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

Percentage Accurate: 83.7% → 97.2%

Time: 12.0s

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: 83.7% 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: 97.2% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 82.2%

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

   1. *-commutative 82.2%

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

   2. associate-*l/ 98.1%

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

   3. *-commutative 98.1%

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

3. Simplified 98.1%

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

5. Final simplification 98.1%

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

Alternative 2: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-6}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 3:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -2.3e-6)
     t_2
     (if (<= t 2.4e-98)
       t_1
       (if (<= t 2.7e-54) (* x (/ y (- t z))) (if (<= t 3.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -2.3e-6) {
		tmp = t_2;
	} else if (t <= 2.4e-98) {
		tmp = t_1;
	} else if (t <= 2.7e-54) {
		tmp = x * (y / (t - z));
	} else if (t <= 3.0) {
		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 = x * (1.0d0 - (y / z))
    t_2 = x * ((y - z) / t)
    if (t <= (-2.3d-6)) then
        tmp = t_2
    else if (t <= 2.4d-98) then
        tmp = t_1
    else if (t <= 2.7d-54) then
        tmp = x * (y / (t - z))
    else if (t <= 3.0d0) 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 = x * (1.0 - (y / z));
	double t_2 = x * ((y - z) / t);
	double tmp;
	if (t <= -2.3e-6) {
		tmp = t_2;
	} else if (t <= 2.4e-98) {
		tmp = t_1;
	} else if (t <= 2.7e-54) {
		tmp = x * (y / (t - z));
	} else if (t <= 3.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	t_2 = x * ((y - z) / t)
	tmp = 0
	if t <= -2.3e-6:
		tmp = t_2
	elif t <= 2.4e-98:
		tmp = t_1
	elif t <= 2.7e-54:
		tmp = x * (y / (t - z))
	elif t <= 3.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -2.3e-6)
		tmp = t_2;
	elseif (t <= 2.4e-98)
		tmp = t_1;
	elseif (t <= 2.7e-54)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 3.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	t_2 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -2.3e-6)
		tmp = t_2;
	elseif (t <= 2.4e-98)
		tmp = t_1;
	elseif (t <= 2.7e-54)
		tmp = x * (y / (t - z));
	elseif (t <= 3.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-6], t$95$2, If[LessEqual[t, 2.4e-98], t$95$1, If[LessEqual[t, 2.7e-54], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e-6 or 3 < t

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l/ 98.0%

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

      3. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 80.9%

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

   if -2.3e-6 < t < 2.40000000000000005e-98 or 2.70000000000000026e-54 < t < 3

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. div-sub 85.1%

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

      3. sub-neg 85.1%

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

      4. *-inverses 85.1%

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

      5. metadata-eval 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in x around 0 85.1%

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

   if 2.40000000000000005e-98 < t < 2.70000000000000026e-54

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 85.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 3:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 4.4:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= t -5.1e-9)
     (/ x (/ t (- y z)))
     (if (<= t 1.7e-97)
       t_1
       (if (<= t 4.2e-54)
         (* x (/ y (- t z)))
         (if (<= t 4.4) t_1 (* x (/ (- y z) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (t <= -5.1e-9) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.7e-97) {
		tmp = t_1;
	} else if (t <= 4.2e-54) {
		tmp = x * (y / (t - z));
	} else if (t <= 4.4) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (t <= (-5.1d-9)) then
        tmp = x / (t / (y - z))
    else if (t <= 1.7d-97) then
        tmp = t_1
    else if (t <= 4.2d-54) then
        tmp = x * (y / (t - z))
    else if (t <= 4.4d0) then
        tmp = t_1
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (t <= -5.1e-9) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.7e-97) {
		tmp = t_1;
	} else if (t <= 4.2e-54) {
		tmp = x * (y / (t - z));
	} else if (t <= 4.4) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if t <= -5.1e-9:
		tmp = x / (t / (y - z))
	elif t <= 1.7e-97:
		tmp = t_1
	elif t <= 4.2e-54:
		tmp = x * (y / (t - z))
	elif t <= 4.4:
		tmp = t_1
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t <= -5.1e-9)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 1.7e-97)
		tmp = t_1;
	elseif (t <= 4.2e-54)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 4.4)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (t <= -5.1e-9)
		tmp = x / (t / (y - z));
	elseif (t <= 1.7e-97)
		tmp = t_1;
	elseif (t <= 4.2e-54)
		tmp = x * (y / (t - z));
	elseif (t <= 4.4)
		tmp = t_1;
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.1e-9], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-97], t$95$1, If[LessEqual[t, 4.2e-54], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4], t$95$1, N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.10000000000000017e-9

