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

Percentage Accurate: 96.7% → 96.7%

Time: 6.6s

Alternatives: 9

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 98.3%

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

2. Final simplification 98.3%

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

Alternative 2: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-77}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.5e+41)
     t_2
     (if (<= y 2.75e-216)
       t_1
       (if (<= y 1e-77) (* t (/ x (- z y))) (if (<= y 1.18e+48) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.5e+41) {
		tmp = t_2;
	} else if (y <= 2.75e-216) {
		tmp = t_1;
	} else if (y <= 1e-77) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.18e+48) {
		tmp = t_1;
	} 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 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-4.5d+41)) then
        tmp = t_2
    else if (y <= 2.75d-216) then
        tmp = t_1
    else if (y <= 1d-77) then
        tmp = t * (x / (z - y))
    else if (y <= 1.18d+48) then
        tmp = t_1
    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 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.5e+41) {
		tmp = t_2;
	} else if (y <= 2.75e-216) {
		tmp = t_1;
	} else if (y <= 1e-77) {
		tmp = t * (x / (z - y));
	} else if (y <= 1.18e+48) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.5e+41:
		tmp = t_2
	elif y <= 2.75e-216:
		tmp = t_1
	elif y <= 1e-77:
		tmp = t * (x / (z - y))
	elif y <= 1.18e+48:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.5e+41)
		tmp = t_2;
	elseif (y <= 2.75e-216)
		tmp = t_1;
	elseif (y <= 1e-77)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 1.18e+48)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.5e+41)
		tmp = t_2;
	elseif (y <= 2.75e-216)
		tmp = t_1;
	elseif (y <= 1e-77)
		tmp = t * (x / (z - y));
	elseif (y <= 1.18e+48)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+41], t$95$2, If[LessEqual[y, 2.75e-216], t$95$1, If[LessEqual[y, 1e-77], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e+48], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000001e41 or 1.18000000000000007e48 < y

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. neg-sub0 83.4%

         \[\leadsto \color{blue}{\left(0 - \frac{x - y}{y}\right)} \cdot t \]

      3. div-sub 83.4%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \cdot t \]

      4. *-inverses 83.4%

         \[\leadsto \left(0 - \left(\frac{x}{y} - \color{blue}{1}\right)\right) \cdot t \]

      5. associate-+l- 83.4%

         \[\leadsto \color{blue}{\left(\left(0 - \frac{x}{y}\right) + 1\right)} \cdot t \]

      6. neg-sub0 83.4%

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

      7. neg-mul-1 83.4%

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

      8. +-commutative 83.4%

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

      9. neg-mul-1 83.4%

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

      10. sub-neg 83.4%

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

   6. Simplified 83.4%

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

   if -4.5000000000000001e41 < y < 2.74999999999999995e-216 or 9.9999999999999993e-78 < y < 1.18000000000000007e48

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 78.5%

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

   if 2.74999999999999995e-216 < y < 9.9999999999999993e-78

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 87.8%

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

      1. associate-/l* 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in t around 0 87.8%

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

      1. associate-*r/ 93.6%

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

   7. Simplified 93.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 10^{-77}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+48}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -0.62:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -0.62)
     t_2
     (if (<= x 3.2e-106)
       t_1
       (if (<= x 1.85e-8) (* t (/ (- x y) z)) (if (<= x 9.5e+95) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -0.62) {
		tmp = t_2;
	} else if (x <= 3.2e-106) {
		tmp = t_1;
	} else if (x <= 1.85e-8) {
		tmp = t * ((x - y) / z);
	} else if (x <= 9.5e+95) {
		tmp = t_1;
	} 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 = t / (1.0d0 - (z / y))
    t_2 = t * (x / (z - y))
    if (x <= (-0.62d0)) then
        tmp = t_2
    else if (x <= 3.2d-106) then
        tmp = t_1
    else if (x <= 1.85d-8) then
        tmp = t * ((x - y) / z)
    else if (x <= 9.5d+95) then
        tmp = t_1
    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 = t / (1.0 - (z / y));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -0.62) {
		tmp = t_2;
	} else if (x <= 3.2e-106) {
		tmp = t_1;
	} else if (x <= 1.85e-8) {
		tmp = t * ((x - y) / z);
	} else if (x <= 9.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -0.62:
		tmp = t_2
	elif x <= 3.2e-106:
		tmp = t_1
	elif x <= 1.85e-8:
		tmp = t * ((x - y) / z)
	elif x <= 9.5e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -0.62)
		tmp = t_2;
	elseif (x <= 3.2e-106)
		tmp = t_1;
	elseif (x <= 1.85e-8)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (x <= 9.5e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -0.62)
		tmp = t_2;
	elseif (x <= 3.2e-106)
		tmp = t_1;
	elseif (x <= 1.85e-8)
		tmp = t * ((x - y) / z);
	elseif (x <= 9.5e+95)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.62], t$95$2, If[LessEqual[x, 3.2e-106], t$95$1, If[LessEqual[x, 1.85e-8], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+95], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.619999999999999996 or 9.5000000000000004e95 < x

