Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.3% → 96.7%

Time: 11.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = ((y - z) / (t - z)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. *-commutative 84.1%

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

   2. associate-*l/ 95.8%

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

4. Applied egg-rr 95.8%

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

5. Final simplification 95.8%

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

Alternative 2: 68.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ t_2 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+97}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))) (t_2 (* x (/ y (- t z)))))
   (if (<= z -1.05e+109)
     x
     (if (<= z -1.06e-192)
       t_2
       (if (<= z 4e-260)
         t_1
         (if (<= z 9000.0)
           t_2
           (if (<= z 6.9e+37) t_1 (if (<= z 1.6e+97) t_2 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double t_2 = x * (y / (t - z));
	double tmp;
	if (z <= -1.05e+109) {
		tmp = x;
	} else if (z <= -1.06e-192) {
		tmp = t_2;
	} else if (z <= 4e-260) {
		tmp = t_1;
	} else if (z <= 9000.0) {
		tmp = t_2;
	} else if (z <= 6.9e+37) {
		tmp = t_1;
	} else if (z <= 1.6e+97) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * (x / t)
    t_2 = x * (y / (t - z))
    if (z <= (-1.05d+109)) then
        tmp = x
    else if (z <= (-1.06d-192)) then
        tmp = t_2
    else if (z <= 4d-260) then
        tmp = t_1
    else if (z <= 9000.0d0) then
        tmp = t_2
    else if (z <= 6.9d+37) then
        tmp = t_1
    else if (z <= 1.6d+97) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double t_2 = x * (y / (t - z));
	double tmp;
	if (z <= -1.05e+109) {
		tmp = x;
	} else if (z <= -1.06e-192) {
		tmp = t_2;
	} else if (z <= 4e-260) {
		tmp = t_1;
	} else if (z <= 9000.0) {
		tmp = t_2;
	} else if (z <= 6.9e+37) {
		tmp = t_1;
	} else if (z <= 1.6e+97) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / t)
	t_2 = x * (y / (t - z))
	tmp = 0
	if z <= -1.05e+109:
		tmp = x
	elif z <= -1.06e-192:
		tmp = t_2
	elif z <= 4e-260:
		tmp = t_1
	elif z <= 9000.0:
		tmp = t_2
	elif z <= 6.9e+37:
		tmp = t_1
	elif z <= 1.6e+97:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	t_2 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.05e+109)
		tmp = x;
	elseif (z <= -1.06e-192)
		tmp = t_2;
	elseif (z <= 4e-260)
		tmp = t_1;
	elseif (z <= 9000.0)
		tmp = t_2;
	elseif (z <= 6.9e+37)
		tmp = t_1;
	elseif (z <= 1.6e+97)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / t);
	t_2 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -1.05e+109)
		tmp = x;
	elseif (z <= -1.06e-192)
		tmp = t_2;
	elseif (z <= 4e-260)
		tmp = t_1;
	elseif (z <= 9000.0)
		tmp = t_2;
	elseif (z <= 6.9e+37)
		tmp = t_1;
	elseif (z <= 1.6e+97)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+109], x, If[LessEqual[z, -1.06e-192], t$95$2, If[LessEqual[z, 4e-260], t$95$1, If[LessEqual[z, 9000.0], t$95$2, If[LessEqual[z, 6.9e+37], t$95$1, If[LessEqual[z, 1.6e+97], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e109 or 1.60000000000000008e97 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -1.0500000000000001e109 < z < -1.06e-192 or 3.99999999999999985e-260 < z < 9e3 or 6.8999999999999996e37 < z < 1.60000000000000008e97

