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

Percentage Accurate: 97.0% → 97.0%

Time: 8.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. lower--.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.6

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

4. Applied rewrites 97.6%

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

5. Final simplification 97.6%

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

Alternative 2: 79.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ t z) (- x y))))
   (if (<= t_1 -1e+100)
     (* (/ x z) t)
     (if (<= t_1 -5e+18)
       (/ (* (- x) t) y)
       (if (<= t_1 0.6)
         t_2
         (if (<= t_1 2.0)
           (* (/ y (- y z)) t)
           (if (<= t_1 2e+104) (* (/ (- x) y) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (t / z) * (x - y);
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = (x / z) * t;
	} else if (t_1 <= -5e+18) {
		tmp = (-x * t) / y;
	} else if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else if (t_1 <= 2e+104) {
		tmp = (-x / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) / (y - z)
    t_2 = (t / z) * (x - y)
    if (t_1 <= (-1d+100)) then
        tmp = (x / z) * t
    else if (t_1 <= (-5d+18)) then
        tmp = (-x * t) / y
    else if (t_1 <= 0.6d0) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else if (t_1 <= 2d+104) then
        tmp = (-x / y) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (t / z) * (x - y);
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = (x / z) * t;
	} else if (t_1 <= -5e+18) {
		tmp = (-x * t) / y;
	} else if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else if (t_1 <= 2e+104) {
		tmp = (-x / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) / (y - z)
	t_2 = (t / z) * (x - y)
	tmp = 0
	if t_1 <= -1e+100:
		tmp = (x / z) * t
	elif t_1 <= -5e+18:
		tmp = (-x * t) / y
	elif t_1 <= 0.6:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	elif t_1 <= 2e+104:
		tmp = (-x / y) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(t / z) * Float64(x - y))
	tmp = 0.0
	if (t_1 <= -1e+100)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= -5e+18)
		tmp = Float64(Float64(Float64(-x) * t) / y);
	elseif (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	elseif (t_1 <= 2e+104)
		tmp = Float64(Float64(Float64(-x) / y) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) / (y - z);
	t_2 = (t / z) * (x - y);
	tmp = 0.0;
	if (t_1 <= -1e+100)
		tmp = (x / z) * t;
	elseif (t_1 <= -5e+18)
		tmp = (-x * t) / y;
	elseif (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	elseif (t_1 <= 2e+104)
		tmp = (-x / y) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+100], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, -5e+18], N[(N[((-x) * t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 0.6], t$95$2, If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+104], N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000002e100

   1. Initial program 93.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 65.4

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

   5. Applied rewrites 65.4%

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

   if -1.00000000000000002e100 < (/.f64 (-.f64 x y) (-.f64 z y)) < -5e18

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 73.6%

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

   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 73.6%

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

   10. Applied rewrites 73.7%

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

   if -5e18 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 2e104 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 86.9

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

   5. Applied rewrites 86.9%

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

   7. Applied rewrites 92.0%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. 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. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lift--.f64 N/A

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

      7. flip3-- N/A

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

      8. clear-num N/A

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

      9. lower-*.f64 N/A

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

   4. Applied rewrites 69.8%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 98.1

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

   7. Applied rewrites 98.1%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e104

   1. Initial program 99.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 67.1%

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

   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 60.6%

      \[\leadsto \left(-t\right) \cdot \color{blue}{\frac{x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x z) t)))
   (if (<= t_1 -1e+100)
     t_2
     (if (<= t_1 -5e+18)
       (/ (* (- x) t) y)
       (if (<= t_1 2e-48)
         t_2
         (if (<= t_1 2.0)
           (* (/ y (- y z)) t)
           (if (<= t_1 2e+104) (* (/ (- x) y) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = t_2;
	} else if (t_1 <= -5e+18) {
		tmp = (-x * t) / y;
	} else if (t_1 <= 2e-48) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else if (t_1 <= 2e+104) {
		tmp = (-x / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) / (y - z)
    t_2 = (x / z) * t
    if (t_1 <= (-1d+100)) then
        tmp = t_2
    else if (t_1 <= (-5d+18)) then
        tmp = (-x * t) / y
    else if (t_1 <= 2d-48) then
        tmp = t_2
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else if (t_1 <= 2d+104) then
        tmp = (-x / y) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = t_2;
	} else if (t_1 <= -5e+18) {
		tmp = (-x * t) / y;
	} else if (t_1 <= 2e-48) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else if (t_1 <= 2e+104) {
		tmp = (-x / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) / (y - z)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= -1e+100:
		tmp = t_2
	elif t_1 <= -5e+18:
		tmp = (-x * t) / y
	elif t_1 <= 2e-48:
		tmp = t_2
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	elif t_1 <= 2e+104:
		tmp = (-x / y) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= -1e+100)
		tmp = t_2;
	elseif (t_1 <= -5e+18)
		tmp = Float64(Float64(Float64(-x) * t) / y);
	elseif (t_1 <= 2e-48)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	elseif (t_1 <= 2e+104)
		tmp = Float64(Float64(Float64(-x) / y) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) / (y - z);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= -1e+100)
		tmp = t_2;
	elseif (t_1 <= -5e+18)
		tmp = (-x * t) / y;
	elseif (t_1 <= 2e-48)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	elseif (t_1 <= 2e+104)
		tmp = (-x / y) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+100], t$95$2, If[LessEqual[t$95$1, -5e+18], N[(N[((-x) * t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e-48], t$95$2, If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e+104], N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000002e100 or -5e18 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-48 or 2e104 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.9

