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

Percentage Accurate: 97.2% → 97.2%

Time: 7.2s

Alternatives: 14

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: 97.2% 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: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

Alternative 2: 93.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -50.0)
     t_2
     (if (<= t_1 -5e-81)
       (* (/ t z) (- x y))
       (if (<= t_1 1e-9)
         (/ (* (- x y) t) z)
         (if (<= t_1 2.0) (* (- 1.0 (/ x y)) t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-50.0d0)) then
        tmp = t_2
    else if (t_1 <= (-5d-81)) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 1d-9) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_2
	elif t_1 <= -5e-81:
		tmp = (t / z) * (x - y)
	elif t_1 <= 1e-9:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 1e-9)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 1e-9)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, -5e-81], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -50 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.7

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

   5. Applied rewrites 96.7%

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

   if -50 < (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81

   1. Initial program 99.7%

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

      1. lift-*.f64 N/A

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

      2. 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 90.5

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

   4. Applied rewrites 90.5%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 86.4

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

   7. Applied rewrites 86.4%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000006e-9

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.2

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

   5. Applied rewrites 97.2%

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

   if 1.00000000000000006e-9 < (/.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

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 97.5%

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

Alternative 3: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x \cdot t}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* x t) (- z y))))
   (if (<= t_1 -1e+17)
     t_2
     (if (<= t_1 -5e-81)
       (* (/ t z) (- x y))
       (if (<= t_1 1e-9)
         (/ (* (- x y) t) z)
         (if (<= t_1 2.0) (* (- 1.0 (/ x y)) t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x * t) / (z - y)
    if (t_1 <= (-1d+17)) then
        tmp = t_2
    else if (t_1 <= (-5d-81)) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 1d-9) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x * t) / (z - y)
	tmp = 0
	if t_1 <= -1e+17:
		tmp = t_2
	elif t_1 <= -5e-81:
		tmp = (t / z) * (x - y)
	elif t_1 <= 1e-9:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x * t) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 1e-9)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x * t) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 1e-9)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+17], t$95$2, If[LessEqual[t$95$1, -5e-81], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e17 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   7. Applied rewrites 91.3%

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

   if -1e17 < (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81

   1. Initial program 99.6%

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

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000006e-9

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.2

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

   5. Applied rewrites 97.2%

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

   if 1.00000000000000006e-9 < (/.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

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 97.5%

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

Alternative 4: 90.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x \cdot t}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(\frac{z}{y} + 1\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* x t) (- z y))))
   (if (<= t_1 -1e+17)
     t_2
     (if (<= t_1 -5e-81)
       (* (/ t z) (- x y))
       (if (<= t_1 5e-6)
         (/ (* (- x y) t) z)
         (if (<= t_1 2.0) (* (+ (/ z y) 1.0) t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = ((z / y) + 1.0) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x * t) / (z - y)
    if (t_1 <= (-1d+17)) then
        tmp = t_2
    else if (t_1 <= (-5d-81)) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 5d-6) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = ((z / y) + 1.0d0) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = ((z / y) + 1.0) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x * t) / (z - y)
	tmp = 0
	if t_1 <= -1e+17:
		tmp = t_2
	elif t_1 <= -5e-81:
		tmp = (t / z) * (x - y)
	elif t_1 <= 5e-6:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = ((z / y) + 1.0) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x * t) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 5e-6)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(Float64(z / y) + 1.0) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x * t) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 5e-6)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = ((z / y) + 1.0) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+17], t$95$2, If[LessEqual[t$95$1, -5e-81], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-6], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(N[(z / y), $MachinePrecision] + 1.0), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e17 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   7. Applied rewrites 91.3%

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

   if -1e17 < (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81

   1. Initial program 99.6%

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

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000041e-6

   1. Initial program 94.2%

      \[\frac{x - y}{z - y} \cdot t \]
   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 95.8

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

   5. Applied rewrites 95.8%

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

   if 5.00000000000000041e-6 < (/.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