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 98.2%

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

      3. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 58.6%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -5.10000000000000017e-9 < t < 1.6999999999999999e-97 or 4.2e-54 < t < 4.4000000000000004

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. div-sub 85.1%

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

      3. sub-neg 85.1%

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

      4. *-inverses 85.1%

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

      5. metadata-eval 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in x around 0 85.1%

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

   if 1.6999999999999999e-97 < t < 4.2e-54

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 85.2%

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

   if 4.4000000000000004 < t

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 97.8%

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

      3. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around inf 86.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 4.4:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 5.6:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= t -2.3e-10)
     (/ x (/ t (- y z)))
     (if (<= t 1.7e-97)
       t_1
       (if (<= t 8.5e-54)
         (/ x (/ (- t z) y))
         (if (<= t 5.6) t_1 (* x (/ (- y z) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (t <= -2.3e-10) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.7e-97) {
		tmp = t_1;
	} else if (t <= 8.5e-54) {
		tmp = x / ((t - z) / y);
	} else if (t <= 5.6) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (t <= (-2.3d-10)) then
        tmp = x / (t / (y - z))
    else if (t <= 1.7d-97) then
        tmp = t_1
    else if (t <= 8.5d-54) then
        tmp = x / ((t - z) / y)
    else if (t <= 5.6d0) then
        tmp = t_1
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (t <= -2.3e-10) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.7e-97) {
		tmp = t_1;
	} else if (t <= 8.5e-54) {
		tmp = x / ((t - z) / y);
	} else if (t <= 5.6) {
		tmp = t_1;
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if t <= -2.3e-10:
		tmp = x / (t / (y - z))
	elif t <= 1.7e-97:
		tmp = t_1
	elif t <= 8.5e-54:
		tmp = x / ((t - z) / y)
	elif t <= 5.6:
		tmp = t_1
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (t <= -2.3e-10)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 1.7e-97)
		tmp = t_1;
	elseif (t <= 8.5e-54)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (t <= 5.6)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (t <= -2.3e-10)
		tmp = x / (t / (y - z));
	elseif (t <= 1.7e-97)
		tmp = t_1;
	elseif (t <= 8.5e-54)
		tmp = x / ((t - z) / y);
	elseif (t <= 5.6)
		tmp = t_1;
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e-10], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-97], t$95$1, If[LessEqual[t, 8.5e-54], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6], t$95$1, N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.30000000000000007e-10

   1. Initial program 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*l/ 98.2%

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

      3. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 58.6%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -2.30000000000000007e-10 < t < 1.6999999999999999e-97 or 8.5e-54 < t < 5.5999999999999996

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. div-sub 85.1%

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

      3. sub-neg 85.1%

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

      4. *-inverses 85.1%

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

      5. metadata-eval 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in x around 0 85.1%

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

   if 1.6999999999999999e-97 < t < 8.5e-54

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 5.5999999999999996 < t

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 97.8%

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

      3. *-commutative 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around inf 86.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 5.6:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.24e-14)
   x
   (if (<= z 1.6e-30) (/ x (/ t y)) (if (<= z 5.5e+122) (/ (* x (- y)) z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.24e-14) {
		tmp = x;
	} else if (z <= 1.6e-30) {
		tmp = x / (t / y);
	} else if (z <= 5.5e+122) {
		tmp = (x * -y) / 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 <= (-1.24d-14)) then
        tmp = x
    else if (z <= 1.6d-30) then
        tmp = x / (t / y)
    else if (z <= 5.5d+122) then
        tmp = (x * -y) / 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 <= -1.24e-14) {
		tmp = x;
	} else if (z <= 1.6e-30) {
		tmp = x / (t / y);
	} else if (z <= 5.5e+122) {
		tmp = (x * -y) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.24e-14:
		tmp = x
	elif z <= 1.6e-30:
		tmp = x / (t / y)
	elif z <= 5.5e+122:
		tmp = (x * -y) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.24e-14)
		tmp = x;
	elseif (z <= 1.6e-30)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 5.5e+122)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.24e-14)
		tmp = x;
	elseif (z <= 1.6e-30)
		tmp = x / (t / y);
	elseif (z <= 5.5e+122)
		tmp = (x * -y) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.24e-14], x, If[LessEqual[z, 1.6e-30], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+122], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24e-14 or 5.4999999999999998e122 < z