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around inf 73.7%

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

   if -1.06e-192 < z < 3.99999999999999985e-260 or 9e3 < z < 6.8999999999999996e37

   1. Initial program 91.5%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 86.4%

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

      1. associate-/l* 80.5%

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

      2. associate-/r/ 90.6%

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

   7. Applied egg-rr 90.6%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 9000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+37}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -1.26e+113)
     x
     (if (<= z -1.4e-192)
       t_1
       (if (<= z 5e-260)
         (* (- y z) (/ x t))
         (if (<= z 8.8e-85)
           (* y (/ x (- t z)))
           (if (<= z 3.45e+41)
             (/ x (/ t (- y z)))
             (if (<= z 1.25e+95) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -1.26e+113) {
		tmp = x;
	} else if (z <= -1.4e-192) {
		tmp = t_1;
	} else if (z <= 5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.8e-85) {
		tmp = y * (x / (t - z));
	} else if (z <= 3.45e+41) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+95) {
		tmp = t_1;
	} else {
		tmp = 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 = x * (y / (t - z))
    if (z <= (-1.26d+113)) then
        tmp = x
    else if (z <= (-1.4d-192)) then
        tmp = t_1
    else if (z <= 5d-260) then
        tmp = (y - z) * (x / t)
    else if (z <= 8.8d-85) then
        tmp = y * (x / (t - z))
    else if (z <= 3.45d+41) then
        tmp = x / (t / (y - z))
    else if (z <= 1.25d+95) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -1.26e+113) {
		tmp = x;
	} else if (z <= -1.4e-192) {
		tmp = t_1;
	} else if (z <= 5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 8.8e-85) {
		tmp = y * (x / (t - z));
	} else if (z <= 3.45e+41) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+95) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -1.26e+113:
		tmp = x
	elif z <= -1.4e-192:
		tmp = t_1
	elif z <= 5e-260:
		tmp = (y - z) * (x / t)
	elif z <= 8.8e-85:
		tmp = y * (x / (t - z))
	elif z <= 3.45e+41:
		tmp = x / (t / (y - z))
	elif z <= 1.25e+95:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.26e+113)
		tmp = x;
	elseif (z <= -1.4e-192)
		tmp = t_1;
	elseif (z <= 5e-260)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 8.8e-85)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	elseif (z <= 3.45e+41)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 1.25e+95)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -1.26e+113)
		tmp = x;
	elseif (z <= -1.4e-192)
		tmp = t_1;
	elseif (z <= 5e-260)
		tmp = (y - z) * (x / t);
	elseif (z <= 8.8e-85)
		tmp = y * (x / (t - z));
	elseif (z <= 3.45e+41)
		tmp = x / (t / (y - z));
	elseif (z <= 1.25e+95)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e+113], x, If[LessEqual[z, -1.4e-192], t$95$1, If[LessEqual[z, 5e-260], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-85], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.45e+41], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+95], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2599999999999999e113 or 1.25000000000000006e95 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -1.2599999999999999e113 < z < -1.40000000000000002e-192 or 3.4500000000000001e41 < z < 1.25000000000000006e95

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf 64.6%

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

   if -1.40000000000000002e-192 < z < 5.0000000000000003e-260

   1. Initial program 93.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 93.8%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 96.9%

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

   7. Applied egg-rr 96.9%

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

   if 5.0000000000000003e-260 < z < 8.8e-85

   1. Initial program 99.8%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around inf 94.5%

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

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

   7. Simplified 90.2%

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

   if 8.8e-85 < z < 3.4500000000000001e41

   1. Initial program 90.2%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around inf 69.0%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -8.5e+112)
     x
     (if (<= z -2.8e-192)
       t_1
       (if (<= z 3.5e-260)
         (* (- y z) (/ x t))
         (if (<= z 2.35e-88)
           (/ y (/ (- t z) x))
           (if (<= z 1.15e+38)
             (/ x (/ t (- y z)))
             (if (<= z 3e+96) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -8.5e+112) {
		tmp = x;
	} else if (z <= -2.8e-192) {
		tmp = t_1;
	} else if (z <= 3.5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.35e-88) {
		tmp = y / ((t - z) / x);
	} else if (z <= 1.15e+38) {
		tmp = x / (t / (y - z));
	} else if (z <= 3e+96) {
		tmp = t_1;
	} else {
		tmp = 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 = x * (y / (t - z))
    if (z <= (-8.5d+112)) then
        tmp = x
    else if (z <= (-2.8d-192)) then
        tmp = t_1
    else if (z <= 3.5d-260) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.35d-88) then
        tmp = y / ((t - z) / x)
    else if (z <= 1.15d+38) then
        tmp = x / (t / (y - z))
    else if (z <= 3d+96) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -8.5e+112) {
		tmp = x;
	} else if (z <= -2.8e-192) {
		tmp = t_1;
	} else if (z <= 3.5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.35e-88) {
		tmp = y / ((t - z) / x);
	} else if (z <= 1.15e+38) {
		tmp = x / (t / (y - z));
	} else if (z <= 3e+96) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -8.5e+112:
		tmp = x
	elif z <= -2.8e-192:
		tmp = t_1
	elif z <= 3.5e-260:
		tmp = (y - z) * (x / t)
	elif z <= 2.35e-88:
		tmp = y / ((t - z) / x)
	elif z <= 1.15e+38:
		tmp = x / (t / (y - z))
	elif z <= 3e+96:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -8.5e+112)
		tmp = x;
	elseif (z <= -2.8e-192)
		tmp = t_1;
	elseif (z <= 3.5e-260)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.35e-88)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	elseif (z <= 1.15e+38)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 3e+96)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -8.5e+112)
		tmp = x;
	elseif (z <= -2.8e-192)
		tmp = t_1;
	elseif (z <= 3.5e-260)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.35e-88)
		tmp = y / ((t - z) / x);
	elseif (z <= 1.15e+38)
		tmp = x / (t / (y - z));
	elseif (z <= 3e+96)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+112], x, If[LessEqual[z, -2.8e-192], t$95$1, If[LessEqual[z, 3.5e-260], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-88], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+38], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+96], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.50000000000000047e112 or 3e96 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -8.50000000000000047e112 < z < -2.80000000000000004e-192 or 1.1500000000000001e38 < z < 3e96

