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

Percentage Accurate: 84.0% → 96.8%

Time: 8.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% 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 84.9%

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

   1. associate-/l* 97.0%

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

3. Simplified 97.0%

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

5. Final simplification 97.0%

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

Alternative 2: 75.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{\frac{t}{-z} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -6.4e+46)
     t_1
     (if (<= y -1.8e-31)
       (* x (- 1.0 (/ y z)))
       (if (<= y -1.52e-38)
         t_1
         (if (<= y 1.5e+88)
           (/ x (- (/ t (- z)) -1.0))
           (/ x (/ (- t z) y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -6.4e+46) {
		tmp = t_1;
	} else if (y <= -1.8e-31) {
		tmp = x * (1.0 - (y / z));
	} else if (y <= -1.52e-38) {
		tmp = t_1;
	} else if (y <= 1.5e+88) {
		tmp = x / ((t / -z) - -1.0);
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-6.4d+46)) then
        tmp = t_1
    else if (y <= (-1.8d-31)) then
        tmp = x * (1.0d0 - (y / z))
    else if (y <= (-1.52d-38)) then
        tmp = t_1
    else if (y <= 1.5d+88) then
        tmp = x / ((t / -z) - (-1.0d0))
    else
        tmp = x / ((t - z) / y)
    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 <= -6.4e+46) {
		tmp = t_1;
	} else if (y <= -1.8e-31) {
		tmp = x * (1.0 - (y / z));
	} else if (y <= -1.52e-38) {
		tmp = t_1;
	} else if (y <= 1.5e+88) {
		tmp = x / ((t / -z) - -1.0);
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -6.4e+46:
		tmp = t_1
	elif y <= -1.8e-31:
		tmp = x * (1.0 - (y / z))
	elif y <= -1.52e-38:
		tmp = t_1
	elif y <= 1.5e+88:
		tmp = x / ((t / -z) - -1.0)
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -6.4e+46)
		tmp = t_1;
	elseif (y <= -1.8e-31)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (y <= -1.52e-38)
		tmp = t_1;
	elseif (y <= 1.5e+88)
		tmp = Float64(x / Float64(Float64(t / Float64(-z)) - -1.0));
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -6.4e+46)
		tmp = t_1;
	elseif (y <= -1.8e-31)
		tmp = x * (1.0 - (y / z));
	elseif (y <= -1.52e-38)
		tmp = t_1;
	elseif (y <= 1.5e+88)
		tmp = x / ((t / -z) - -1.0);
	else
		tmp = x / ((t - z) / y);
	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, -6.4e+46], t$95$1, If[LessEqual[y, -1.8e-31], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.52e-38], t$95$1, If[LessEqual[y, 1.5e+88], N[(x / N[(N[(t / (-z)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.3999999999999996e46 or -1.80000000000000002e-31 < y < -1.5200000000000001e-38

   1. Initial program 86.0%

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

      1. associate-/l* 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 76.8%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

   if -6.3999999999999996e46 < y < -1.80000000000000002e-31

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. distribute-frac-neg 68.9%

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

      5. neg-sub0 68.9%

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

      6. associate--r- 68.9%

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

      7. neg-sub0 68.9%

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

      8. +-commutative 68.9%

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

      9. sub-neg 68.9%

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

      10. div-sub 68.9%

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

      11. *-inverses 68.9%

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

   7. Simplified 68.9%

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

   if -1.5200000000000001e-38 < y < 1.50000000000000003e88

   1. Initial program 86.9%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in y around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. div-sub 84.1%