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

   5. Applied rewrites 70.9%

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

   if -1.00000000000000002e100 < (/.f64 (-.f64 x y) (-.f64 z y)) < -5e18

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 73.6%

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

   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 73.6%

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

   10. Applied rewrites 73.7%

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

   if 1.9999999999999999e-48 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. 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. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lift--.f64 N/A

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

      7. flip3-- N/A

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

      8. clear-num N/A

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

      9. lower-*.f64 N/A

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

   4. Applied rewrites 70.7%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 96.1

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

   7. Applied rewrites 96.1%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e104

   1. Initial program 99.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 67.1%

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

   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 60.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x z) t)))
   (if (<= t_1 -1e+100)
     t_2
     (if (<= t_1 -5e+18)
       (/ (* (- x) t) y)
       (if (<= t_1 0.6)
         t_2
         (if (<= t_1 2.0)
           (fma t (/ z y) t)
           (if (<= t_1 2e+104) (* (/ (- x) y) t) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= -1e+100) {
		tmp = t_2;
	} else if (t_1 <= -5e+18) {
		tmp = (-x * t) / y;
	} else if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = fma(t, (z / y), t);
	} else if (t_1 <= 2e+104) {
		tmp = (-x / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= -1e+100)
		tmp = t_2;
	elseif (t_1 <= -5e+18)
		tmp = Float64(Float64(Float64(-x) * t) / y);
	elseif (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = fma(t, Float64(z / y), t);
	elseif (t_1 <= 2e+104)
		tmp = Float64(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[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+100], t$95$2, If[LessEqual[t$95$1, -5e+18], N[(N[((-x) * t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 0.6], t$95$2, If[LessEqual[t$95$1, 2.0], N[(t * N[(z / y), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[t$95$1, 2e+104], N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000002e100 or -5e18 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 2e104 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 69.2

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

   5. Applied rewrites 69.2%

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

   if -1.00000000000000002e100 < (/.f64 (-.f64 x y) (-.f64 z y)) < -5e18

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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 73.6%

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

   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 73.6%

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

   10. Applied rewrites 73.7%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 98.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 96.8%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e104

   1. Initial program 99.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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 67.1%

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

   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 60.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{\left(-x\right) \cdot t}{y}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{y} \cdot t\\ t_2 := \frac{y - x}{y - z}\\ t_3 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.6:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- x) y) t)) (t_2 (/ (- y x) (- y z))) (t_3 (* (/ x z) t)))
   (if (<= t_2 -1e+100)
     t_3
     (if (<= t_2 -5e+18)
       t_1
       (if (<= t_2 0.6)
         t_3
         (if (<= t_2 2.0) (fma t (/ z y) t) (if (<= t_2 2e+104) t_1 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-x / y) * t;
	double t_2 = (y - x) / (y - z);
	double t_3 = (x / z) * t;
	double tmp;
	if (t_2 <= -1e+100) {
		tmp = t_3;
	} else if (t_2 <= -5e+18) {
		tmp = t_1;
	} else if (t_2 <= 0.6) {
		tmp = t_3;
	} else if (t_2 <= 2.0) {
		tmp = fma(t, (z / y), t);
	} else if (t_2 <= 2e+104) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / y) * t)
	t_2 = Float64(Float64(y - x) / Float64(y - z))
	t_3 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_2 <= -1e+100)
		tmp = t_3;
	elseif (t_2 <= -5e+18)
		tmp = t_1;
	elseif (t_2 <= 0.6)
		tmp = t_3;
	elseif (t_2 <= 2.0)
		tmp = fma(t, Float64(z / y), t);
	elseif (t_2 <= 2e+104)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / y), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+100], t$95$3, If[LessEqual[t$95$2, -5e+18], t$95$1, If[LessEqual[t$95$2, 0.6], t$95$3, If[LessEqual[t$95$2, 2.0], N[(t * N[(z / y), $MachinePrecision] + t), $MachinePrecision], If[LessEqual[t$95$2, 2e+104], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000002e100 or -5e18 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 2e104 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 69.2