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 73.9%

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

      1. associate-/l* 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in t around 0 73.9%

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

      1. associate-*r/ 83.4%

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

   7. Simplified 83.4%

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

   if -0.619999999999999996 < x < 3.2e-106 or 1.85e-8 < x < 9.5000000000000004e95

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*r/ 84.5%

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

      3. associate-/l* 98.2%

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

      4. sub-neg 98.2%

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

      5. +-commutative 98.2%

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

      6. neg-sub0 98.2%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 98.2%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 98.2%

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

      9. neg-mul-1 98.2%

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

      10. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around 0 72.1%

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

      1. expm1-log1p-u 60.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t \cdot y}{y - z}\right)\right)} \]

      2. expm1-udef 31.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t \cdot y}{y - z}\right)} - 1} \]

      3. associate-/l* 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{y - z}{y}}}\right)} - 1 \]

      4. div-sub 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{\frac{y}{y} - \frac{z}{y}}}\right)} - 1 \]

      5. *-inverses 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{1} - \frac{z}{y}}\right)} - 1 \]

   6. Applied egg-rr 35.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{1 - \frac{z}{y}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 68.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{1 - \frac{z}{y}}\right)\right)} \]

      2. expm1-log1p 86.4%

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

   8. Simplified 86.4%

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

   if 3.2e-106 < x < 1.85e-8

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 77.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.62:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;x \leq -2900000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= x -2900000.0)
     (* t (/ x (- z y)))
     (if (<= x 3.5e-106)
       t_1
       (if (<= x 4.4e-5)
         (* t (/ (- x y) z))
         (if (<= x 2.25e+89) t_1 (/ t (/ (- z y) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (x <= -2900000.0) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.5e-106) {
		tmp = t_1;
	} else if (x <= 4.4e-5) {
		tmp = t * ((x - y) / z);
	} else if (x <= 2.25e+89) {
		tmp = t_1;
	} else {
		tmp = t / ((z - y) / x);
	}
	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 / (1.0d0 - (z / y))
    if (x <= (-2900000.0d0)) then
        tmp = t * (x / (z - y))
    else if (x <= 3.5d-106) then
        tmp = t_1
    else if (x <= 4.4d-5) then
        tmp = t * ((x - y) / z)
    else if (x <= 2.25d+89) then
        tmp = t_1
    else
        tmp = t / ((z - y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (x <= -2900000.0) {
		tmp = t * (x / (z - y));
	} else if (x <= 3.5e-106) {
		tmp = t_1;
	} else if (x <= 4.4e-5) {
		tmp = t * ((x - y) / z);
	} else if (x <= 2.25e+89) {
		tmp = t_1;
	} else {
		tmp = t / ((z - y) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if x <= -2900000.0:
		tmp = t * (x / (z - y))
	elif x <= 3.5e-106:
		tmp = t_1
	elif x <= 4.4e-5:
		tmp = t * ((x - y) / z)
	elif x <= 2.25e+89:
		tmp = t_1
	else:
		tmp = t / ((z - y) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (x <= -2900000.0)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= 3.5e-106)
		tmp = t_1;
	elseif (x <= 4.4e-5)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (x <= 2.25e+89)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(Float64(z - y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (x <= -2900000.0)
		tmp = t * (x / (z - y));
	elseif (x <= 3.5e-106)
		tmp = t_1;
	elseif (x <= 4.4e-5)
		tmp = t * ((x - y) / z);
	elseif (x <= 2.25e+89)
		tmp = t_1;
	else
		tmp = t / ((z - y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2900000.0], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-106], t$95$1, If[LessEqual[x, 4.4e-5], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.25e+89], t$95$1, N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.9e6

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 74.8%

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

      1. associate-/l* 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around 0 74.8%

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

      1. associate-*r/ 80.9%

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

   7. Simplified 80.9%

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

   if -2.9e6 < x < 3.5e-106 or 4.3999999999999999e-5 < x < 2.25e89

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-*r/ 84.5%

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

      3. associate-/l* 98.2%

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

      4. sub-neg 98.2%

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

      5. +-commutative 98.2%

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

      6. neg-sub0 98.2%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{\left(0 - y\right)} + x}} \]

      7. associate-+l- 98.2%

         \[\leadsto \frac{t}{\frac{z - y}{\color{blue}{0 - \left(y - x\right)}}} \]

      8. sub0-neg 98.2%

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

      9. neg-mul-1 98.2%

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

      10. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around 0 72.1%

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

      1. expm1-log1p-u 60.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t \cdot y}{y - z}\right)\right)} \]

      2. expm1-udef 31.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t \cdot y}{y - z}\right)} - 1} \]

      3. associate-/l* 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{t}{\frac{y - z}{y}}}\right)} - 1 \]

      4. div-sub 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{\frac{y}{y} - \frac{z}{y}}}\right)} - 1 \]

      5. *-inverses 35.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{1} - \frac{z}{y}}\right)} - 1 \]

   6. Applied egg-rr 35.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{1 - \frac{z}{y}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 68.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{1 - \frac{z}{y}}\right)\right)} \]