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

      3. sub-neg 84.1%

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

      4. *-inverses 84.1%

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

      5. metadata-eval 84.1%

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

   9. Simplified 84.1%

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

   if 1.50000000000000003e88 < y

   1. Initial program 76.1%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.4%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in y around inf 73.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{\frac{t}{-z} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-39} \lor \neg \left(y \leq 1.45 \cdot 10^{+88}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -1.7e+43)
     t_1
     (if (<= y -2.25e-32)
       (* x (- 1.0 (/ y z)))
       (if (or (<= y -8.2e-39) (not (<= y 1.45e+88)))
         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 <= -1.7e+43) {
		tmp = t_1;
	} else if (y <= -2.25e-32) {
		tmp = x * (1.0 - (y / z));
	} else if ((y <= -8.2e-39) || !(y <= 1.45e+88)) {
		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 <= (-1.7d+43)) then
        tmp = t_1
    else if (y <= (-2.25d-32)) then
        tmp = x * (1.0d0 - (y / z))
    else if ((y <= (-8.2d-39)) .or. (.not. (y <= 1.45d+88))) 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 <= -1.7e+43) {
		tmp = t_1;
	} else if (y <= -2.25e-32) {
		tmp = x * (1.0 - (y / z));
	} else if ((y <= -8.2e-39) || !(y <= 1.45e+88)) {
		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 <= -1.7e+43:
		tmp = t_1
	elif y <= -2.25e-32:
		tmp = x * (1.0 - (y / z))
	elif (y <= -8.2e-39) or not (y <= 1.45e+88):
		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 <= -1.7e+43)
		tmp = t_1;
	elseif (y <= -2.25e-32)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif ((y <= -8.2e-39) || !(y <= 1.45e+88))
		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 <= -1.7e+43)
		tmp = t_1;
	elseif (y <= -2.25e-32)
		tmp = x * (1.0 - (y / z));
	elseif ((y <= -8.2e-39) || ~((y <= 1.45e+88)))
		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, -1.7e+43], t$95$1, If[LessEqual[y, -2.25e-32], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.2e-39], N[Not[LessEqual[y, 1.45e+88]], $MachinePrecision]], t$95$1, N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000006e43 or -2.25000000000000002e-32 < y < -8.2e-39 or 1.45e88 < y

   1. Initial program 82.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around inf 73.6%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if -1.70000000000000006e43 < y < -2.25000000000000002e-32

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. distribute-frac-neg 68.9%

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

      5. neg-sub0 68.9%

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

      6. associate--r- 68.9%

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

      7. neg-sub0 68.9%

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

      8. +-commutative 68.9%

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

      9. sub-neg 68.9%

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

      10. div-sub 68.9%

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

      11. *-inverses 68.9%

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

   7. Simplified 68.9%

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

   if -8.2e-39 < y < 1.45e88

   1. Initial program 86.9%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-neg-frac2 74.0%

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

      3. neg-sub0 74.0%

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

      4. associate--r- 74.0%

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

      5. neg-sub0 74.0%

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

      6. +-commutative 74.0%

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

      7. sub-neg 74.0%

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

      8. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-39} \lor \neg \left(y \leq 1.45 \cdot 10^{+88}\right):\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -2.4e+45)
     t_1
     (if (<= y -7e-33)
       (* x (- 1.0 (/ y z)))
       (if (<= y -2.25e-38)
         t_1
         (if (<= y 1.35e+89) (* x (/ z (- z t))) (/ x (/ (- t z) y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -2.4e+45) {
		tmp = t_1;
	} else if (y <= -7e-33) {
		tmp = x * (1.0 - (y / z));
	} else if (y <= -2.25e-38) {
		tmp = t_1;
	} else if (y <= 1.35e+89) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-2.4d+45)) then
        tmp = t_1
    else if (y <= (-7d-33)) then
        tmp = x * (1.0d0 - (y / z))
    else if (y <= (-2.25d-38)) then
        tmp = t_1
    else if (y <= 1.35d+89) then
        tmp = x * (z / (z - t))
    else
        tmp = x / ((t - z) / y)
    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 <= -2.4e+45) {
		tmp = t_1;
	} else if (y <= -7e-33) {
		tmp = x * (1.0 - (y / z));
	} else if (y <= -2.25e-38) {
		tmp = t_1;
	} else if (y <= 1.35e+89) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -2.4e+45:
		tmp = t_1
	elif y <= -7e-33:
		tmp = x * (1.0 - (y / z))
	elif y <= -2.25e-38:
		tmp = t_1
	elif y <= 1.35e+89:
		tmp = x * (z / (z - t))
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -2.4e+45)
		tmp = t_1;
	elseif (y <= -7e-33)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (y <= -2.25e-38)
		tmp = t_1;
	elseif (y <= 1.35e+89)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -2.4e+45)
		tmp = t_1;
	elseif (y <= -7e-33)
		tmp = x * (1.0 - (y / z));
	elseif (y <= -2.25e-38)
		tmp = t_1;
	elseif (y <= 1.35e+89)
		tmp = x * (z / (z - t));
	else
		tmp = x / ((t - z) / y);
	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, -2.4e+45], t$95$1, If[LessEqual[y, -7e-33], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.25e-38], t$95$1, If[LessEqual[y, 1.35e+89], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.39999999999999989e45 or -6.9999999999999997e-33 < y < -2.25000000000000004e-38