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.7%

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

   if -1.24e-14 < z < 1.6e-30

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 95.7%

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

      3. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 68.9%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if 1.6e-30 < z < 5.4999999999999998e122

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 56.4%

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

      1. associate-/l* 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in t around 0 53.1%

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

      1. neg-mul-1 53.1%

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

      2. distribute-neg-frac 53.1%

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

   10. Simplified 53.1%

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

       1. frac-2neg 53.1%

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

       2. distribute-frac-neg 53.1%

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

       3. add-sqr-sqrt 29.1%

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

       4. sqrt-unprod 25.1%

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

       5. sqr-neg 25.1%

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

       6. sqrt-unprod 3.9%

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

       7. add-sqr-sqrt 8.5%

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

       8. frac-2neg 8.5%

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

       9. associate-/r/ 8.5%

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

       10. associate-*l/ 8.5%

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

       11. add-sqr-sqrt 0.0%

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

       12. sqrt-unprod 45.4%

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

       13. sqr-neg 45.4%

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

       14. sqrt-unprod 45.2%

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

       15. add-sqr-sqrt 45.4%

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

   12. Applied egg-rr 45.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.24 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-15)
   x
   (if (<= z 1.48e-30)
     (/ x (/ t y))
     (if (<= z 4.8e+122) (* x (/ (- y) z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-15) {
		tmp = x;
	} else if (z <= 1.48e-30) {
		tmp = x / (t / y);
	} else if (z <= 4.8e+122) {
		tmp = x * (-y / 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 <= (-4.8d-15)) then
        tmp = x
    else if (z <= 1.48d-30) then
        tmp = x / (t / y)
    else if (z <= 4.8d+122) then
        tmp = x * (-y / 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 <= -4.8e-15) {
		tmp = x;
	} else if (z <= 1.48e-30) {
		tmp = x / (t / y);
	} else if (z <= 4.8e+122) {
		tmp = x * (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-15:
		tmp = x
	elif z <= 1.48e-30:
		tmp = x / (t / y)
	elif z <= 4.8e+122:
		tmp = x * (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-15)
		tmp = x;
	elseif (z <= 1.48e-30)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= 4.8e+122)
		tmp = Float64(x * Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-15)
		tmp = x;
	elseif (z <= 1.48e-30)
		tmp = x / (t / y);
	elseif (z <= 4.8e+122)
		tmp = x * (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-15], x, If[LessEqual[z, 1.48e-30], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+122], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999999e-15 or 4.8000000000000004e122 < z

   1. Initial program 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.7%

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

   if -4.7999999999999999e-15 < z < 1.4799999999999999e-30

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 95.7%

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

      3. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 68.9%

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

      1. associate-/l* 74.4%

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

   7. Simplified 74.4%

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

   if 1.4799999999999999e-30 < z < 4.8000000000000004e122

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 72.3%

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

   6. Taylor expanded in t around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. associate-*r/ 53.2%

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

      3. *-commutative 53.2%

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

      4. distribute-rgt-neg-in 53.2%

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

   8. Simplified 53.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-6} \lor \neg \left(z \leq 4.2 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e-6) (not (<= z 4.2e+122)))
   (/ (- x) (+ (/ t z) -1.0))
   (* y (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-6) || !(z <= 4.2e+122)) {
		tmp = -x / ((t / z) + -1.0);
	} else {
		tmp = y * (x / (t - 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 ((z <= (-2.2d-6)) .or. (.not. (z <= 4.2d+122))) then
        tmp = -x / ((t / z) + (-1.0d0))
    else
        tmp = y * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-6) || !(z <= 4.2e+122)) {
		tmp = -x / ((t / z) + -1.0);
	} else {
		tmp = y * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e-6) or not (z <= 4.2e+122):
		tmp = -x / ((t / z) + -1.0)
	else:
		tmp = y * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e-6) || !(z <= 4.2e+122))
		tmp = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0));
	else
		tmp = Float64(y * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e-6) || ~((z <= 4.2e+122)))
		tmp = -x / ((t / z) + -1.0);
	else
		tmp = y * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e-6], N[Not[LessEqual[z, 4.2e+122]], $MachinePrecision]], N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e-6 or 4.20000000000000032e122 < z

