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

Percentage Accurate: 96.7% → 96.7%

Time: 8.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

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

Alternative 2: 63.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+209}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -2.3e+169)
     t
     (if (<= y -1e-204)
       t_1
       (if (<= y 9.8e-54) (* t (/ x z)) (if (<= y 8e+209) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -2.3e+169) {
		tmp = t;
	} else if (y <= -1e-204) {
		tmp = t_1;
	} else if (y <= 9.8e-54) {
		tmp = t * (x / z);
	} else if (y <= 8e+209) {
		tmp = t_1;
	} else {
		tmp = 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 = (y - x) * (t / y)
    if (y <= (-2.3d+169)) then
        tmp = t
    else if (y <= (-1d-204)) then
        tmp = t_1
    else if (y <= 9.8d-54) then
        tmp = t * (x / z)
    else if (y <= 8d+209) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -2.3e+169) {
		tmp = t;
	} else if (y <= -1e-204) {
		tmp = t_1;
	} else if (y <= 9.8e-54) {
		tmp = t * (x / z);
	} else if (y <= 8e+209) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -2.3e+169:
		tmp = t
	elif y <= -1e-204:
		tmp = t_1
	elif y <= 9.8e-54:
		tmp = t * (x / z)
	elif y <= 8e+209:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -2.3e+169)
		tmp = t;
	elseif (y <= -1e-204)
		tmp = t_1;
	elseif (y <= 9.8e-54)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 8e+209)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -2.3e+169)
		tmp = t;
	elseif (y <= -1e-204)
		tmp = t_1;
	elseif (y <= 9.8e-54)
		tmp = t * (x / z);
	elseif (y <= 8e+209)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+169], t, If[LessEqual[y, -1e-204], t$95$1, If[LessEqual[y, 9.8e-54], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+209], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999999e169 or 8.0000000000000006e209 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 84.4%

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

   if -2.2999999999999999e169 < y < -1e-204 or 9.80000000000000042e-54 < y < 8.0000000000000006e209

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x - y\right)\right)\right), \color{blue}{y}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(t \cdot \left(x - y\right)\right)\right), y\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right)\right), y\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-1 \cdot \left(x - y\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-1 \cdot \left(x - y\right)\right)\right), y\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(x - y\right)\right)\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right), y\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right), y\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right), y\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right)\right), y\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - x\right)\right), y\right) \]

      13. --lowering--.f64 51.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, x\right)\right), y\right) \]

   5. Simplified 51.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), \color{blue}{\left(\frac{t}{y}\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(x\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y - x\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      15. /-lowering-/.f64 55.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 55.6%

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

   if -1e-204 < y < 9.80000000000000042e-54

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), t\right) \]

   5. Simplified 78.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+169}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-204}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+209}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+209}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+133)
   t
   (if (<= y 2.2e-51)
     (* t (/ x (- z y)))
     (if (<= y 5.8e+209) (* (- y x) (/ t y)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+133) {
		tmp = t;
	} else if (y <= 2.2e-51) {
		tmp = t * (x / (z - y));
	} else if (y <= 5.8e+209) {
		tmp = (y - x) * (t / y);
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.5d+133)) then
        tmp = t
    else if (y <= 2.2d-51) then
        tmp = t * (x / (z - y))
    else if (y <= 5.8d+209) then
        tmp = (y - x) * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+133) {
		tmp = t;
	} else if (y <= 2.2e-51) {
		tmp = t * (x / (z - y));
	} else if (y <= 5.8e+209) {
		tmp = (y - x) * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+133:
		tmp = t
	elif y <= 2.2e-51:
		tmp = t * (x / (z - y))
	elif y <= 5.8e+209:
		tmp = (y - x) * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+133)
		tmp = t;
	elseif (y <= 2.2e-51)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 5.8e+209)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+133)
		tmp = t;
	elseif (y <= 2.2e-51)
		tmp = t * (x / (z - y));
	elseif (y <= 5.8e+209)
		tmp = (y - x) * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+133], t, If[LessEqual[y, 2.2e-51], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+209], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000003e133 or 5.79999999999999999e209 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 79.4%

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

   if -1.50000000000000003e133 < y < 2.2e-51

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x}{z - y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(z - y\right)\right), t\right) \]

      2. --lowering--.f64 76.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(z, y\right)\right), t\right) \]

   5. Simplified 76.8%

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

   if 2.2e-51 < y < 5.79999999999999999e209

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x - y\right)\right)\right), \color{blue}{y}\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(t \cdot \left(x - y\right)\right)\right), y\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(\left(x - y\right)\right)\right)\right), y\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \left(-1 \cdot \left(x - y\right)\right)\right), y\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(-1 \cdot \left(x - y\right)\right)\right), y\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(x - y\right)\right)\right)\right), y\right) \]

      8. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right), y\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right)\right), y\right) \]

      10. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right)\right), y\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right)\right), y\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(y - x\right)\right), y\right) \]

      13. --lowering--.f64 43.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, x\right)\right), y\right) \]

   5. Simplified 43.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

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

      4. remove-double-neg N/A

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

      5. distribute-neg-in N/A

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

      6. +-commutative N/A

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

      7. sub-neg N/A

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

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), \color{blue}{\left(\frac{t}{y}\right)}\right) \]