   1. Initial program 86.0%

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

      1. associate-/l* 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 76.8%

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

      1. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

   if -2.39999999999999989e45 < y < -6.9999999999999997e-33

   1. Initial program 83.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. distribute-frac-neg 68.9%

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

      5. neg-sub0 68.9%

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

      6. associate--r- 68.9%

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

      7. neg-sub0 68.9%

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

      8. +-commutative 68.9%

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

      9. sub-neg 68.9%

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

      10. div-sub 68.9%

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

      11. *-inverses 68.9%

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

   7. Simplified 68.9%

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

   if -2.25000000000000004e-38 < y < 1.35e89

   1. Initial program 86.9%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-neg-frac2 74.0%

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

      3. neg-sub0 74.0%

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

      4. associate--r- 74.0%

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

      5. neg-sub0 74.0%

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

      6. +-commutative 74.0%

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

      7. sub-neg 74.0%

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

      8. associate-/l* 84.1%

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

   7. Simplified 84.1%

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

   if 1.35e89 < y

   1. Initial program 76.1%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. clear-num 89.1%

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

      2. un-div-inv 89.4%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in y around inf 73.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-38}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{\frac{z}{-y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.55e+115)
   x
   (if (<= z -1.45e+53) (/ x (/ z (- y))) (if (<= z 3e+93) (* x (/ y t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.55e+115) {
		tmp = x;
	} else if (z <= -1.45e+53) {
		tmp = x / (z / -y);
	} else if (z <= 3e+93) {
		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 <= (-3.55d+115)) then
        tmp = x
    else if (z <= (-1.45d+53)) then
        tmp = x / (z / -y)
    else if (z <= 3d+93) 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 <= -3.55e+115) {
		tmp = x;
	} else if (z <= -1.45e+53) {
		tmp = x / (z / -y);
	} else if (z <= 3e+93) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.55e+115:
		tmp = x
	elif z <= -1.45e+53:
		tmp = x / (z / -y)
	elif z <= 3e+93:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.55e+115)
		tmp = x;
	elseif (z <= -1.45e+53)
		tmp = Float64(x / Float64(z / Float64(-y)));
	elseif (z <= 3e+93)
		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 <= -3.55e+115)
		tmp = x;
	elseif (z <= -1.45e+53)
		tmp = x / (z / -y);
	elseif (z <= 3e+93)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.55e+115], x, If[LessEqual[z, -1.45e+53], N[(x / N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+93], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5499999999999998e115 or 2.99999999999999978e93 < z

   1. Initial program 71.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 z around inf 75.6%

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

   if -3.5499999999999998e115 < z < -1.4500000000000001e53

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 83.1%

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

      1. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in t around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-/l* 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. mul-1-neg 70.9%

