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

Percentage Accurate: 83.5% → 97.0%

Time: 9.5s

Alternatives: 13

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: 83.5% 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: 97.0% 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 83.9%

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

   1. associate-/l* 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. Final simplification 96.6%

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

Alternative 2: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \left(\frac{y}{t} - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (* x (- (/ y t) (/ z t)))))
   (if (<= t -1.35e-21)
     t_2
     (if (<= t 6.8e-39)
       t_1
       (if (<= t 3.3e-18) (/ x (/ (- t z) y)) (if (<= t 2.25e+15) 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 / t) - (z / t));
	double tmp;
	if (t <= -1.35e-21) {
		tmp = t_2;
	} else if (t <= 6.8e-39) {
		tmp = t_1;
	} else if (t <= 3.3e-18) {
		tmp = x / ((t - z) / y);
	} else if (t <= 2.25e+15) {
		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 / t) - (z / t))
    if (t <= (-1.35d-21)) then
        tmp = t_2
    else if (t <= 6.8d-39) then
        tmp = t_1
    else if (t <= 3.3d-18) then
        tmp = x / ((t - z) / y)
    else if (t <= 2.25d+15) 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 / t) - (z / t));
	double tmp;
	if (t <= -1.35e-21) {
		tmp = t_2;
	} else if (t <= 6.8e-39) {
		tmp = t_1;
	} else if (t <= 3.3e-18) {
		tmp = x / ((t - z) / y);
	} else if (t <= 2.25e+15) {
		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 / t) - (z / t))
	tmp = 0
	if t <= -1.35e-21:
		tmp = t_2
	elif t <= 6.8e-39:
		tmp = t_1
	elif t <= 3.3e-18:
		tmp = x / ((t - z) / y)
	elif t <= 2.25e+15:
		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 / t) - Float64(z / t)))
	tmp = 0.0
	if (t <= -1.35e-21)
		tmp = t_2;
	elseif (t <= 6.8e-39)
		tmp = t_1;
	elseif (t <= 3.3e-18)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (t <= 2.25e+15)
		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 / t) - (z / t));
	tmp = 0.0;
	if (t <= -1.35e-21)
		tmp = t_2;
	elseif (t <= 6.8e-39)
		tmp = t_1;
	elseif (t <= 3.3e-18)
		tmp = x / ((t - z) / y);
	elseif (t <= 2.25e+15)
		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 / t), $MachinePrecision] - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-21], t$95$2, If[LessEqual[t, 6.8e-39], t$95$1, If[LessEqual[t, 3.3e-18], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+15], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3500000000000001e-21 or 2.25e15 < t

   1. Initial program 83.0%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

      1. div-sub 81.8%

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

   9. Applied egg-rr 81.8%

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

   if -1.3500000000000001e-21 < t < 6.7999999999999998e-39 or 3.3000000000000002e-18 < t < 2.25e15

