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

Percentage Accurate: 97.1% → 97.1%

Time: 12.8s

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: 97.1% 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: 97.1% 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 95.9%

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

2. Final simplification 95.9%

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

Alternative 2: 62.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -1.8e+94)
     t
     (if (<= y -1.65e-143)
       t_1
       (if (<= y 9.5e-167)
         (* t (/ x z))
         (if (<= y 1.75e-110)
           t_1
           (if (<= y 520000000000.0)
             (/ t (/ z x))
             (if (<= y 1.08e+194) 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 <= -1.8e+94) {
		tmp = t;
	} else if (y <= -1.65e-143) {
		tmp = t_1;
	} else if (y <= 9.5e-167) {
		tmp = t * (x / z);
	} else if (y <= 1.75e-110) {
		tmp = t_1;
	} else if (y <= 520000000000.0) {
		tmp = t / (z / x);
	} else if (y <= 1.08e+194) {
		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 <= (-1.8d+94)) then
        tmp = t
    else if (y <= (-1.65d-143)) then
        tmp = t_1
    else if (y <= 9.5d-167) then
        tmp = t * (x / z)
    else if (y <= 1.75d-110) then
        tmp = t_1
    else if (y <= 520000000000.0d0) then
        tmp = t / (z / x)
    else if (y <= 1.08d+194) 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 <= -1.8e+94) {
		tmp = t;
	} else if (y <= -1.65e-143) {
		tmp = t_1;
	} else if (y <= 9.5e-167) {
		tmp = t * (x / z);
	} else if (y <= 1.75e-110) {
		tmp = t_1;
	} else if (y <= 520000000000.0) {
		tmp = t / (z / x);
	} else if (y <= 1.08e+194) {
		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 <= -1.8e+94:
		tmp = t
	elif y <= -1.65e-143:
		tmp = t_1
	elif y <= 9.5e-167:
		tmp = t * (x / z)
	elif y <= 1.75e-110:
		tmp = t_1
	elif y <= 520000000000.0:
		tmp = t / (z / x)
	elif y <= 1.08e+194:
		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 <= -1.8e+94)
		tmp = t;
	elseif (y <= -1.65e-143)
		tmp = t_1;
	elseif (y <= 9.5e-167)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 1.75e-110)
		tmp = t_1;
	elseif (y <= 520000000000.0)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.08e+194)
		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 <= -1.8e+94)
		tmp = t;
	elseif (y <= -1.65e-143)
		tmp = t_1;
	elseif (y <= 9.5e-167)
		tmp = t * (x / z);
	elseif (y <= 1.75e-110)
		tmp = t_1;
	elseif (y <= 520000000000.0)
		tmp = t / (z / x);
	elseif (y <= 1.08e+194)
		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, -1.8e+94], t, If[LessEqual[y, -1.65e-143], t$95$1, If[LessEqual[y, 9.5e-167], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-110], t$95$1, If[LessEqual[y, 520000000000.0], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+194], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.79999999999999996e94 or 1.08e194 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.4%

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

   if -1.79999999999999996e94 < y < -1.65e-143 or 9.49999999999999955e-167 < y < 1.74999999999999987e-110 or 5.2e11 < y < 1.08e194

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 91.9%

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

      3. associate-/l* 93.6%

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

      4. sub-neg 93.6%

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

      5. +-commutative 93.6%

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

      6. neg-sub0 93.6%

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

      7. associate-+l- 93.6%

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

      8. sub0-neg 93.6%

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

      9. neg-mul-1 93.6%

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

      10. associate-/r* 93.6%

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

   3. Simplified 93.6%

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

      1. associate-/r/ 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in z around 0 58.7%