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf 64.6%

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

   if -2.80000000000000004e-192 < z < 3.5e-260

   1. Initial program 93.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 93.8%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 96.9%

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

   7. Applied egg-rr 96.9%

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

   if 3.5e-260 < z < 2.35e-88

   1. Initial program 99.8%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 94.4%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

      1. clear-num 89.8%

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

      2. un-div-inv 90.0%

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

   9. Applied egg-rr 90.0%

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

   if 2.35e-88 < z < 1.1500000000000001e38

   1. Initial program 90.4%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -9.2e+108)
     x
     (if (<= z -6.4e-193)
       t_1
       (if (<= z 4.5e-260)
         (* (- y z) (/ x t))
         (if (<= z 1.1e-87)
           (/ (* y x) (- t z))
           (if (<= z 3.05e+41)
             (/ x (/ t (- y z)))
             (if (<= z 1.25e+94) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -9.2e+108) {
		tmp = x;
	} else if (z <= -6.4e-193) {
		tmp = t_1;
	} else if (z <= 4.5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.1e-87) {
		tmp = (y * x) / (t - z);
	} else if (z <= 3.05e+41) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+94) {
		tmp = t_1;
	} else {
		tmp = 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 = x * (y / (t - z))
    if (z <= (-9.2d+108)) then
        tmp = x
    else if (z <= (-6.4d-193)) then
        tmp = t_1
    else if (z <= 4.5d-260) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.1d-87) then
        tmp = (y * x) / (t - z)
    else if (z <= 3.05d+41) then
        tmp = x / (t / (y - z))
    else if (z <= 1.25d+94) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -9.2e+108) {
		tmp = x;
	} else if (z <= -6.4e-193) {
		tmp = t_1;
	} else if (z <= 4.5e-260) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.1e-87) {
		tmp = (y * x) / (t - z);
	} else if (z <= 3.05e+41) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+94) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -9.2e+108:
		tmp = x
	elif z <= -6.4e-193:
		tmp = t_1
	elif z <= 4.5e-260:
		tmp = (y - z) * (x / t)
	elif z <= 1.1e-87:
		tmp = (y * x) / (t - z)
	elif z <= 3.05e+41:
		tmp = x / (t / (y - z))
	elif z <= 1.25e+94:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -9.2e+108)
		tmp = x;
	elseif (z <= -6.4e-193)
		tmp = t_1;
	elseif (z <= 4.5e-260)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.1e-87)
		tmp = Float64(Float64(y * x) / Float64(t - z));
	elseif (z <= 3.05e+41)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 1.25e+94)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -9.2e+108)
		tmp = x;
	elseif (z <= -6.4e-193)
		tmp = t_1;
	elseif (z <= 4.5e-260)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.1e-87)
		tmp = (y * x) / (t - z);
	elseif (z <= 3.05e+41)
		tmp = x / (t / (y - z));
	elseif (z <= 1.25e+94)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+108], x, If[LessEqual[z, -6.4e-193], t$95$1, If[LessEqual[z, 4.5e-260], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-87], N[(N[(y * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+41], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+94], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.1999999999999996e108 or 1.25000000000000003e94 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -9.1999999999999996e108 < z < -6.40000000000000011e-193 or 3.04999999999999999e41 < z < 1.25000000000000003e94