   1. Initial program 84.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-frac-neg 83.0%

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

      5. neg-sub0 83.0%

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

      6. associate--r- 83.0%

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

      7. neg-sub0 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

      10. div-sub 83.0%

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

      11. *-inverses 83.0%

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

   7. Simplified 83.0%

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

   if 6.7999999999999998e-39 < t < 3.3000000000000002e-18

   1. Initial program 84.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.5%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 82.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(\frac{y}{t} - \frac{z}{t}\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t} - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64} \lor \neg \left(y \leq 4.2 \cdot 10^{+57}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -2e+49)
     t_1
     (if (<= y -5.3e-13)
       (* x (- 1.0 (/ y z)))
       (if (or (<= y -4.8e-64) (not (<= y 4.2e+57)))
         t_1
         (* x (/ z (- z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2e+49) {
		tmp = t_1;
	} else if (y <= -5.3e-13) {
		tmp = x * (1.0 - (y / z));
	} else if ((y <= -4.8e-64) || !(y <= 4.2e+57)) {
		tmp = t_1;
	} else {
		tmp = x * (z / (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 * (y / (t - z))
    if (y <= (-2d+49)) then
        tmp = t_1
    else if (y <= (-5.3d-13)) then
        tmp = x * (1.0d0 - (y / z))
    else if ((y <= (-4.8d-64)) .or. (.not. (y <= 4.2d+57))) then
        tmp = t_1
    else
        tmp = x * (z / (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 * (y / (t - z));
	double tmp;
	if (y <= -2e+49) {
		tmp = t_1;
	} else if (y <= -5.3e-13) {
		tmp = x * (1.0 - (y / z));
	} else if ((y <= -4.8e-64) || !(y <= 4.2e+57)) {
		tmp = t_1;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -2e+49:
		tmp = t_1
	elif y <= -5.3e-13:
		tmp = x * (1.0 - (y / z))
	elif (y <= -4.8e-64) or not (y <= 4.2e+57):
		tmp = t_1
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -2e+49)
		tmp = t_1;
	elseif (y <= -5.3e-13)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif ((y <= -4.8e-64) || !(y <= 4.2e+57))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -2e+49)
		tmp = t_1;
	elseif (y <= -5.3e-13)
		tmp = x * (1.0 - (y / z));
	elseif ((y <= -4.8e-64) || ~((y <= 4.2e+57)))
		tmp = t_1;
	else
		tmp = x * (z / (z - t));
	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[y, -2e+49], t$95$1, If[LessEqual[y, -5.3e-13], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.8e-64], N[Not[LessEqual[y, 4.2e+57]], $MachinePrecision]], t$95$1, N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999989e49 or -5.2999999999999996e-13 < y < -4.79999999999999997e-64 or 4.19999999999999982e57 < y

   1. Initial program 87.7%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around inf 78.0%

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

      1. associate-/l* 78.3%

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

   7. Simplified 78.3%

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

   if -1.99999999999999989e49 < y < -5.2999999999999996e-13

   1. Initial program 68.9%

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

      1. associate-/l* 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 t around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. associate-/l* 84.9%

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

      3. distribute-rgt-neg-in 84.9%

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

      4. distribute-frac-neg 84.9%

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

      5. neg-sub0 84.9%

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

      6. associate--r- 84.9%

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

      7. neg-sub0 84.9%

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

      8. +-commutative 84.9%

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

      9. sub-neg 84.9%

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

      10. div-sub 84.9%

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

      11. *-inverses 84.9%

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

   7. Simplified 84.9%

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

   if -4.79999999999999997e-64 < y < 4.19999999999999982e57

   1. Initial program 81.9%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-neg-frac2 66.3%

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

      3. neg-sub0 66.3%

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

      4. associate--r- 66.3%

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

      5. neg-sub0 66.3%

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

      6. +-commutative 66.3%

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

      7. sub-neg 66.3%

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

      8. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-64} \lor \neg \left(y \leq 4.2 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 88000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -1.35e-21)
     t_2
     (if (<= t 2.35e-39)
       t_1
       (if (<= t 2.9e-18)
         (* x (/ y (- t z)))
         (if (<= t 88000000000000.0) 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 <= -1.35e-21) {
		tmp = t_2;
	} else if (t <= 2.35e-39) {
		tmp = t_1;
	} else if (t <= 2.9e-18) {
		tmp = x * (y / (t - z));
	} else if (t <= 88000000000000.0) {
		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 <= (-1.35d-21)) then
        tmp = t_2
    else if (t <= 2.35d-39) then
        tmp = t_1
    else if (t <= 2.9d-18) then
        tmp = x * (y / (t - z))
    else if (t <= 88000000000000.0d0) 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 <= -1.35e-21) {
		tmp = t_2;
	} else if (t <= 2.35e-39) {
		tmp = t_1;
	} else if (t <= 2.9e-18) {
		tmp = x * (y / (t - z));
	} else if (t <= 88000000000000.0) {
		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 <= -1.35e-21:
		tmp = t_2
	elif t <= 2.35e-39:
		tmp = t_1
	elif t <= 2.9e-18:
		tmp = x * (y / (t - z))
	elif t <= 88000000000000.0:
		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 <= -1.35e-21)
		tmp = t_2;
	elseif (t <= 2.35e-39)
		tmp = t_1;
	elseif (t <= 2.9e-18)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (t <= 88000000000000.0)
		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 <= -1.35e-21)
		tmp = t_2;
	elseif (t <= 2.35e-39)
		tmp = t_1;
	elseif (t <= 2.9e-18)
		tmp = x * (y / (t - z));
	elseif (t <= 88000000000000.0)
		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, -1.35e-21], t$95$2, If[LessEqual[t, 2.35e-39], t$95$1, If[LessEqual[t, 2.9e-18], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 88000000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3500000000000001e-21 or 8.8e13 < t