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

      1. associate-/l* 59.4%

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

      2. associate-/r/ 61.7%

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

   8. Simplified 61.7%

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

   if -1.65e-143 < y < 9.49999999999999955e-167

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 80.0%

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

   if 1.74999999999999987e-110 < y < 5.2e11

   1. Initial program 96.5%

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

   2. Taylor expanded in y around 0 54.1%

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

      1. associate-/l* 57.3%

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

   4. Simplified 57.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-167}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-110}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 520000000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+194}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y - z} \cdot \left(y - x\right)\\ t_2 := \frac{t}{\frac{y - z}{y}}\\ \mathbf{if}\;y \leq -3.55 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ t (- y z)) (- y x))) (t_2 (/ t (/ (- y z) y))))
   (if (<= y -3.55e+78)
     t_2
     (if (<= y -5.6e-259)
       t_1
       (if (<= y 1.15e-227) (* t (/ x (- z y))) (if (<= y 4e+157) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / (y - z)) * (y - x);
	double t_2 = t / ((y - z) / y);
	double tmp;
	if (y <= -3.55e+78) {
		tmp = t_2;
	} else if (y <= -5.6e-259) {
		tmp = t_1;
	} else if (y <= 1.15e-227) {
		tmp = t * (x / (z - y));
	} else if (y <= 4e+157) {
		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 / (y - z)) * (y - x)
    t_2 = t / ((y - z) / y)
    if (y <= (-3.55d+78)) then
        tmp = t_2
    else if (y <= (-5.6d-259)) then
        tmp = t_1
    else if (y <= 1.15d-227) then
        tmp = t * (x / (z - y))
    else if (y <= 4d+157) 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 / (y - z)) * (y - x);
	double t_2 = t / ((y - z) / y);
	double tmp;
	if (y <= -3.55e+78) {
		tmp = t_2;
	} else if (y <= -5.6e-259) {
		tmp = t_1;
	} else if (y <= 1.15e-227) {
		tmp = t * (x / (z - y));
	} else if (y <= 4e+157) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / (y - z)) * (y - x)
	t_2 = t / ((y - z) / y)
	tmp = 0
	if y <= -3.55e+78:
		tmp = t_2
	elif y <= -5.6e-259:
		tmp = t_1
	elif y <= 1.15e-227:
		tmp = t * (x / (z - y))
	elif y <= 4e+157:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / Float64(y - z)) * Float64(y - x))
	t_2 = Float64(t / Float64(Float64(y - z) / y))
	tmp = 0.0
	if (y <= -3.55e+78)
		tmp = t_2;
	elseif (y <= -5.6e-259)
		tmp = t_1;
	elseif (y <= 1.15e-227)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 4e+157)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / (y - z)) * (y - x);
	t_2 = t / ((y - z) / y);
	tmp = 0.0;
	if (y <= -3.55e+78)
		tmp = t_2;
	elseif (y <= -5.6e-259)
		tmp = t_1;
	elseif (y <= 1.15e-227)
		tmp = t * (x / (z - y));
	elseif (y <= 4e+157)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.55e+78], t$95$2, If[LessEqual[y, -5.6e-259], t$95$1, If[LessEqual[y, 1.15e-227], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+157], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.54999999999999996e78 or 3.99999999999999993e157 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*r/ 63.4%

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

      3. associate-/l* 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 93.2%

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

   if -3.54999999999999996e78 < y < -5.5999999999999999e-259 or 1.15000000000000006e-227 < y < 3.99999999999999993e157

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 91.5%

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

      3. associate-/l* 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

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

      7. associate-+l- 94.0%

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

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

   3. Simplified 94.0%

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

      1. associate-/r/ 94.6%

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

   5. Applied egg-rr 94.6%

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

   if -5.5999999999999999e-259 < y < 1.15000000000000006e-227

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 90.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+78}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{t}{y - z} \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+157}:\\ \;\;\;\;\frac{t}{y - z} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]

Alternative 4: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 10^{+120}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e+25)
   t
   (if (<= y -1.02e-97)
     (/ (* t (- y)) z)
     (if (<= y 1e+120) (* t (/ x (- z y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e+25) {
		tmp = t;
	} else if (y <= -1.02e-97) {
		tmp = (t * -y) / z;
	} else if (y <= 1e+120) {
		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 <= (-1.55d+25)) then
        tmp = t
    else if (y <= (-1.02d-97)) then
        tmp = (t * -y) / z
    else if (y <= 1d+120) 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 <= -1.55e+25) {
		tmp = t;
	} else if (y <= -1.02e-97) {
		tmp = (t * -y) / z;
	} else if (y <= 1e+120) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e+25:
		tmp = t
	elif y <= -1.02e-97:
		tmp = (t * -y) / z
	elif y <= 1e+120:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e+25)
		tmp = t;
	elseif (y <= -1.02e-97)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= 1e+120)
		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 <= -1.55e+25)
		tmp = t;
	elseif (y <= -1.02e-97)
		tmp = (t * -y) / z;
	elseif (y <= 1e+120)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e+25], t, If[LessEqual[y, -1.02e-97], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1e+120], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e25 or 9.9999999999999998e119 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 72.0%