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in y around inf 64.6%

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

   if -6.40000000000000011e-193 < z < 4.4999999999999997e-260

   1. Initial program 93.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in t around inf 93.8%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 96.9%

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

   7. Applied egg-rr 96.9%

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

   if 4.4999999999999997e-260 < z < 1.09999999999999994e-87

   1. Initial program 99.8%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 94.4%

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

   if 1.09999999999999994e-87 < z < 3.04999999999999999e41

   1. Initial program 90.4%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-260}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-87}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-86}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -2.7e+111)
     x
     (if (<= z -5e-217)
       t_1
       (if (<= z 5.8e-260)
         (/ (- y z) (/ t x))
         (if (<= z 8e-86)
           (/ (* y x) (- t z))
           (if (<= z 2.7e+38)
             (/ x (/ t (- y z)))
             (if (<= z 8.5e+92) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -2.7e+111) {
		tmp = x;
	} else if (z <= -5e-217) {
		tmp = t_1;
	} else if (z <= 5.8e-260) {
		tmp = (y - z) / (t / x);
	} else if (z <= 8e-86) {
		tmp = (y * x) / (t - z);
	} else if (z <= 2.7e+38) {
		tmp = x / (t / (y - z));
	} else if (z <= 8.5e+92) {
		tmp = t_1;
	} else {
		tmp = 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 = x * (y / (t - z))
    if (z <= (-2.7d+111)) then
        tmp = x
    else if (z <= (-5d-217)) then
        tmp = t_1
    else if (z <= 5.8d-260) then
        tmp = (y - z) / (t / x)
    else if (z <= 8d-86) then
        tmp = (y * x) / (t - z)
    else if (z <= 2.7d+38) then
        tmp = x / (t / (y - z))
    else if (z <= 8.5d+92) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -2.7e+111) {
		tmp = x;
	} else if (z <= -5e-217) {
		tmp = t_1;
	} else if (z <= 5.8e-260) {
		tmp = (y - z) / (t / x);
	} else if (z <= 8e-86) {
		tmp = (y * x) / (t - z);
	} else if (z <= 2.7e+38) {
		tmp = x / (t / (y - z));
	} else if (z <= 8.5e+92) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -2.7e+111:
		tmp = x
	elif z <= -5e-217:
		tmp = t_1
	elif z <= 5.8e-260:
		tmp = (y - z) / (t / x)
	elif z <= 8e-86:
		tmp = (y * x) / (t - z)
	elif z <= 2.7e+38:
		tmp = x / (t / (y - z))
	elif z <= 8.5e+92:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -2.7e+111)
		tmp = x;
	elseif (z <= -5e-217)
		tmp = t_1;
	elseif (z <= 5.8e-260)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= 8e-86)
		tmp = Float64(Float64(y * x) / Float64(t - z));
	elseif (z <= 2.7e+38)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 8.5e+92)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -2.7e+111)
		tmp = x;
	elseif (z <= -5e-217)
		tmp = t_1;
	elseif (z <= 5.8e-260)
		tmp = (y - z) / (t / x);
	elseif (z <= 8e-86)
		tmp = (y * x) / (t - z);
	elseif (z <= 2.7e+38)
		tmp = x / (t / (y - z));
	elseif (z <= 8.5e+92)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+111], x, If[LessEqual[z, -5e-217], t$95$1, If[LessEqual[z, 5.8e-260], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-86], N[(N[(y * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+38], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+92], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6999999999999999e111 or 8.5000000000000001e92 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -2.6999999999999999e111 < z < -5.0000000000000002e-217 or 2.69999999999999996e38 < z < 8.5000000000000001e92

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l/ 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in y around inf 67.7%