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 96.2%

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

Alternative 5: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x \cdot t}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (/ (* x t) (- z y))))
   (if (<= t_1 -1e+17)
     t_2
     (if (<= t_1 -5e-81)
       (* (/ t z) (- x y))
       (if (<= t_1 1e-9)
         (/ (* (- x y) t) z)
         (if (<= t_1 2.0) (* 1.0 t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x * t) / (z - y)
    if (t_1 <= (-1d+17)) then
        tmp = t_2
    else if (t_1 <= (-5d-81)) then
        tmp = (t / z) * (x - y)
    else if (t_1 <= 1d-9) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x * t) / (z - y);
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_2;
	} else if (t_1 <= -5e-81) {
		tmp = (t / z) * (x - y);
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x * t) / (z - y)
	tmp = 0
	if t_1 <= -1e+17:
		tmp = t_2
	elif t_1 <= -5e-81:
		tmp = (t / z) * (x - y)
	elif t_1 <= 1e-9:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x * t) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = Float64(Float64(t / z) * Float64(x - y));
	elseif (t_1 <= 1e-9)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x * t) / (z - y);
	tmp = 0.0;
	if (t_1 <= -1e+17)
		tmp = t_2;
	elseif (t_1 <= -5e-81)
		tmp = (t / z) * (x - y);
	elseif (t_1 <= 1e-9)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+17], t$95$2, If[LessEqual[t$95$1, -5e-81], N[(N[(t / z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e17 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.0

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

   5. Applied rewrites 87.0%

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

   7. Applied rewrites 91.3%

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

   if -1e17 < (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81

   1. Initial program 99.6%

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

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 79.9

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

   7. Applied rewrites 79.9%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000006e-9

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 97.2

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

   5. Applied rewrites 97.2%

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

   if 1.00000000000000006e-9 < (/.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 94.1%

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

Alternative 6: 80.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-58}:\\ \;\;\;\;\frac{\left(-y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -5e-81)
     (* (/ t (- z y)) x)
     (if (<= t_1 5e-58)
       (/ (* (- y) t) z)
       (if (<= t_1 4e-22)
         (* (/ x z) t)
         (if (<= t_1 2.0) (* 1.0 t) (/ (* x t) (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5e-81) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 5e-58) {
		tmp = (-y * t) / z;
	} else if (t_1 <= 4e-22) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-5d-81)) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 5d-58) then
        tmp = (-y * t) / z
    else if (t_1 <= 4d-22) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (x * t) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -5e-81) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 5e-58) {
		tmp = (-y * t) / z;
	} else if (t_1 <= 4e-22) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -5e-81:
		tmp = (t / (z - y)) * x
	elif t_1 <= 5e-58:
		tmp = (-y * t) / z
	elif t_1 <= 4e-22:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = (x * t) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -5e-81)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 5e-58)
		tmp = Float64(Float64(Float64(-y) * t) / z);
	elseif (t_1 <= 4e-22)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(x * t) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -5e-81)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 5e-58)
		tmp = (-y * t) / z;
	elseif (t_1 <= 4e-22)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = (x * t) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-81], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 5e-58], N[(N[((-y) * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e-22], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 73.3

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

   5. Applied rewrites 73.3%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-58

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   if 4.99999999999999977e-58 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000002e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if 4.0000000000000002e-22 < (/.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 93.3%

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

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

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   7. Applied rewrites 92.4%