      2. expm1-log1p 86.4%

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

   8. Simplified 86.4%

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

   if 3.5e-106 < x < 4.3999999999999999e-5

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 77.0%

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

   if 2.25e89 < x

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 72.3%

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

      1. associate-/l* 87.8%

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

   4. Simplified 87.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2900000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-5}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+89}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 5: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+45} \lor \neg \left(y \leq 3.4 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+45) (not (<= y 3.4e+49)))
   (* t (- 1.0 (/ x y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+45) || !(y <= 3.4e+49)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (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) :: tmp
    if ((y <= (-1.9d+45)) .or. (.not. (y <= 3.4d+49))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+45) || !(y <= 3.4e+49)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+45) or not (y <= 3.4e+49):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+45) || !(y <= 3.4e+49))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e+45) || ~((y <= 3.4e+49)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+45], N[Not[LessEqual[y, 3.4e+49]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9000000000000001e45 or 3.4000000000000001e49 < y

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. neg-sub0 83.2%

         \[\leadsto \color{blue}{\left(0 - \frac{x - y}{y}\right)} \cdot t \]

      3. div-sub 83.2%

         \[\leadsto \left(0 - \color{blue}{\left(\frac{x}{y} - \frac{y}{y}\right)}\right) \cdot t \]

      4. *-inverses 83.2%

         \[\leadsto \left(0 - \left(\frac{x}{y} - \color{blue}{1}\right)\right) \cdot t \]

      5. associate-+l- 83.2%

         \[\leadsto \color{blue}{\left(\left(0 - \frac{x}{y}\right) + 1\right)} \cdot t \]

      6. neg-sub0 83.2%

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

      7. neg-mul-1 83.2%

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

      8. +-commutative 83.2%

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

      9. neg-mul-1 83.2%

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

      10. sub-neg 83.2%

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

   6. Simplified 83.2%

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

   if -1.9000000000000001e45 < y < 3.4000000000000001e49

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 74.1%

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

      1. associate-/l* 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. associate-*r/ 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+45} \lor \neg \left(y \leq 3.4 \cdot 10^{+49}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 6: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+119) t (if (<= y 1.15e+49) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+119) {
		tmp = t;
	} else if (y <= 1.15e+49) {
		tmp = t * (x / (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 <= (-1.05d+119)) then
        tmp = t
    else if (y <= 1.15d+49) then
        tmp = t * (x / (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 <= -1.05e+119) {
		tmp = t;
	} else if (y <= 1.15e+49) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+119:
		tmp = t
	elif y <= 1.15e+49:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+119)
		tmp = t;
	elseif (y <= 1.15e+49)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+119)
		tmp = t;
	elseif (y <= 1.15e+49)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+119], t, If[LessEqual[y, 1.15e+49], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999991e119 or 1.15000000000000001e49 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.5%

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

   if -1.04999999999999991e119 < y < 1.15000000000000001e49

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf 71.9%

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

      1. associate-/l* 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in t around 0 71.9%

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

      1. associate-*r/ 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+119}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+103) t (if (<= y 2.25e+41) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+103) {
		tmp = t;
	} else if (y <= 2.25e+41) {
		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 <= (-1.2d+103)) then
        tmp = t
    else if (y <= 2.25d+41) 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 <= -1.2e+103) {
		tmp = t;
	} else if (y <= 2.25e+41) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+103:
		tmp = t
	elif y <= 2.25e+41:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+103)
		tmp = t;
	elseif (y <= 2.25e+41)
		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 <= -1.2e+103)
		tmp = t;
	elseif (y <= 2.25e+41)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+103], t, If[LessEqual[y, 2.25e+41], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1999999999999999e103 or 2.2500000000000001e41 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 62.4%

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

   if -1.1999999999999999e103 < y < 2.2500000000000001e41

   1. Initial program 97.4%

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

      1. clear-num 96.7%

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

      2. associate-/r/ 97.3%

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

   3. Applied egg-rr 97.3%

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

   4. Taylor expanded in y around 0 62.9%

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

      1. associate-*l/ 58.8%

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

   6. Simplified 58.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+103}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+107) t (if (<= y 1.6e+51) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+107) {
		tmp = t;
	} else if (y <= 1.6e+51) {
		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 <= (-3.7d+107)) then
        tmp = t
    else if (y <= 1.6d+51) 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 <= -3.7e+107) {
		tmp = t;
	} else if (y <= 1.6e+51) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+107:
		tmp = t
	elif y <= 1.6e+51:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+107)
		tmp = t;
	elseif (y <= 1.6e+51)
		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 <= -3.7e+107)
		tmp = t;
	elseif (y <= 1.6e+51)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+107], t, If[LessEqual[y, 1.6e+51], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e107 or 1.6000000000000001e51 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 63.5%

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

   if -3.7e107 < y < 1.6000000000000001e51

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 66.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 35.2% 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 98.3%

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

2. Taylor expanded in y around inf 32.6%

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

3. Final simplification 32.6%

   \[\leadsto t \]

Developer target: 96.8% 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 2023297 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))