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

   if -5.0000000000000002e-217 < z < 5.7999999999999999e-260

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 96.4%

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

   if 5.7999999999999999e-260 < z < 8.00000000000000068e-86

   1. Initial program 99.8%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around inf 94.4%

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

   if 8.00000000000000068e-86 < z < 2.69999999999999996e38

   1. Initial program 90.4%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. associate-/l* 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-260}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-86}:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+38}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))))
   (if (<= z -1.95e+114)
     x
     (if (<= z 2.5e-86)
       t_1
       (if (<= z 5.9e+38) (* (- y z) (/ x t)) (if (<= z 3.2e+95) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -1.95e+114) {
		tmp = x;
	} else if (z <= 2.5e-86) {
		tmp = t_1;
	} else if (z <= 5.9e+38) {
		tmp = (y - z) * (x / t);
	} else if (z <= 3.2e+95) {
		tmp = t_1;
	} else {
		tmp = 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 = y * (x / (t - z))
    if (z <= (-1.95d+114)) then
        tmp = x
    else if (z <= 2.5d-86) then
        tmp = t_1
    else if (z <= 5.9d+38) then
        tmp = (y - z) * (x / t)
    else if (z <= 3.2d+95) then
        tmp = t_1
    else
        tmp = x
    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 - z));
	double tmp;
	if (z <= -1.95e+114) {
		tmp = x;
	} else if (z <= 2.5e-86) {
		tmp = t_1;
	} else if (z <= 5.9e+38) {
		tmp = (y - z) * (x / t);
	} else if (z <= 3.2e+95) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	tmp = 0
	if z <= -1.95e+114:
		tmp = x
	elif z <= 2.5e-86:
		tmp = t_1
	elif z <= 5.9e+38:
		tmp = (y - z) * (x / t)
	elif z <= 3.2e+95:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.95e+114)
		tmp = x;
	elseif (z <= 2.5e-86)
		tmp = t_1;
	elseif (z <= 5.9e+38)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 3.2e+95)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	tmp = 0.0;
	if (z <= -1.95e+114)
		tmp = x;
	elseif (z <= 2.5e-86)
		tmp = t_1;
	elseif (z <= 5.9e+38)
		tmp = (y - z) * (x / t);
	elseif (z <= 3.2e+95)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+114], x, If[LessEqual[z, 2.5e-86], t$95$1, If[LessEqual[z, 5.9e+38], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+95], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e114 or 3.2000000000000001e95 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -1.95e114 < z < 2.4999999999999999e-86 or 5.89999999999999981e38 < z < 3.2000000000000001e95

   1. Initial program 90.0%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 75.6%

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

      1. associate-*l/ 76.6%

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

      2. *-commutative 76.6%

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

   7. Simplified 76.6%

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

   if 2.4999999999999999e-86 < z < 5.89999999999999981e38

   1. Initial program 90.4%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf 69.8%

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

      1. associate-/l* 72.3%

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

      2. associate-/r/ 69.8%

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

   7. Applied egg-rr 69.8%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+114}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+38}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+216}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+89}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.4e+216)
   (/ (- x) (/ z (- y z)))
   (if (<= z 3.6e+89) (* (- y z) (/ x (- t z))) (* (- x) (+ (/ y z) -1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+216) {
		tmp = -x / (z / (y - z));
	} else if (z <= 3.6e+89) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = -x * ((y / z) + -1.0);
	}
	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 <= (-5.4d+216)) then
        tmp = -x / (z / (y - z))
    else if (z <= 3.6d+89) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = -x * ((y / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+216) {
		tmp = -x / (z / (y - z));
	} else if (z <= 3.6e+89) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = -x * ((y / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.4e+216:
		tmp = -x / (z / (y - z))
	elif z <= 3.6e+89:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = -x * ((y / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.4e+216)
		tmp = Float64(Float64(-x) / Float64(z / Float64(y - z)));
	elseif (z <= 3.6e+89)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(Float64(-x) * Float64(Float64(y / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.4e+216)
		tmp = -x / (z / (y - z));
	elseif (z <= 3.6e+89)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = -x * ((y / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.4e+216], N[((-x) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+89], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4000000000000003e216

   1. Initial program 60.2%

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

      1. associate-*l/ 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in t around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-/l* 99.9%

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

      3. distribute-neg-frac 99.9%

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

   7. Simplified 99.9%

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

   if -5.4000000000000003e216 < z < 3.6e89

   1. Initial program 89.8%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   if 3.6e89 < z

   1. Initial program 66.3%

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

      1. *-commutative 66.3%

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

      2. associate-*l/ 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in t around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. div-sub 84.3%