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

Alternative 7: 81.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z - y} \cdot x\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-58}:\\ \;\;\;\;\frac{\left(-y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t (- z y)) x)))
   (if (<= t_1 -5e-81)
     t_2
     (if (<= t_1 5e-58)
       (/ (* (- y) t) z)
       (if (<= t_1 4e-22) (* (/ x z) t) (if (<= t_1 2.0) (* 1.0 t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -5e-81) {
		tmp = t_2;
	} else if (t_1 <= 5e-58) {
		tmp = (-y * t) / z;
	} else if (t_1 <= 4e-22) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / (z - y)) * x
    if (t_1 <= (-5d-81)) then
        tmp = t_2
    else if (t_1 <= 5d-58) then
        tmp = (-y * t) / z
    else if (t_1 <= 4d-22) then
        tmp = (x / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / (z - y)) * x;
	double tmp;
	if (t_1 <= -5e-81) {
		tmp = t_2;
	} else if (t_1 <= 5e-58) {
		tmp = (-y * t) / z;
	} else if (t_1 <= 4e-22) {
		tmp = (x / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / (z - y)) * x
	tmp = 0
	if t_1 <= -5e-81:
		tmp = t_2
	elif t_1 <= 5e-58:
		tmp = (-y * t) / z
	elif t_1 <= 4e-22:
		tmp = (x / z) * t
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / Float64(z - y)) * x)
	tmp = 0.0
	if (t_1 <= -5e-81)
		tmp = t_2;
	elseif (t_1 <= 5e-58)
		tmp = Float64(Float64(Float64(-y) * t) / z);
	elseif (t_1 <= 4e-22)
		tmp = Float64(Float64(x / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / (z - y)) * x;
	tmp = 0.0;
	if (t_1 <= -5e-81)
		tmp = t_2;
	elseif (t_1 <= 5e-58)
		tmp = (-y * t) / z;
	elseif (t_1 <= 4e-22)
		tmp = (x / z) * t;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-81], t$95$2, If[LessEqual[t$95$1, 5e-58], N[(N[((-y) * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e-22], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999981e-81 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -4.99999999999999981e-81 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.99999999999999977e-58

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.1%

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

   if 4.99999999999999977e-58 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000002e-22

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if 4.0000000000000002e-22 < (/.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 93.3%

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

Alternative 8: 95.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x - z}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -50.0)
     t_2
     (if (<= t_1 5e-6)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* (- 1.0 (/ (- x z) y)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - ((x - z) / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-50.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-6) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - ((x - z) / y)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - ((x - z) / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_2
	elif t_1 <= 5e-6:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = (1.0 - ((x - z) / y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 5e-6)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(Float64(x - z) / y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 5e-6)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - ((x - z) / y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, 5e-6], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -50 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.7

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

   5. Applied rewrites 96.7%

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

   if -50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000041e-6

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 5.00000000000000041e-6 < (/.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

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

Alternative 9: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z - y} \cdot t\\ \mathbf{if}\;t\_1 \leq -50:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x (- z y)) t)))
   (if (<= t_1 -50.0)
     t_2
     (if (<= t_1 5e-6)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* (- 1.0 (/ x y)) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / (z - y)) * t
    if (t_1 <= (-50.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-6) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / (z - y)) * t;
	double tmp;
	if (t_1 <= -50.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-6) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / (z - y)) * t
	tmp = 0
	if t_1 <= -50.0:
		tmp = t_2
	elif t_1 <= 5e-6:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 5e-6)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / (z - y)) * t;
	tmp = 0.0;
	if (t_1 <= -50.0)
		tmp = t_2;
	elseif (t_1 <= 5e-6)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -50.0], t$95$2, If[LessEqual[t$95$1, 5e-6], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -50 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 96.7

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

   5. Applied rewrites 96.7%

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

   if -50 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000041e-6

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if 5.00000000000000041e-6 < (/.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

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

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

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. metadata-eval N/A

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

      6. *-lft-identity N/A

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

      7. associate-+l- N/A

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

      8. div-sub N/A

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

      9. lower--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 98.4%

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

Alternative 10: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -0.002:\\ \;\;\;\;\frac{t}{z - y} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{-9}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -0.002)
     (* (/ t (- z y)) x)
     (if (<= t_1 1e-9)
       (/ (* (- x y) t) z)
       (if (<= t_1 2.0) (* 1.0 t) (/ (* x t) (- 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 <= -0.002) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-0.002d0)) then
        tmp = (t / (z - y)) * x
    else if (t_1 <= 1d-9) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (x * t) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -0.002) {
		tmp = (t / (z - y)) * x;
	} else if (t_1 <= 1e-9) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -0.002:
		tmp = (t / (z - y)) * x
	elif t_1 <= 1e-9:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = (x * t) / (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 <= -0.002)
		tmp = Float64(Float64(t / Float64(z - y)) * x);
	elseif (t_1 <= 1e-9)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(x * t) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -0.002)
		tmp = (t / (z - y)) * x;
	elseif (t_1 <= 1e-9)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = (x * t) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -0.002], N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e-9], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if -2e-3 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.00000000000000006e-9