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

   if -1.5499999999999999e25 < y < -1.02000000000000004e-97

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf 58.1%

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

   3. Taylor expanded in x around 0 59.4%

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

      1. mul-1-neg 59.4%

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

   5. Simplified 59.4%

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

   if -1.02000000000000004e-97 < y < 9.9999999999999998e119

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 77.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-97}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 10^{+120}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= z -2.4e+200)
     t_1
     (if (<= z -1.12e-6)
       (/ t (/ (- y z) y))
       (if (<= z 6e-43) (- t (* x (/ t 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 <= -2.4e+200) {
		tmp = t_1;
	} else if (z <= -1.12e-6) {
		tmp = t / ((y - z) / y);
	} else if (z <= 6e-43) {
		tmp = t - (x * (t / 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 <= (-2.4d+200)) then
        tmp = t_1
    else if (z <= (-1.12d-6)) then
        tmp = t / ((y - z) / y)
    else if (z <= 6d-43) then
        tmp = t - (x * (t / 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 <= -2.4e+200) {
		tmp = t_1;
	} else if (z <= -1.12e-6) {
		tmp = t / ((y - z) / y);
	} else if (z <= 6e-43) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if z <= -2.4e+200:
		tmp = t_1
	elif z <= -1.12e-6:
		tmp = t / ((y - z) / y)
	elif z <= 6e-43:
		tmp = t - (x * (t / 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 <= -2.4e+200)
		tmp = t_1;
	elseif (z <= -1.12e-6)
		tmp = Float64(t / Float64(Float64(y - z) / y));
	elseif (z <= 6e-43)
		tmp = Float64(t - Float64(x * Float64(t / 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 <= -2.4e+200)
		tmp = t_1;
	elseif (z <= -1.12e-6)
		tmp = t / ((y - z) / y);
	elseif (z <= 6e-43)
		tmp = t - (x * (t / 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, -2.4e+200], t$95$1, If[LessEqual[z, -1.12e-6], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-43], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4000000000000001e200 or 6.00000000000000007e-43 < z

   1. Initial program 96.0%

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

   2. Taylor expanded in z around inf 81.2%

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

   if -2.4000000000000001e200 < z < -1.12000000000000008e-6

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-*r/ 77.5%

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

      3. associate-/l* 97.5%

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

      4. sub-neg 97.5%

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

      5. +-commutative 97.5%

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

      6. neg-sub0 97.5%

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

      7. associate-+l- 97.5%

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

      8. sub0-neg 97.5%

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

      9. neg-mul-1 97.5%

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

      10. associate-/r* 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in x around 0 73.1%

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

   if -1.12000000000000008e-6 < z < 6.00000000000000007e-43

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 85.1%

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

      1. associate--l+ 85.1%

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

      2. associate-*r/ 85.1%

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

      3. associate-*r/ 85.1%

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

      4. div-sub 85.1%

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

      5. distribute-lft-out-- 85.1%

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

      6. associate-*r/ 85.1%

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

      7. mul-1-neg 85.1%

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

      8. unsub-neg 85.1%

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

      9. distribute-lft-out-- 85.1%

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

      10. associate-/l* 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in x around inf 85.1%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+200}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-6}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;\frac{-x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+63)
   t
   (if (<= y -1.65e-143)
     (/ (- x) (/ y t))
     (if (<= y 2.4e+76) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+63) {
		tmp = t;
	} else if (y <= -1.65e-143) {
		tmp = -x / (y / t);
	} else if (y <= 2.4e+76) {
		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 <= (-1.7d+63)) then
        tmp = t
    else if (y <= (-1.65d-143)) then
        tmp = -x / (y / t)
    else if (y <= 2.4d+76) 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 <= -1.7e+63) {
		tmp = t;
	} else if (y <= -1.65e-143) {
		tmp = -x / (y / t);
	} else if (y <= 2.4e+76) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+63:
		tmp = t
	elif y <= -1.65e-143:
		tmp = -x / (y / t)
	elif y <= 2.4e+76:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+63)
		tmp = t;
	elseif (y <= -1.65e-143)
		tmp = Float64(Float64(-x) / Float64(y / t));
	elseif (y <= 2.4e+76)
		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 <= -1.7e+63)
		tmp = t;
	elseif (y <= -1.65e-143)
		tmp = -x / (y / t);
	elseif (y <= 2.4e+76)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+63], t, If[LessEqual[y, -1.65e-143], N[((-x) / N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+76], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e63 or 2.4e76 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 74.5%