   1. Initial program 83.0%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

   if -1.3500000000000001e-21 < t < 2.3500000000000001e-39 or 2.9e-18 < t < 8.8e13

   1. Initial program 84.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-frac-neg 83.0%

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

      5. neg-sub0 83.0%

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

      6. associate--r- 83.0%

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

      7. neg-sub0 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

      10. div-sub 83.0%

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

      11. *-inverses 83.0%

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

   7. Simplified 83.0%

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

   if 2.3500000000000001e-39 < t < 2.9e-18

   1. Initial program 84.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 76.8%

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

      1. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;t \leq 88000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))) (t_2 (* x (/ (- y z) t))))
   (if (<= t -1.15e-21)
     t_2
     (if (<= t 1.5e-38)
       t_1
       (if (<= t 3.4e-18) (/ x (/ (- t z) y)) (if (<= t 9.8e+14) 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 <= -1.15e-21) {
		tmp = t_2;
	} else if (t <= 1.5e-38) {
		tmp = t_1;
	} else if (t <= 3.4e-18) {
		tmp = x / ((t - z) / y);
	} else if (t <= 9.8e+14) {
		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 <= (-1.15d-21)) then
        tmp = t_2
    else if (t <= 1.5d-38) then
        tmp = t_1
    else if (t <= 3.4d-18) then
        tmp = x / ((t - z) / y)
    else if (t <= 9.8d+14) 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 <= -1.15e-21) {
		tmp = t_2;
	} else if (t <= 1.5e-38) {
		tmp = t_1;
	} else if (t <= 3.4e-18) {
		tmp = x / ((t - z) / y);
	} else if (t <= 9.8e+14) {
		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 <= -1.15e-21:
		tmp = t_2
	elif t <= 1.5e-38:
		tmp = t_1
	elif t <= 3.4e-18:
		tmp = x / ((t - z) / y)
	elif t <= 9.8e+14:
		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 <= -1.15e-21)
		tmp = t_2;
	elseif (t <= 1.5e-38)
		tmp = t_1;
	elseif (t <= 3.4e-18)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (t <= 9.8e+14)
		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 <= -1.15e-21)
		tmp = t_2;
	elseif (t <= 1.5e-38)
		tmp = t_1;
	elseif (t <= 3.4e-18)
		tmp = x / ((t - z) / y);
	elseif (t <= 9.8e+14)
		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, -1.15e-21], t$95$2, If[LessEqual[t, 1.5e-38], t$95$1, If[LessEqual[t, 3.4e-18], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-21 or 9.8e14 < t

   1. Initial program 83.0%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in t around inf 73.2%

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

      1. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

   if -1.15e-21 < t < 1.49999999999999994e-38 or 3.40000000000000001e-18 < t < 9.8e14

   1. Initial program 84.7%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-/l* 83.0%

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

      3. distribute-rgt-neg-in 83.0%

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

      4. distribute-frac-neg 83.0%

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

      5. neg-sub0 83.0%

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

      6. associate--r- 83.0%

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

      7. neg-sub0 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

      10. div-sub 83.0%

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

      11. *-inverses 83.0%

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

   7. Simplified 83.0%

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

   if 1.49999999999999994e-38 < t < 3.40000000000000001e-18

   1. Initial program 84.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.5%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 82.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+60)
   x
   (if (<= z 1.7e-92)
     (/ (* x y) t)
     (if (<= z 2.6e-58) (/ x (/ (- z) y)) (if (<= z 6e-22) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+60) {
		tmp = x;
	} else if (z <= 1.7e-92) {
		tmp = (x * y) / t;
	} else if (z <= 2.6e-58) {
		tmp = x / (-z / y);
	} else if (z <= 6e-22) {
		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 <= (-6.8d+60)) then
        tmp = x
    else if (z <= 1.7d-92) then
        tmp = (x * y) / t
    else if (z <= 2.6d-58) then
        tmp = x / (-z / y)
    else if (z <= 6d-22) 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 <= -6.8e+60) {
		tmp = x;
	} else if (z <= 1.7e-92) {
		tmp = (x * y) / t;
	} else if (z <= 2.6e-58) {
		tmp = x / (-z / y);
	} else if (z <= 6e-22) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+60:
		tmp = x
	elif z <= 1.7e-92:
		tmp = (x * y) / t
	elif z <= 2.6e-58:
		tmp = x / (-z / y)
	elif z <= 6e-22:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+60)
		tmp = x;
	elseif (z <= 1.7e-92)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 2.6e-58)
		tmp = Float64(x / Float64(Float64(-z) / y));
	elseif (z <= 6e-22)
		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 <= -6.8e+60)
		tmp = x;
	elseif (z <= 1.7e-92)
		tmp = (x * y) / t;
	elseif (z <= 2.6e-58)
		tmp = x / (-z / y);
	elseif (z <= 6e-22)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+60], x, If[LessEqual[z, 1.7e-92], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.6e-58], N[(x / N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-22], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.7999999999999999e60 or 5.9999999999999998e-22 < z