      9. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      11. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      12. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y + \left(\mathsf{neg}\left(x\right)\right)\right), \left(\frac{t}{y}\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y - x\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\frac{\color{blue}{t}}{y}\right)\right) \]

      15. /-lowering-/.f64 56.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 56.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+209}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+223}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+175)
   (* t (/ (- y x) y))
   (if (<= y 1.2e+223) (* (- x y) (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+175) {
		tmp = t * ((y - x) / y);
	} else if (y <= 1.2e+223) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.3d+175)) then
        tmp = t * ((y - x) / y)
    else if (y <= 1.2d+223) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+175) {
		tmp = t * ((y - x) / y);
	} else if (y <= 1.2e+223) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+175:
		tmp = t * ((y - x) / y)
	elif y <= 1.2e+223:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+175)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 1.2e+223)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e+175)
		tmp = t * ((y - x) / y);
	elseif (y <= 1.2e+223)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+175], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+223], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e175

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 93.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 93.1%

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

   if -1.3e175 < y < 1.20000000000000006e223

   1. Initial program 97.4%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z - y}\right), \color{blue}{\left(x - y\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(z - y\right)\right), \left(\color{blue}{x} - y\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), \left(x - y\right)\right) \]

      7. --lowering--.f64 89.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(z, y\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 89.6%

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

   if 1.20000000000000006e223 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 100.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+175}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+223}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= z -2.2e-52) t_1 (if (<= z 1.15e-24) (* t (/ (- y x) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (z <= -2.2e-52) {
		tmp = t_1;
	} else if (z <= 1.15e-24) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    if (z <= (-2.2d-52)) then
        tmp = t_1
    else if (z <= 1.15d-24) then
        tmp = t * ((y - x) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (z <= -2.2e-52) {
		tmp = t_1;
	} else if (z <= 1.15e-24) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if z <= -2.2e-52:
		tmp = t_1
	elif z <= 1.15e-24:
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (z <= -2.2e-52)
		tmp = t_1;
	elseif (z <= 1.15e-24)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	tmp = 0.0;
	if (z <= -2.2e-52)
		tmp = t_1;
	elseif (z <= 1.15e-24)
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-52], t$95$1, If[LessEqual[z, 1.15e-24], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000009e-52 or 1.1500000000000001e-24 < z

   1. Initial program 97.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x - y}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(x - y\right), z\right), t\right) \]

      2. --lowering--.f64 71.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), z\right), t\right) \]

   5. Simplified 71.8%

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

   if -2.20000000000000009e-52 < z < 1.1500000000000001e-24

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(-1 \cdot \frac{x - y}{y}\right)}, t\right) \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{-1 \cdot \left(x - y\right)}{y}\right), t\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(x - y\right)\right), y\right), t\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x - y\right)\right)\right), y\right), t\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right), y\right), t\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(y\right)\right) + x\right)\right)\right), y\right), t\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(x\right)\right)\right), y\right), t\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) - x\right), y\right), t\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - x\right), y\right), t\right) \]

      9. --lowering--.f64 81.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, x\right), y\right), t\right) \]

   5. Simplified 81.7%

      \[\leadsto \color{blue}{\frac{y - x}{y}} \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4100:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+34) t (if (<= y 4100.0) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+34) {
		tmp = t;
	} else if (y <= 4100.0) {
		tmp = t * (x / z);
	} else {
		tmp = 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) :: tmp
    if (y <= (-2.8d+34)) then
        tmp = t
    else if (y <= 4100.0d0) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+34) {
		tmp = t;
	} else if (y <= 4100.0) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+34:
		tmp = t
	elif y <= 4100.0:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+34)
		tmp = t;
	elseif (y <= 4100.0)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+34)
		tmp = t;
	elseif (y <= 4100.0)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+34], t, If[LessEqual[y, 4100.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.80000000000000008e34 or 4100 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 55.6%

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

   if -2.80000000000000008e34 < y < 4100

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, t\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), t\right) \]

   5. Simplified 63.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4100:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+21}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e+21) t (if (<= y 4000.0) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+21) {
		tmp = t;
	} else if (y <= 4000.0) {
		tmp = x * (t / z);
	} else {
		tmp = 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) :: tmp
    if (y <= (-2.4d+21)) then
        tmp = t
    else if (y <= 4000.0d0) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+21) {
		tmp = t;
	} else if (y <= 4000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e+21:
		tmp = t
	elif y <= 4000.0:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e+21)
		tmp = t;
	elseif (y <= 4000.0)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e+21)
		tmp = t;
	elseif (y <= 4000.0)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e+21], t, If[LessEqual[y, 4000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e21 or 4e3 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 55.6%

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

   if -2.4e21 < y < 4e3

   1. Initial program 96.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{t}{z}\right)}\right) \]

      4. /-lowering-/.f64 60.9%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 60.9%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 34.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 97.8%

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

3. Taylor expanded in y around inf

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

5. Simplified 32.7%

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

Developer Target 1: 96.7% accurate, 1.0× 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 2024158 
(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))