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

Percentage Accurate: 96.9% → 97.0%

Time: 9.4s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 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]

Derivation

1. Initial program 96.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. clear-num N/A

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 96.2

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

4. Applied rewrites 96.2%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -2e-44)
     t_2
     (if (<= t_1 5e-7)
       (* (- x y) (/ t z))
       (if (<= t_1 2.0) (fma t (/ (- z x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -2e-44) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -2e-44)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		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[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-44], t$95$2, If[LessEqual[t$95$1, 5e-7], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 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)) < -1.99999999999999991e-44 or 2 < (/.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 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 91.8

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

   5. Applied rewrites 91.8%

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

   if -1.99999999999999991e-44 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 92.8%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 99.5%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -2e-44)
     t_2
     (if (<= t_1 5e-7)
       (* (- x y) (/ t z))
       (if (<= t_1 2.0) (* t (/ y (- y z))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -2e-44) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / (z - y))
    if (t_1 <= (-2d-44)) then
        tmp = t_2
    else if (t_1 <= 5d-7) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * (y / (y - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -2e-44) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / (z - y))
	tmp = 0
	if t_1 <= -2e-44:
		tmp = t_2
	elif t_1 <= 5e-7:
		tmp = (x - y) * (t / z)
	elif t_1 <= 2.0:
		tmp = t * (y / (y - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -2e-44)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (t_1 <= -2e-44)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 2.0)
		tmp = t * (y / (y - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-44], t$95$2, If[LessEqual[t$95$1, 5e-7], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.99999999999999991e-44 or 2 < (/.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 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 91.8

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

   5. Applied rewrites 91.8%

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

   if -1.99999999999999991e-44 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 92.8%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 98.8

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

   8. Applied rewrites 98.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{-y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -2e-44)
     t_2
     (if (<= t_1 5e-7)
       (* (- x y) (/ t z))
       (if (<= t_1 2.0) (fma t (/ x (- y)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -2e-44) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = fma(t, (x / -y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -2e-44)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		tmp = fma(t, Float64(x / Float64(-y)), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-44], t$95$2, If[LessEqual[t$95$1, 5e-7], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], 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)) < -1.99999999999999991e-44 or 2 < (/.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 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 91.8

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

   5. Applied rewrites 91.8%

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

   if -1.99999999999999991e-44 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 92.8%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

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

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 98.6

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

   5. Applied rewrites 98.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{-y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- y)))))
   (if (<= t_1 -2e+58)
     t_2
     (if (<= t_1 5e-7) (* t (/ x z)) (if (<= t_1 2.0) (* t 1.0) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / -y);
	double tmp;
	if (t_1 <= -2e+58) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 2.0) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / -y)
    if (t_1 <= (-2d+58)) then
        tmp = t_2
    else if (t_1 <= 5d-7) then
        tmp = t * (x / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / -y);
	double tmp;
	if (t_1 <= -2e+58) {
		tmp = t_2;
	} else if (t_1 <= 5e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 2.0) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / -y)
	tmp = 0
	if t_1 <= -2e+58:
		tmp = t_2
	elif t_1 <= 5e-7:
		tmp = t * (x / z)
	elif t_1 <= 2.0:
		tmp = t * 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (t_1 <= -2e+58)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = Float64(t * Float64(x / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * 1.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / -y);
	tmp = 0.0;
	if (t_1 <= -2e+58)
		tmp = t_2;
	elseif (t_1 <= 5e-7)
		tmp = t * (x / z);
	elseif (t_1 <= 2.0)
		tmp = t * 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+58], t$95$2, If[LessEqual[t$95$1, 5e-7], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * 1.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.99999999999999989e58 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

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

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 65.9%

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

   if -1.99999999999999989e58 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 94.2%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 64.9

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

   5. Applied rewrites 64.9%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.999998:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 0.999998)
     (* (- x y) (/ t (- z y)))
     (if (<= t_1 2.0) (fma t (/ (- z x) y) t) (* t (/ x (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.999998) {
		tmp = (x - y) * (t / (z - y));
	} else if (t_1 <= 2.0) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.999998)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2.0)
		tmp = fma(t, Float64(Float64(z - x) / y), t);
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.999998], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.999998000000000054

   1. Initial program 94.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 92.7

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

   4. Applied rewrites 92.7%

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

   if 0.999998000000000054 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(t + -1 \cdot \frac{t \cdot x}{y}\right) - -1 \cdot \frac{t \cdot z}{y}} \]
   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 99.8%