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

   if -1.6999999999999999e63 < y < -1.65e-143

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*r/ 93.4%

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

      3. associate-/l* 90.4%

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

      4. sub-neg 90.4%

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

      5. +-commutative 90.4%

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

      6. neg-sub0 90.4%

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

      7. associate-+l- 90.4%

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

      8. sub0-neg 90.4%

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

      9. neg-mul-1 90.4%

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

      10. associate-/r* 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in x around inf 43.0%

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

      1. *-commutative 43.0%

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

      2. associate-*r/ 46.7%

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

      3. neg-mul-1 46.7%

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

      4. distribute-rgt-neg-in 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in y around inf 38.3%

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

      1. associate-*r/ 38.3%

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

      2. neg-mul-1 38.3%

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

      3. *-commutative 38.3%

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

      4. distribute-rgt-neg-out 38.3%

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

   9. Simplified 38.3%

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

       1. frac-2neg 38.3%

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

       2. distribute-frac-neg 38.3%

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

       3. add-sqr-sqrt 20.3%

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

       4. sqrt-unprod 21.0%

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

       5. sqr-neg 21.0%

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

       6. sqrt-unprod 5.9%

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

       7. add-sqr-sqrt 10.3%

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

       8. distribute-rgt-neg-in 10.3%

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

       9. frac-2neg 10.3%

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

       10. associate-/l* 10.3%

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

       11. add-sqr-sqrt 5.8%

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

       12. sqrt-unprod 20.9%

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

       13. sqr-neg 20.9%

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

       14. sqrt-unprod 21.7%

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

       15. add-sqr-sqrt 39.8%

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

   11. Applied egg-rr 39.8%

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

   if -1.65e-143 < y < 2.4e76

   1. Initial program 94.6%

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

   2. Taylor expanded in y around 0 63.1%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+63}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;\frac{-x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e+24)
   t
   (if (<= y -1.4e-144)
     (/ (* t (- y)) z)
     (if (<= y 8.5e+74) (* t (/ x z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+24) {
		tmp = t;
	} else if (y <= -1.4e-144) {
		tmp = (t * -y) / z;
	} else if (y <= 8.5e+74) {
		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 <= (-2.3d+24)) then
        tmp = t
    else if (y <= (-1.4d-144)) then
        tmp = (t * -y) / z
    else if (y <= 8.5d+74) 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 <= -2.3e+24) {
		tmp = t;
	} else if (y <= -1.4e-144) {
		tmp = (t * -y) / z;
	} else if (y <= 8.5e+74) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e+24:
		tmp = t
	elif y <= -1.4e-144:
		tmp = (t * -y) / z
	elif y <= 8.5e+74:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e+24)
		tmp = t;
	elseif (y <= -1.4e-144)
		tmp = Float64(Float64(t * Float64(-y)) / z);
	elseif (y <= 8.5e+74)
		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 <= -2.3e+24)
		tmp = t;
	elseif (y <= -1.4e-144)
		tmp = (t * -y) / z;
	elseif (y <= 8.5e+74)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e+24], t, If[LessEqual[y, -1.4e-144], N[(N[(t * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 8.5e+74], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999999e24 or 8.50000000000000028e74 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 70.2%