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

      3. sub-neg 84.3%

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

      4. *-inverses 84.3%

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

      5. metadata-eval 84.3%

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

   7. Simplified 84.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+216}:\\ \;\;\;\;\frac{-x}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+89}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{y}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-90}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-7)
   (* (- y z) (/ x t))
   (if (<= t 8.5e-90) (* (- x) (+ (/ y z) -1.0)) (/ x (/ t (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-7) {
		tmp = (y - z) * (x / t);
	} else if (t <= 8.5e-90) {
		tmp = -x * ((y / z) + -1.0);
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d-7)) then
        tmp = (y - z) * (x / t)
    else if (t <= 8.5d-90) then
        tmp = -x * ((y / z) + (-1.0d0))
    else
        tmp = x / (t / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-7) {
		tmp = (y - z) * (x / t);
	} else if (t <= 8.5e-90) {
		tmp = -x * ((y / z) + -1.0);
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-7:
		tmp = (y - z) * (x / t)
	elif t <= 8.5e-90:
		tmp = -x * ((y / z) + -1.0)
	else:
		tmp = x / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-7)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (t <= 8.5e-90)
		tmp = Float64(Float64(-x) * Float64(Float64(y / z) + -1.0));
	else
		tmp = Float64(x / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-7)
		tmp = (y - z) * (x / t);
	elseif (t <= 8.5e-90)
		tmp = -x * ((y / z) + -1.0);
	else
		tmp = x / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-7], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-90], N[((-x) * N[(N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4999999999999999e-7

   1. Initial program 85.9%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 71.1%

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

      1. associate-/l* 73.6%

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

      2. associate-/r/ 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -1.4999999999999999e-7 < t < 8.5000000000000001e-90

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in t around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. div-sub 84.0%

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

      3. sub-neg 84.0%

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

      4. *-inverses 84.0%

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

      5. metadata-eval 84.0%

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

   7. Simplified 84.0%

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

   if 8.5000000000000001e-90 < t

   1. Initial program 85.7%

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

      1. associate-*l/ 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in t around inf 71.6%

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

      1. associate-/l* 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-90}:\\ \;\;\;\;\left(-x\right) \cdot \left(\frac{y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+110) x (if (<= z 6.2e+91) (* y (/ x (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+110) {
		tmp = x;
	} else if (z <= 6.2e+91) {
		tmp = y * (x / (t - z));
	} else {
		tmp = 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) :: tmp
    if (z <= (-6.6d+110)) then
        tmp = x
    else if (z <= 6.2d+91) then
        tmp = y * (x / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+110) {
		tmp = x;
	} else if (z <= 6.2e+91) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+110:
		tmp = x
	elif z <= 6.2e+91:
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+110)
		tmp = x;
	elseif (z <= 6.2e+91)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+110)
		tmp = x;
	elseif (z <= 6.2e+91)
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+110], x, If[LessEqual[z, 6.2e+91], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.59999999999999942e110 or 6.19999999999999995e91 < z

   1. Initial program 71.5%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in z around inf 63.1%

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

   if -6.59999999999999942e110 < z < 6.19999999999999995e91

   1. Initial program 90.1%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in y around inf 71.7%

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

      1. associate-*l/ 72.7%

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

      2. *-commutative 72.7%

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

   7. Simplified 72.7%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -850000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -850000000000.0) x (if (<= z 1.4e+19) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -850000000000.0) {
		tmp = x;
	} else if (z <= 1.4e+19) {
		tmp = y * (x / t);
	} else {
		tmp = 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) :: tmp
    if (z <= (-850000000000.0d0)) then
        tmp = x
    else if (z <= 1.4d+19) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -850000000000.0) {
		tmp = x;
	} else if (z <= 1.4e+19) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -850000000000.0:
		tmp = x
	elif z <= 1.4e+19:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -850000000000.0)
		tmp = x;
	elseif (z <= 1.4e+19)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -850000000000.0)
		tmp = x;
	elseif (z <= 1.4e+19)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -850000000000.0], x, If[LessEqual[z, 1.4e+19], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e11 or 1.4e19 < z

   1. Initial program 75.8%

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

      1. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 54.6%

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

   if -8.5e11 < z < 1.4e19

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 92.4%

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in y around inf 78.8%

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

   6. Taylor expanded in t around inf 66.0%

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

      1. associate-*l/ 68.0%

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

      2. *-commutative 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -850000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

   1. associate-*l/ 86.9%

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

3. Simplified 86.9%

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

5. Taylor expanded in z around inf 29.5%

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

6. Final simplification 29.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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