   1. Initial program 69.9%

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

      1. associate-/l* 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 57.7%

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

   if -6.7999999999999999e60 < z < 1.7000000000000001e-92

   1. Initial program 95.5%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 59.0%

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

   if 1.7000000000000001e-92 < z < 2.60000000000000007e-58

   1. Initial program 99.9%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. associate-/l* 71.6%

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

      3. distribute-rgt-neg-in 71.6%

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

      4. distribute-frac-neg 71.6%

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

      5. neg-sub0 71.6%

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

      6. associate--r- 71.6%

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

      7. neg-sub0 71.6%

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

      8. +-commutative 71.6%

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

      9. sub-neg 71.6%

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

      10. div-sub 71.6%

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

      11. *-inverses 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in y around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. mul-1-neg 64.8%

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

      3. distribute-rgt-neg-in 64.8%

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

      4. associate-*r/ 56.2%

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

   10. Simplified 56.2%

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

       1. clear-num 56.3%

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

       2. un-div-inv 56.2%

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

       3. add-sqr-sqrt 55.2%

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

       4. sqrt-unprod 56.5%

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

       5. sqr-neg 56.5%

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

       6. sqrt-unprod 10.5%

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

       7. add-sqr-sqrt 11.3%

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

   12. Applied egg-rr 11.3%

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

       1. associate-/r/ 11.7%

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

       2. associate-*l/ 11.3%

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

       3. associate-*r/ 11.3%

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

   14. Simplified 11.3%

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

       1. add-sqr-sqrt 10.7%

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

       2. sqrt-unprod 21.0%

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

       3. sqr-neg 21.0%

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

       4. sqrt-unprod 10.0%

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

       5. add-sqr-sqrt 56.2%

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

       6. distribute-lft-neg-out 56.2%

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

       7. clear-num 56.3%

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

       8. un-div-inv 56.2%

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

   16. Applied egg-rr 56.2%

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

   if 2.60000000000000007e-58 < z < 5.9999999999999998e-22

   1. Initial program 100.0%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 47.1%

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

      1. associate-/l* 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{\frac{-z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+61)
   x
   (if (<= z 2.5e-92)
     (/ (* x y) t)
     (if (<= z 1.35e-59)
       (/ (* x y) (- z))
       (if (<= z 2.8e-22) (* x (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+61) {
		tmp = x;
	} else if (z <= 2.5e-92) {
		tmp = (x * y) / t;
	} else if (z <= 1.35e-59) {
		tmp = (x * y) / -z;
	} else if (z <= 2.8e-22) {
		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 <= (-6.6d+61)) then
        tmp = x
    else if (z <= 2.5d-92) then
        tmp = (x * y) / t
    else if (z <= 1.35d-59) then
        tmp = (x * y) / -z
    else if (z <= 2.8d-22) 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 <= -6.6e+61) {
		tmp = x;
	} else if (z <= 2.5e-92) {
		tmp = (x * y) / t;
	} else if (z <= 1.35e-59) {
		tmp = (x * y) / -z;
	} else if (z <= 2.8e-22) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+61:
		tmp = x
	elif z <= 2.5e-92:
		tmp = (x * y) / t
	elif z <= 1.35e-59:
		tmp = (x * y) / -z
	elif z <= 2.8e-22:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+61)
		tmp = x;
	elseif (z <= 2.5e-92)
		tmp = Float64(Float64(x * y) / t);
	elseif (z <= 1.35e-59)
		tmp = Float64(Float64(x * y) / Float64(-z));
	elseif (z <= 2.8e-22)
		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 <= -6.6e+61)
		tmp = x;
	elseif (z <= 2.5e-92)
		tmp = (x * y) / t;
	elseif (z <= 1.35e-59)
		tmp = (x * y) / -z;
	elseif (z <= 2.8e-22)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+61], x, If[LessEqual[z, 2.5e-92], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.35e-59], N[(N[(x * y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 2.8e-22], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999995e61 or 2.79999999999999995e-22 < z