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

   if -2.2999999999999999e24 < y < -1.39999999999999999e-144

   1. Initial program 86.8%

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

   2. Taylor expanded in z around inf 49.8%

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

   3. Taylor expanded in x around 0 50.7%

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

      1. mul-1-neg 50.7%

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

   5. Simplified 50.7%

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

   if -1.39999999999999999e-144 < y < 8.50000000000000028e74

   1. Initial program 94.7%

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

   2. Taylor expanded in y around 0 63.0%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-144}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+69} \lor \neg \left(z \leq 4.2 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e+69) (not (<= z 4.2e-43)))
   (* t (/ (- x y) z))
   (* (- y x) (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+69) || !(z <= 4.2e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = (y - x) * (t / 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 ((z <= (-2.7d+69)) .or. (.not. (z <= 4.2d-43))) then
        tmp = t * ((x - y) / z)
    else
        tmp = (y - x) * (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+69) || !(z <= 4.2e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = (y - x) * (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e+69) or not (z <= 4.2e-43):
		tmp = t * ((x - y) / z)
	else:
		tmp = (y - x) * (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e+69) || !(z <= 4.2e-43))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(Float64(y - x) * Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e+69) || ~((z <= 4.2e-43)))
		tmp = t * ((x - y) / z);
	else
		tmp = (y - x) * (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e+69], N[Not[LessEqual[z, 4.2e-43]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999998e69 or 4.2000000000000001e-43 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in z around inf 76.4%

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

   if -2.6999999999999998e69 < z < 4.2000000000000001e-43

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*r/ 87.7%

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

      3. associate-/l* 96.4%

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

      4. sub-neg 96.4%

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

      5. +-commutative 96.4%

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

      6. neg-sub0 96.4%

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

      7. associate-+l- 96.4%

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

      8. sub0-neg 96.4%

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

      9. neg-mul-1 96.4%

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

      10. associate-/r* 96.4%

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

   3. Simplified 96.4%

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

      1. associate-/r/ 84.6%

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

   5. Applied egg-rr 84.6%

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

   6. Taylor expanded in z around 0 77.0%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 72.7%

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

   8. Simplified 72.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+69} \lor \neg \left(z \leq 4.2 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \end{array} \]

Alternative 9: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+86} \lor \neg \left(z \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.5e+86) (not (<= z 3.2e-43)))
   (* t (/ (- x y) z))
   (* t (/ (- y x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+86) || !(z <= 3.2e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.5d+86)) .or. (.not. (z <= 3.2d-43))) then
        tmp = t * ((x - y) / z)
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+86) || !(z <= 3.2e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.5e+86) or not (z <= 3.2e-43):
		tmp = t * ((x - y) / z)
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.5e+86) || !(z <= 3.2e-43))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.5e+86) || ~((z <= 3.2e-43)))
		tmp = t * ((x - y) / z);
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e+86], N[Not[LessEqual[z, 3.2e-43]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999996e86 or 3.19999999999999985e-43 < z

   1. Initial program 96.3%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -6.49999999999999996e86 < z < 3.19999999999999985e-43

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. neg-mul-1 82.3%

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

      3. neg-sub0 82.3%

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

      4. associate--r- 82.3%

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

      5. neg-sub0 82.3%

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

      6. +-commutative 82.3%

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

      7. sub-neg 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+86} \lor \neg \left(z \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+86} \lor \neg \left(z \leq 4.4 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e+86) (not (<= z 4.4e-43)))
   (* t (/ (- x y) z))
   (- t (* x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+86) || !(z <= 4.4e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (x * (t / 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 ((z <= (-2.15d+86)) .or. (.not. (z <= 4.4d-43))) then
        tmp = t * ((x - y) / z)
    else
        tmp = t - (x * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+86) || !(z <= 4.4e-43)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - (x * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.15e+86) or not (z <= 4.4e-43):
		tmp = t * ((x - y) / z)
	else:
		tmp = t - (x * (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+86) || !(z <= 4.4e-43))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t - Float64(x * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.15e+86) || ~((z <= 4.4e-43)))
		tmp = t * ((x - y) / z);
	else
		tmp = t - (x * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.15e+86], N[Not[LessEqual[z, 4.4e-43]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1500000000000001e86 or 4.39999999999999994e-43 < z

   1. Initial program 96.3%

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

   2. Taylor expanded in z around inf 77.3%

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

   if -2.1500000000000001e86 < z < 4.39999999999999994e-43

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 80.2%

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

      1. associate--l+ 80.2%

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

      2. associate-*r/ 80.2%

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

      3. associate-*r/ 80.2%

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

      4. div-sub 80.2%

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

      5. distribute-lft-out-- 80.2%

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

      6. associate-*r/ 80.2%

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

      7. mul-1-neg 80.2%

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

      8. unsub-neg 80.2%

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

      9. distribute-lft-out-- 80.2%

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

      10. associate-/l* 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in x around inf 81.7%