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

      5. associate-*r/ 70.9%

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

      6. neg-mul-1 70.9%

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

   10. Simplified 70.9%

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

       1. distribute-frac-neg 70.9%

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

       2. distribute-rgt-neg-out 70.9%

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

       3. add-sqr-sqrt 34.5%

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

       4. sqrt-unprod 29.8%

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

       5. sqr-neg 29.8%

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

       6. sqrt-unprod 11.4%

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

       7. add-sqr-sqrt 20.3%

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

       8. clear-num 20.3%

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

       9. un-div-inv 20.3%

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

       10. add-sqr-sqrt 11.4%

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

       11. sqrt-unprod 29.8%

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

       12. sqr-neg 29.8%

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

       13. sqrt-unprod 34.5%

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

       14. add-sqr-sqrt 71.2%

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

   12. Applied egg-rr 71.2%

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

   if -1.4500000000000001e53 < z < 2.99999999999999978e93

   1. Initial program 91.4%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in z around 0 60.1%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{\frac{z}{-y}}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-39} \lor \neg \left(z \leq 4.2 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-39) (not (<= z 4.2e-112)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-39) || !(z <= 4.2e-112)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / 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 ((z <= (-9d-39)) .or. (.not. (z <= 4.2d-112))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-39) || !(z <= 4.2e-112)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-39) or not (z <= 4.2e-112):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-39) || !(z <= 4.2e-112))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-39) || ~((z <= 4.2e-112)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-39], N[Not[LessEqual[z, 4.2e-112]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.0000000000000002e-39 or 4.2000000000000001e-112 < z

   1. Initial program 80.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-/l* 72.1%

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

      3. distribute-rgt-neg-in 72.1%

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

      4. distribute-frac-neg 72.1%

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

      5. neg-sub0 72.1%

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

      6. associate--r- 72.1%

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

      7. neg-sub0 72.1%

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

      8. +-commutative 72.1%

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

      9. sub-neg 72.1%

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

      10. div-sub 72.1%

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

      11. *-inverses 72.1%

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

   7. Simplified 72.1%

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

   if -9.0000000000000002e-39 < z < 4.2000000000000001e-112

   1. Initial program 91.4%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around 0 73.2%

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

      1. associate-/l* 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-39} \lor \neg \left(z \leq 4.2 \cdot 10^{-112}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+96} \lor \neg \left(z \leq 7.2 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e+96) (not (<= z 7.2e+94)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+96) || !(z <= 7.2e+94)) {
		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 <= (-4d+96)) .or. (.not. (z <= 7.2d+94))) 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 <= -4e+96) || !(z <= 7.2e+94)) {
		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 <= -4e+96) or not (z <= 7.2e+94):
		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 <= -4e+96) || !(z <= 7.2e+94))
		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 <= -4e+96) || ~((z <= 7.2e+94)))
		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, -4e+96], N[Not[LessEqual[z, 7.2e+94]], $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 < -4.0000000000000002e96 or 7.19999999999999985e94 < z

   1. Initial program 71.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 61.3%

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

      1. mul-1-neg 61.3%

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

      2. associate-/l* 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-frac-neg 83.1%

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

      5. neg-sub0 83.1%

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

      6. associate--r- 83.1%

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

      7. neg-sub0 83.1%

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

      8. +-commutative 83.1%

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

      9. sub-neg 83.1%

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

      10. div-sub 83.1%

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

      11. *-inverses 83.1%

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

   7. Simplified 83.1%

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

   if -4.0000000000000002e96 < z < 7.19999999999999985e94

   1. Initial program 92.0%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in y around inf 70.0%

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

      1. associate-/l* 72.8%

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

   7. Simplified 72.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+96} \lor \neg \left(z \leq 7.2 \cdot 10^{+94}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e+105) x (if (<= z 2.9e+93) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e+105) {
		tmp = x;
	} else if (z <= 2.9e+93) {
		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 <= (-7.8d+105)) then
        tmp = x
    else if (z <= 2.9d+93) 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 <= -7.8e+105) {
		tmp = x;
	} else if (z <= 2.9e+93) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e+105:
		tmp = x
	elif z <= 2.9e+93:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e+105)
		tmp = x;
	elseif (z <= 2.9e+93)
		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 <= -7.8e+105)
		tmp = x;
	elseif (z <= 2.9e+93)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e+105], x, If[LessEqual[z, 2.9e+93], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -7.79999999999999957e105 or 2.8999999999999998e93 < z

   1. Initial program 71.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 74.8%

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

   if -7.79999999999999957e105 < z < 2.8999999999999998e93

   1. Initial program 92.0%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around 0 58.4%

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

      1. associate-/l* 60.7%

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

   7. Simplified 60.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-/l* 97.0%

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

3. Simplified 97.0%

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

5. Taylor expanded in z around inf 36.3%

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

6. Final simplification 36.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.8% 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 2024072 
(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)))