) then
        tmp = x * (t / z)
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    else
        tmp = (x * t) / 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-10) {
		tmp = x * (t / z);
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else {
		tmp = (x * t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-10:
		tmp = x * (t / z)
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	else:
		tmp = (x * t) / 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-10)
		tmp = Float64(x * Float64(t / z));
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(Float64(x * t) / 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-10)
		tmp = x * (t / z);
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	else
		tmp = (x * t) / 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-10], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 93.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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. lower-/.f64 92.7

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

   4. Applied rewrites 92.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 54.3

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

   7. Applied rewrites 54.3%

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

   9. Applied rewrites 55.2%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   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 91.8%

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

   if 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 48.0

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

   5. Applied rewrites 48.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 67.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x \cdot t}{z}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* x t) z)))
   (if (<= t_1 5e-28) t_2 (if (<= t_1 5e+15) (* t 1.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / z;
	double tmp;
	if (t_1 <= 5e-28) {
		tmp = t_2;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} 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 * t) / z
    if (t_1 <= 5d-28) then
        tmp = t_2
    else if (t_1 <= 5d+15) then
        tmp = t * 1.0d0
    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 * t) / z;
	double tmp;
	if (t_1 <= 5e-28) {
		tmp = t_2;
	} else if (t_1 <= 5e+15) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x * t) / z
	tmp = 0
	if t_1 <= 5e-28:
		tmp = t_2
	elif t_1 <= 5e+15:
		tmp = t * 1.0
	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 * t) / z)
	tmp = 0.0
	if (t_1 <= 5e-28)
		tmp = t_2;
	elseif (t_1 <= 5e+15)
		tmp = Float64(t * 1.0);
	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 * t) / z;
	tmp = 0.0;
	if (t_1 <= 5e-28)
		tmp = t_2;
	elseif (t_1 <= 5e+15)
		tmp = t * 1.0;
	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 * t), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-28], t$95$2, If[LessEqual[t$95$1, 5e+15], N[(t * 1.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000002e-28 or 5e15 < (/.f64 (-.f64 x y) (-.f64 z y))

   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 54.3

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

   5. Applied rewrites 54.3%

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

   if 5.0000000000000002e-28 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e15

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 88.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-28}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.1% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

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 * 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 35.6%

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

6. Final simplification 35.6%

   \[\leadsto t \cdot 1 \]
7. 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 2024238 
(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))