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

      1. associate-*l/ 84.0%

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

      2. *-commutative 84.0%

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

   7. Simplified 84.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+86} \lor \neg \left(z \leq 4.4 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \]

Alternative 11: 40.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-127}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-127) t (if (<= y 8.8e-71) (* y (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-127) {
		tmp = t;
	} else if (y <= 8.8e-71) {
		tmp = y * (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 <= (-1.4d-127)) then
        tmp = t
    else if (y <= 8.8d-71) then
        tmp = y * (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 <= -1.4e-127) {
		tmp = t;
	} else if (y <= 8.8e-71) {
		tmp = y * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-127:
		tmp = t
	elif y <= 8.8e-71:
		tmp = y * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-127)
		tmp = t;
	elseif (y <= 8.8e-71)
		tmp = Float64(y * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-127)
		tmp = t;
	elseif (y <= 8.8e-71)
		tmp = y * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-127], t, If[LessEqual[y, 8.8e-71], N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-127 or 8.7999999999999999e-71 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 52.8%

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

   if -1.4e-127 < y < 8.7999999999999999e-71

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 74.7%

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

   3. Taylor expanded in x around 0 25.7%

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

      1. neg-mul-1 25.7%

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

   5. Simplified 25.7%

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

      1. expm1-log1p-u 23.1%

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

      2. expm1-udef 18.7%

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

      3. add-sqr-sqrt 14.6%

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

      4. sqrt-unprod 18.8%

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

      5. sqr-neg 18.8%

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

      6. sqrt-unprod 13.5%

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

      7. add-sqr-sqrt 18.7%

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

      8. *-commutative 18.7%

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

   7. Applied egg-rr 18.7%

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

      1. expm1-def 18.7%

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

      2. expm1-log1p 20.1%

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

      3. associate-*r/ 20.1%

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

      4. associate-*l/ 25.1%

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

      5. *-commutative 25.1%

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

   9. Simplified 25.1%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-127}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2050000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2050000.0) t (if (<= y 1.25e+47) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2050000.0) {
		tmp = t;
	} else if (y <= 1.25e+47) {
		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 <= (-2050000.0d0)) then
        tmp = t
    else if (y <= 1.25d+47) 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 <= -2050000.0) {
		tmp = t;
	} else if (y <= 1.25e+47) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2050000.0:
		tmp = t
	elif y <= 1.25e+47:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2050000.0)
		tmp = t;
	elseif (y <= 1.25e+47)
		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 <= -2050000.0)
		tmp = t;
	elseif (y <= 1.25e+47)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2050000.0], t, If[LessEqual[y, 1.25e+47], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e6 or 1.25000000000000005e47 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 64.7%

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

   if -2.05e6 < y < 1.25000000000000005e47

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 91.1%

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

      3. associate-/l* 92.2%

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

      4. sub-neg 92.2%

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

      5. +-commutative 92.2%

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

      6. neg-sub0 92.2%

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

      7. associate-+l- 92.2%

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

      8. sub0-neg 92.2%

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

      9. neg-mul-1 92.2%

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

      10. associate-/r* 92.2%

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

   3. Simplified 92.2%

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

      1. associate-/r/ 92.8%

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

   5. Applied egg-rr 92.8%

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

   6. Taylor expanded in y around 0 53.1%

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

      1. associate-*l/ 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2050000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -105000.0) t (if (<= y 2.8e+75) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -105000.0) {
		tmp = t;
	} else if (y <= 2.8e+75) {
		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 <= (-105000.0d0)) then
        tmp = t
    else if (y <= 2.8d+75) 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 <= -105000.0) {
		tmp = t;
	} else if (y <= 2.8e+75) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -105000.0:
		tmp = t
	elif y <= 2.8e+75:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -105000.0)
		tmp = t;
	elseif (y <= 2.8e+75)
		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 <= -105000.0)
		tmp = t;
	elseif (y <= 2.8e+75)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -105000.0], t, If[LessEqual[y, 2.8e+75], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -105000 or 2.80000000000000012e75 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 68.0%

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

   if -105000 < y < 2.80000000000000012e75

   1. Initial program 93.0%

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

   2. Taylor expanded in y around 0 56.4%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 35.7% 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 95.9%

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

2. Taylor expanded in y around inf 35.7%

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

3. Final simplification 35.7%

   \[\leadsto t \]

Developer target: 97.1% 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 2023275 
(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))