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

   5. Applied rewrites 69.2%

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

   if -1.00000000000000002e100 < (/.f64 (-.f64 x y) (-.f64 z y)) < -5e18 or 2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e104

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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 70.6%

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

   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 67.6%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 98.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 96.8%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -5 \cdot 10^{+18}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\frac{-x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{-x}{y}, t\right)\\ t_2 := \frac{y - x}{y - z}\\ t_3 := \frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_2 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.6:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma t (/ (- x) y) t))
        (t_2 (/ (- y x) (- y z)))
        (t_3 (* (/ t z) (- x y))))
   (if (<= t_2 -1e+100)
     (* (/ x z) t)
     (if (<= t_2 -2.0)
       t_1
       (if (<= t_2 0.6) t_3 (if (<= t_2 2e+104) t_1 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(t, (-x / y), t);
	double t_2 = (y - x) / (y - z);
	double t_3 = (t / z) * (x - y);
	double tmp;
	if (t_2 <= -1e+100) {
		tmp = (x / z) * t;
	} else if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= 0.6) {
		tmp = t_3;
	} else if (t_2 <= 2e+104) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(t, Float64(Float64(-x) / y), t)
	t_2 = Float64(Float64(y - x) / Float64(y - z))
	t_3 = Float64(Float64(t / z) * Float64(x - y))
	tmp = 0.0
	if (t_2 <= -1e+100)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= 0.6)
		tmp = t_3;
	elseif (t_2 <= 2e+104)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[((-x) / y), $MachinePrecision] + t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+100], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$2, -2.0], t$95$1, If[LessEqual[t$95$2, 0.6], t$95$3, If[LessEqual[t$95$2, 2e+104], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000002e100

   1. Initial program 93.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 65.4

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

   5. Applied rewrites 65.4%

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

   if -1.00000000000000002e100 < (/.f64 (-.f64 x y) (-.f64 z y)) < -2 or 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e104

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 88.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 87.4%

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

   if -2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 2e104 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 88.3

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

   5. Applied rewrites 88.3%

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

   7. Applied rewrites 93.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq -2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-x}{y}, t\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.999:\\ \;\;\;\;\frac{t}{y - z} \cdot \left(y - x\right)\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1e-29)
     t_2
     (if (<= t_1 0.999)
       (* (/ t (- y z)) (- y x))
       (if (<= t_1 20.0) (fma t (/ (- z x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -1e-29) {
		tmp = t_2;
	} else if (t_1 <= 0.999) {
		tmp = (t / (y - z)) * (y - x);
	} else if (t_1 <= 20.0) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1e-29)
		tmp = t_2;
	elseif (t_1 <= 0.999)
		tmp = Float64(Float64(t / Float64(y - z)) * Float64(y - x));
	elseif (t_1 <= 20.0)
		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[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-29], t$95$2, If[LessEqual[t$95$1, 0.999], N[(N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20.0], 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)) < -9.99999999999999943e-30 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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 93.8

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

   5. Applied rewrites 93.8%

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

   if -9.99999999999999943e-30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.998999999999999999

   1. Initial program 95.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 99.0

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

   4. Applied rewrites 99.0%

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

   if 0.998999999999999999 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 99.3%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.999:\\ \;\;\;\;\frac{t}{y - z} \cdot \left(y - x\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1e-29)
     t_2
     (if (<= t_1 0.6)
       (* (/ t z) (- x y))
       (if (<= t_1 20.0) (fma t (/ (- z x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -1e-29) {
		tmp = t_2;
	} else if (t_1 <= 0.6) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 20.0) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1e-29)
		tmp = t_2;
	elseif (t_1 <= 0.6)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 20.0)
		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[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-29], t$95$2, If[LessEqual[t$95$1, 0.6], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20.0], 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)) < -9.99999999999999943e-30 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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 93.8

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

   5. Applied rewrites 93.8%

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

   if -9.99999999999999943e-30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 93.1