   1. Initial program 69.9%

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

      1. associate-/l* 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 57.7%

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

   if -6.5999999999999995e61 < z < 2.50000000000000006e-92

   1. Initial program 95.5%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around 0 59.0%

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

   if 2.50000000000000006e-92 < z < 1.3499999999999999e-59

   1. Initial program 99.9%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. associate-/l* 71.6%

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

      3. distribute-rgt-neg-in 71.6%

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

      4. distribute-frac-neg 71.6%

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

      5. neg-sub0 71.6%

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

      6. associate--r- 71.6%

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

      7. neg-sub0 71.6%

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

      8. +-commutative 71.6%

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

      9. sub-neg 71.6%

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

      10. div-sub 71.6%

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

      11. *-inverses 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in y around inf 64.8%

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

      1. associate-*r/ 64.8%

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

      2. associate-*r* 64.8%

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

      3. neg-mul-1 64.8%

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

   10. Simplified 64.8%

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

   if 1.3499999999999999e-59 < z < 2.79999999999999995e-22

   1. Initial program 100.0%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 47.1%

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

      1. associate-/l* 47.1%

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

   7. Simplified 47.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y}{-z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.35e-21)
   (* x (/ y t))
   (if (<= t 2.8e+15)
     (* x (- 1.0 (/ y z)))
     (if (<= t 5.7e+249) (/ x (/ t y)) (* x (/ (- z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-21) {
		tmp = x * (y / t);
	} else if (t <= 2.8e+15) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 5.7e+249) {
		tmp = x / (t / y);
	} else {
		tmp = x * (-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) :: tmp
    if (t <= (-1.35d-21)) then
        tmp = x * (y / t)
    else if (t <= 2.8d+15) then
        tmp = x * (1.0d0 - (y / z))
    else if (t <= 5.7d+249) then
        tmp = x / (t / y)
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-21) {
		tmp = x * (y / t);
	} else if (t <= 2.8e+15) {
		tmp = x * (1.0 - (y / z));
	} else if (t <= 5.7e+249) {
		tmp = x / (t / y);
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.35e-21:
		tmp = x * (y / t)
	elif t <= 2.8e+15:
		tmp = x * (1.0 - (y / z))
	elif t <= 5.7e+249:
		tmp = x / (t / y)
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.35e-21)
		tmp = Float64(x * Float64(y / t));
	elseif (t <= 2.8e+15)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (t <= 5.7e+249)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e-21)
		tmp = x * (y / t);
	elseif (t <= 2.8e+15)
		tmp = x * (1.0 - (y / z));
	elseif (t <= 5.7e+249)
		tmp = x / (t / y);
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.35e-21], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+15], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.7e+249], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3500000000000001e-21

   1. Initial program 88.5%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 56.3%

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

      1. associate-/l* 56.7%

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

   7. Simplified 56.7%

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

   if -1.3500000000000001e-21 < t < 2.8e15

   1. Initial program 84.6%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in t around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. associate-/l* 79.5%

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

      3. distribute-rgt-neg-in 79.5%

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

      4. distribute-frac-neg 79.5%

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

      5. neg-sub0 79.5%

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

      6. associate--r- 79.5%

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

      7. neg-sub0 79.5%

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

      8. +-commutative 79.5%

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

      9. sub-neg 79.5%

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

      10. div-sub 79.5%

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

      11. *-inverses 79.5%

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

   7. Simplified 79.5%

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

   if 2.8e15 < t < 5.70000000000000035e249

   1. Initial program 78.8%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.2%

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

      2. un-div-inv 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in z around 0 57.0%

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

   if 5.70000000000000035e249 < t

   1. Initial program 61.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in t around inf 61.7%

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

      1. associate-/l* 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in y around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. associate-/l* 95.0%