   1. Initial program 95.4%

      \[\frac{x - y}{z - y} \cdot t \]
   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 88.8

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

   5. Applied rewrites 88.8%

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

   if 1.00000000000000006e-9 < (/.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 94.1%

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

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

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 87.5

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

   5. Applied rewrites 87.5%

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

   7. Applied rewrites 92.4%

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

Alternative 11: 69.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-22} \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 4e-22) (not (<= t_1 2.0))) (* (/ x z) t) (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0)) {
		tmp = (x / z) * t;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if ((t_1 <= 4d-22) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = (x / z) * t
    else
        tmp = 1.0d0 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0)) {
		tmp = (x / z) * t;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 4e-22) or not (t_1 <= 2.0):
		tmp = (x / z) * t
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0))
		tmp = Float64(Float64(x / z) * t);
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 4e-22) || ~((t_1 <= 2.0)))
		tmp = (x / z) * t;
	else
		tmp = 1.0 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 4e-22], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000002e-22 or 2 < (/.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 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 4.0000000000000002e-22 < (/.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 93.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 4 \cdot 10^{-22} \lor \neg \left(\frac{x - y}{z - y} \leq 2\right):\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-22} \lor \neg \left(t\_1 \leq 2\right):\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (or (<= t_1 4e-22) (not (<= t_1 2.0))) (* (/ t z) x) (* 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0)) {
		tmp = (t / z) * x;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if ((t_1 <= 4d-22) .or. (.not. (t_1 <= 2.0d0))) then
        tmp = (t / z) * x
    else
        tmp = 1.0d0 * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0)) {
		tmp = (t / z) * x;
	} else {
		tmp = 1.0 * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if (t_1 <= 4e-22) or not (t_1 <= 2.0):
		tmp = (t / z) * x
	else:
		tmp = 1.0 * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if ((t_1 <= 4e-22) || !(t_1 <= 2.0))
		tmp = Float64(Float64(t / z) * x);
	else
		tmp = Float64(1.0 * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if ((t_1 <= 4e-22) || ~((t_1 <= 2.0)))
		tmp = (t / z) * x;
	else
		tmp = 1.0 * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, 4e-22], N[Not[LessEqual[t$95$1, 2.0]], $MachinePrecision]], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000002e-22 or 2 < (/.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

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 56.6%

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

   if 4.0000000000000002e-22 < (/.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 93.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 4 \cdot 10^{-22} \lor \neg \left(\frac{x - y}{z - y} \leq 2\right):\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 4e-22)
     (* (/ t z) x)
     (if (<= t_1 2.0) (* 1.0 t) (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 4e-22) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 4d-22) then
        tmp = (t / z) * x
    else if (t_1 <= 2.0d0) then
        tmp = 1.0d0 * t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 4e-22) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = 1.0 * t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 4e-22:
		tmp = (t / z) * x
	elif t_1 <= 2.0:
		tmp = 1.0 * t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 4e-22)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 2.0)
		tmp = Float64(1.0 * t);
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 4e-22)
		tmp = (t / z) * x;
	elseif (t_1 <= 2.0)
		tmp = 1.0 * t;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 4e-22], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(1.0 * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 4.0000000000000002e-22

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 67.9

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

   5. Applied rewrites 67.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 58.1%

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

   if 4.0000000000000002e-22 < (/.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 93.3%

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

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

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.2

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

   5. Applied rewrites 54.2%

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

Alternative 14: 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 98.0%

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

3. Taylor expanded in y around inf

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

5. Applied rewrites 39.6%

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

Developer Target 1: 97.1% 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 2024337 
(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))