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

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

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 0.999998:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-7)
     (* (- x y) (/ t z))
     (if (<= t_1 2.0) (* t 1.0) (* t (/ x (- y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * 1.0;
	} else {
		tmp = t * (x / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-7) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 2.0d0) then
        tmp = t * 1.0d0
    else
        tmp = t * (x / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2.0) {
		tmp = t * 1.0;
	} else {
		tmp = t * (x / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-7:
		tmp = (x - y) * (t / z)
	elif t_1 <= 2.0:
		tmp = t * 1.0
	else:
		tmp = t * (x / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-7)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2.0)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(t * Float64(x / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-7)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 2.0)
		tmp = t * 1.0;
	else
		tmp = t * (x / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-7], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(t * 1.0), $MachinePrecision], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 94.0%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 97.4%

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

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

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 65.4%

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

4. Final simplification 81.6%

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

Alternative 8: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-7)
     (* t (/ x z))
     (if (<= t_1 1000000000000.0) (* t 1.0) (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-7) then
        tmp = t * (x / z)
    else if (t_1 <= 1000000000000.0d0) then
        tmp = t * 1.0d0
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-7:
		tmp = t * (x / z)
	elif t_1 <= 1000000000000.0:
		tmp = t * 1.0
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-7)
		tmp = Float64(t * Float64(x / z));
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-7)
		tmp = t * (x / z);
	elseif (t_1 <= 1000000000000.0)
		tmp = t * 1.0;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-7], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000000000.0], N[(t * 1.0), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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 61.7

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

   5. Applied rewrites 61.7%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e12

   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 95.1%

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

   if 1e12 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-7)
     (* x (/ t z))
     (if (<= t_1 1000000000000.0) (* t 1.0) (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = x * (t / z);
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-7) then
        tmp = x * (t / z)
    else if (t_1 <= 1000000000000.0d0) then
        tmp = t * 1.0d0
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = x * (t / z);
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-7:
		tmp = x * (t / z)
	elif t_1 <= 1000000000000.0:
		tmp = t * 1.0
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-7)
		tmp = Float64(x * Float64(t / z));
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-7)
		tmp = x * (t / z);
	elseif (t_1 <= 1000000000000.0)
		tmp = t * 1.0;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-7], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000000000.0], N[(t * 1.0), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 94.0%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 93.7

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

   4. Applied rewrites 93.7%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.1

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

   7. Applied rewrites 59.1%

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

   9. Applied rewrites 61.1%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e12

   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 95.1%

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

   if 1e12 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 47.7

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

   5. Applied rewrites 47.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t \cdot x}{z}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* t x) z)))
   (if (<= t_1 5e-7) t_2 (if (<= t_1 1000000000000.0) (* t 1.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = t_2;
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t * x) / z
    if (t_1 <= 5d-7) then
        tmp = t_2
    else if (t_1 <= 1000000000000.0d0) then
        tmp = t * 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t * x) / z;
	double tmp;
	if (t_1 <= 5e-7) {
		tmp = t_2;
	} else if (t_1 <= 1000000000000.0) {
		tmp = t * 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t * x) / z
	tmp = 0
	if t_1 <= 5e-7:
		tmp = t_2
	elif t_1 <= 1000000000000.0:
		tmp = t * 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t * x) / z)
	tmp = 0.0
	if (t_1 <= 5e-7)
		tmp = t_2;
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(t * 1.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t * x) / z;
	tmp = 0.0;
	if (t_1 <= 5e-7)
		tmp = t_2;
	elseif (t_1 <= 1000000000000.0)
		tmp = t * 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-7], t$95$2, If[LessEqual[t$95$1, 1000000000000.0], N[(t * 1.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7 or 1e12 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 56.3

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

   5. Applied rewrites 56.3%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e12

   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 95.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 1000000000000:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{x}{-y}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x y) (- z y)) 5e-7) (* (- x y) (/ t z)) (fma t (/ x (- y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x - y) / (z - y)) <= 5e-7) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = fma(t, (x / -y), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= 5e-7)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = fma(t, Float64(x / Float64(-y)), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], 5e-7], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / (-y)), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-7

   1. Initial program 94.0%

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

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if 4.99999999999999977e-7 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. *-inverses N/A

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

      6. metadata-eval N/A

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

      7. distribute-lft-in N/A

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

      8. neg-mul-1 N/A

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

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

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

      10. *-commutative N/A

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

      11. neg-mul-1 N/A

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

      12. remove-double-neg N/A

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

      13. neg-mul-1 N/A

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

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

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

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

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

      16. mul-1-neg N/A

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

      17. lower-fma.f64 N/A

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

      18. mul-1-neg N/A

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

      19. distribute-neg-frac2 N/A

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

      20. lower-/.f64 N/A

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

      21. lower-neg.f64 85.8

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

   5. Applied rewrites 85.8%

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

Alternative 12: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Final simplification 96.0%

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

Alternative 13: 34.9% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.0%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 30.6%

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

6. Final simplification 30.6%

   \[\leadsto t \cdot 1 \]
7. 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 2024220 
(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))