   1. Initial program 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 84.7%

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

      3. distribute-neg-frac 84.7%

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

      4. div-sub 84.7%

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

      5. *-inverses 84.7%

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

   7. Simplified 84.7%

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

   if -2.2000000000000001e-6 < z < 4.20000000000000032e122

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 79.1%

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

   7. Simplified 79.1%

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

      1. associate-/r/ 80.1%

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

   9. Applied egg-rr 80.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-6} \lor \neg \left(z \leq 4.2 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-36} \lor \neg \left(z \leq 1.3 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e-36) (not (<= z 1.3e-62)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e-36) || !(z <= 1.3e-62)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = 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 <= (-3.9d-36)) .or. (.not. (z <= 1.3d-62))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = 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 <= -3.9e-36) || !(z <= 1.3e-62)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e-36) or not (z <= 1.3e-62):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e-36) || !(z <= 1.3e-62))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e-36) || ~((z <= 1.3e-62)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e-36], N[Not[LessEqual[z, 1.3e-62]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000001e-36 or 1.3e-62 < z

   1. Initial program 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. div-sub 70.5%

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

      3. sub-neg 70.5%

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

      4. *-inverses 70.5%

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

      5. metadata-eval 70.5%

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

   7. Simplified 70.5%

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

   8. Taylor expanded in x around 0 70.5%

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

   if -3.9000000000000001e-36 < z < 1.3e-62

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 95.2%

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

      3. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 72.4%

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

      1. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-36} \lor \neg \left(z \leq 1.3 \cdot 10^{-62}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-28} \lor \neg \left(z \leq 1.02 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-28) (not (<= z 1.02e+70)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-28) || !(z <= 1.02e+70)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - 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 ((z <= (-1.8d-28)) .or. (.not. (z <= 1.02d+70))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-28) || !(z <= 1.02e+70)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-28) or not (z <= 1.02e+70):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-28) || !(z <= 1.02e+70))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-28) || ~((z <= 1.02e+70)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-28], N[Not[LessEqual[z, 1.02e+70]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e-28 or 1.02e70 < z

   1. Initial program 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. div-sub 74.1%

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

      3. sub-neg 74.1%

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

      4. *-inverses 74.1%

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

      5. metadata-eval 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in x around 0 74.1%

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

   if -1.7999999999999999e-28 < z < 1.02e70

   1. Initial program 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l/ 96.4%

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

      3. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around inf 80.4%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-28} \lor \neg \left(z \leq 1.02 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3e-26) x (if (<= z 8.2e+112) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3e-26) {
		tmp = x;
	} else if (z <= 8.2e+112) {
		tmp = x * (y / 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 <= (-3d-26)) then
        tmp = x
    else if (z <= 8.2d+112) then
        tmp = x * (y / 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 <= -3e-26) {
		tmp = x;
	} else if (z <= 8.2e+112) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3e-26:
		tmp = x
	elif z <= 8.2e+112:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3e-26)
		tmp = x;
	elseif (z <= 8.2e+112)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3e-26)
		tmp = x;
	elseif (z <= 8.2e+112)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3e-26], x, If[LessEqual[z, 8.2e+112], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000012e-26 or 8.19999999999999951e112 < z

   1. Initial program 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 62.5%

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

   if -3.00000000000000012e-26 < z < 8.19999999999999951e112

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 96.6%

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

      3. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 64.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e-15) x (if (<= z 8.2e+112) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-15) {
		tmp = x;
	} else if (z <= 8.2e+112) {
		tmp = x / (t / y);
	} 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 <= (-3.8d-15)) then
        tmp = x
    else if (z <= 8.2d+112) then
        tmp = x / (t / y)
    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 <= -3.8e-15) {
		tmp = x;
	} else if (z <= 8.2e+112) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e-15:
		tmp = x
	elif z <= 8.2e+112:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e-15)
		tmp = x;
	elseif (z <= 8.2e+112)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e-15)
		tmp = x;
	elseif (z <= 8.2e+112)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e-15], x, If[LessEqual[z, 8.2e+112], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e-15 or 8.19999999999999951e112 < z

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.2%

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

   if -3.8000000000000002e-15 < z < 8.19999999999999951e112

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 57.9%

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

      1. associate-/l* 64.1%

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

   7. Simplified 64.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.4% 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 82.2%

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

   1. *-commutative 82.2%

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

   2. associate-*l/ 98.1%

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

   3. *-commutative 98.1%

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

3. Simplified 98.1%

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

5. Taylor expanded in z around inf 33.9%

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

6. Final simplification 33.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 97.3% 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 2024036 
(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)))