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

   5. Applied rewrites 93.1%

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

   7. Applied rewrites 98.9%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   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 98.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -1e-29)
     t_2
     (if (<= t_1 0.6)
       (* (/ t z) (- x y))
       (if (<= t_1 2.0) (* (/ y (- y z)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -1e-29) {
		tmp = t_2;
	} else if (t_1 <= 0.6) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) / (y - z)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-1d-29)) then
        tmp = t_2
    else if (t_1 <= 0.6d0) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -1e-29) {
		tmp = t_2;
	} else if (t_1 <= 0.6) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) / (y - z)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -1e-29:
		tmp = t_2
	elif t_1 <= 0.6:
		tmp = (t / z) * (x - y)
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1e-29)
		tmp = t_2;
	elseif (t_1 <= 0.6)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) / (y - z);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -1e-29)
		tmp = t_2;
	elseif (t_1 <= 0.6)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-29], t$95$2, If[LessEqual[t$95$1, 0.6], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.99999999999999943e-30 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.9%

      \[\frac{x - y}{z - y} \cdot t \]
   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 93.1

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

   5. Applied rewrites 93.1%

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

   if -9.99999999999999943e-30 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 93.1

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

   5. Applied rewrites 93.1%

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

   7. Applied rewrites 98.9%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

      1. lift-*.f64 N/A

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

      2. 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. clear-num N/A

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

      5. associate-/r/ N/A

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

      6. lift--.f64 N/A

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

      7. flip3-- N/A

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

      8. clear-num N/A

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

      9. lower-*.f64 N/A

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

   4. Applied rewrites 69.8%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 98.1

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

   7. Applied rewrites 98.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -1 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -2.0)
     t_2
     (if (<= t_1 0.6)
       (* (/ t z) (- x y))
       (if (<= t_1 20.0) (fma t (/ (- x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -2.0) {
		tmp = t_2;
	} else if (t_1 <= 0.6) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 20.0) {
		tmp = fma(t, (-x / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -2.0)
		tmp = t_2;
	elseif (t_1 <= 0.6)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 20.0)
		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[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -2.0], t$95$2, If[LessEqual[t$95$1, 0.6], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20.0], 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)) < -2 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.6%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 96.6

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

   4. Applied rewrites 96.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 96.4

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

   6. Applied rewrites 96.4%

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

   7. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 86.3

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

   9. Applied rewrites 86.3%

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

   if -2 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 91.2

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

   5. Applied rewrites 91.2%

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

   7. Applied rewrites 96.6%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   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 98.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 97.2%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq -2:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq 0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x z) t)))
   (if (<= t_1 0.6) t_2 (if (<= t_1 20.0) (fma t (/ z y) t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 20.0) {
		tmp = fma(t, (z / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 20.0)
		tmp = fma(t, Float64(z / y), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 0.6], t$95$2, If[LessEqual[t$95$1, 20.0], N[(t * N[(z / y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 61.1

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

   5. Applied rewrites 61.1%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   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 98.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 95.9%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{\color{blue}{y}}, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq 0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (* (/ x z) t)))
   (if (<= t_1 0.6) t_2 (if (<= t_1 20.0) (* 1.0 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 20.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) / (y - z)
    t_2 = (x / z) * t
    if (t_1 <= 0.6d0) then
        tmp = t_2
    else if (t_1 <= 20.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 20.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) / (y - z)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= 0.6:
		tmp = t_2
	elif t_1 <= 20.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 20.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) / (y - z);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 20.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 0.6], t$95$2, If[LessEqual[t$95$1, 20.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.3%

      \[\frac{x - y}{z - y} \cdot t \]
   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 61.1

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

   5. Applied rewrites 61.1%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   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 94.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - x}{y - z}\\ t_2 := \frac{t \cdot x}{z}\\ \mathbf{if}\;t\_1 \leq 0.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 20:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- y x) (- y z))) (t_2 (/ (* t x) z)))
   (if (<= t_1 0.6) t_2 (if (<= t_1 20.0) (* 1.0 t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 20.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) / (y - z)
    t_2 = (t * x) / z
    if (t_1 <= 0.6d0) then
        tmp = t_2
    else if (t_1 <= 20.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) / (y - z);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 0.6) {
		tmp = t_2;
	} else if (t_1 <= 20.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) / (y - z)
	t_2 = (t * x) / z
	tmp = 0
	if t_1 <= 0.6:
		tmp = t_2
	elif t_1 <= 20.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) / Float64(y - z))
	t_2 = Float64(Float64(t * x) / z)
	tmp = 0.0
	if (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 20.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) / (y - z);
	t_2 = (t * x) / z;
	tmp = 0.0;
	if (t_1 <= 0.6)
		tmp = t_2;
	elseif (t_1 <= 20.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, 0.6], t$95$2, If[LessEqual[t$95$1, 20.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978 or 20 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 57.5

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

   5. Applied rewrites 57.5%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 20

   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 94.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - x}{y - z} \leq 0.6:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;\frac{y - x}{y - z} \leq 20:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 15: 34.5% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 34.2%

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

Developer Target 1: 97.0% 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 2024235 
(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))