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

      3. distribute-rgt-neg-in 95.0%

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

      4. distribute-neg-frac2 95.0%

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

   10. Simplified 95.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+62} \lor \neg \left(z \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e+62) (not (<= z 4.1e-22)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e+62) || !(z <= 4.1e-22)) {
		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 <= (-1.45d+62)) .or. (.not. (z <= 4.1d-22))) 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 <= -1.45e+62) || !(z <= 4.1e-22)) {
		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 <= -1.45e+62) or not (z <= 4.1e-22):
		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 <= -1.45e+62) || !(z <= 4.1e-22))
		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 <= -1.45e+62) || ~((z <= 4.1e-22)))
		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, -1.45e+62], N[Not[LessEqual[z, 4.1e-22]], $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 < -1.44999999999999992e62 or 4.0999999999999999e-22 < z

   1. Initial program 69.6%

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

      1. associate-/l* 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 t around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. associate-/l* 77.0%

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

      3. distribute-rgt-neg-in 77.0%

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

      4. distribute-frac-neg 77.0%

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

      5. neg-sub0 77.0%

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

      6. associate--r- 77.0%

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

      7. neg-sub0 77.0%

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

      8. +-commutative 77.0%

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

      9. sub-neg 77.0%

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

      10. div-sub 77.0%

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

      11. *-inverses 77.0%

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

   7. Simplified 77.0%

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

   if -1.44999999999999992e62 < z < 4.0999999999999999e-22

   1. Initial program 96.2%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 70.4%

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

   7. Simplified 70.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+62} \lor \neg \left(z \leq 4.1 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+60) x (if (<= z 6e-22) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+60) {
		tmp = x;
	} else if (z <= 6e-22) {
		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 <= (-6.8d+60)) then
        tmp = x
    else if (z <= 6d-22) 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 <= -6.8e+60) {
		tmp = x;
	} else if (z <= 6e-22) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+60:
		tmp = x
	elif z <= 6e-22:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+60)
		tmp = x;
	elseif (z <= 6e-22)
		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 <= -6.8e+60)
		tmp = x;
	elseif (z <= 6e-22)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+60], x, If[LessEqual[z, 6e-22], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999999e60 or 5.9999999999999998e-22 < z

   1. Initial program 69.9%

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

      1. associate-/l* 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 57.7%

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

   if -6.7999999999999999e60 < z < 5.9999999999999998e-22

   1. Initial program 96.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 54.4%

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

      1. associate-/l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+60) x (if (<= z 5.4e-22) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+60) {
		tmp = x;
	} else if (z <= 5.4e-22) {
		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 <= (-6.8d+60)) then
        tmp = x
    else if (z <= 5.4d-22) 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 <= -6.8e+60) {
		tmp = x;
	} else if (z <= 5.4e-22) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+60:
		tmp = x
	elif z <= 5.4e-22:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+60)
		tmp = x;
	elseif (z <= 5.4e-22)
		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 <= -6.8e+60)
		tmp = x;
	elseif (z <= 5.4e-22)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+60], x, If[LessEqual[z, 5.4e-22], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999999e60 or 5.4000000000000004e-22 < z

   1. Initial program 69.9%

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

      1. associate-/l* 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 57.7%

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

   if -6.7999999999999999e60 < z < 5.4000000000000004e-22

   1. Initial program 96.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 54.4%

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

      1. *-commutative 54.4%

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

      2. associate-/l* 52.9%

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

   7. Applied egg-rr 52.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.8e+60) x (if (<= z 7.5e-23) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.8e+60) {
		tmp = x;
	} else if (z <= 7.5e-23) {
		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 <= (-8.8d+60)) then
        tmp = x
    else if (z <= 7.5d-23) 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 <= -8.8e+60) {
		tmp = x;
	} else if (z <= 7.5e-23) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.8e+60:
		tmp = x
	elif z <= 7.5e-23:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.8e+60)
		tmp = x;
	elseif (z <= 7.5e-23)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.8e+60)
		tmp = x;
	elseif (z <= 7.5e-23)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.8e+60], x, If[LessEqual[z, 7.5e-23], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999984e60 or 7.4999999999999998e-23 < z

   1. Initial program 69.9%

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

      1. associate-/l* 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 57.7%

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

   if -8.79999999999999984e60 < z < 7.4999999999999998e-23

   1. Initial program 96.1%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in z around 0 54.4%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.8% 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 83.9%

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

   1. associate-/l* 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 inf 34.1%

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

6. Final simplification 34.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.9% 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 2024055 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

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