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

Percentage Accurate: 83.8% → 96.9%

Time: 9.2s

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: 83.8% 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: 96.9% 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]

Derivation

1. Initial program 84.1%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

   7. --lowering--.f64 97.6%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 97.6%

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

Alternative 2: 89.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y - t}{z} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e+98)
   (/ x (- 1.0 (/ t z)))
   (if (<= z 2.9e+164) (* (- y z) (/ x (- t z))) (/ x (+ (/ (- y t) z) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+98) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.9e+164) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / (((y - t) / z) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.1d+98)) then
        tmp = x / (1.0d0 - (t / z))
    else if (z <= 2.9d+164) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x / (((y - t) / z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+98) {
		tmp = x / (1.0 - (t / z));
	} else if (z <= 2.9e+164) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / (((y - t) / z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e+98:
		tmp = x / (1.0 - (t / z))
	elif z <= 2.9e+164:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x / (((y - t) / z) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e+98)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	elseif (z <= 2.9e+164)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(Float64(y - t) / z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.1e+98)
		tmp = x / (1.0 - (t / z));
	elseif (z <= 2.9e+164)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x / (((y - t) / z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e+98], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+164], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(N[(y - t), $MachinePrecision] / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000019e98

   1. Initial program 65.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\left(1 + -1 \cdot \frac{t}{z}\right) - -1 \cdot \frac{y}{z}\right)}\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \color{blue}{\left(-1 \cdot \frac{t}{z} - -1 \cdot \frac{y}{z}\right)}\right)\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \color{blue}{\left(\frac{t}{z} - \frac{y}{z}\right)}\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \frac{t - y}{\color{blue}{z}}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{t - y}{z}\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 - \color{blue}{\frac{t - y}{z}}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t - y}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(t - y\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 93.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), z\right)\right)\right) \]

   7. Simplified 93.6%

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

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{t}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 93.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 93.7%

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

   if -3.10000000000000019e98 < z < 2.8999999999999999e164

   1. Initial program 90.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

      7. --lowering--.f64 92.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 92.5%

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

   if 2.8999999999999999e164 < z

   1. Initial program 72.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\left(1 + -1 \cdot \frac{t}{z}\right) - -1 \cdot \frac{y}{z}\right)}\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \color{blue}{\left(-1 \cdot \frac{t}{z} - -1 \cdot \frac{y}{z}\right)}\right)\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \color{blue}{\left(\frac{t}{z} - \frac{y}{z}\right)}\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \frac{t - y}{\color{blue}{z}}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{t - y}{z}\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 - \color{blue}{\frac{t - y}{z}}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t - y}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(t - y\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 90.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), z\right)\right)\right) \]

   7. Simplified 90.5%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t - y}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+164}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y - t}{z} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 (/ t z)))))
   (if (<= z -2.2e+98)
     t_1
     (if (<= z 6.6e+163) (* (- y z) (/ x (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -2.2e+98) {
		tmp = t_1;
	} else if (z <= 6.6e+163) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - (t / z))
    if (z <= (-2.2d+98)) then
        tmp = t_1
    else if (z <= 6.6d+163) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -2.2e+98) {
		tmp = t_1;
	} else if (z <= 6.6e+163) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -2.2e+98:
		tmp = t_1
	elif z <= 6.6e+163:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -2.2e+98)
		tmp = t_1;
	elseif (z <= 6.6e+163)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -2.2e+98)
		tmp = t_1;
	elseif (z <= 6.6e+163)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+98], t$95$1, If[LessEqual[z, 6.6e+163], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000009e98 or 6.5999999999999999e163 < z

   1. Initial program 68.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\left(1 + -1 \cdot \frac{t}{z}\right) - -1 \cdot \frac{y}{z}\right)}\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \color{blue}{\left(-1 \cdot \frac{t}{z} - -1 \cdot \frac{y}{z}\right)}\right)\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \color{blue}{\left(\frac{t}{z} - \frac{y}{z}\right)}\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \frac{t - y}{\color{blue}{z}}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{t - y}{z}\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 - \color{blue}{\frac{t - y}{z}}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t - y}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(t - y\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 92.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), z\right)\right)\right) \]

   7. Simplified 92.3%

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

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{t}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 92.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 92.3%

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

   if -2.20000000000000009e98 < z < 6.5999999999999999e163

   1. Initial program 90.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

      7. --lowering--.f64 92.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 92.5%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+163}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - \frac{t}{z}}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 (/ t z)))))
   (if (<= z -1.55e+22) t_1 (if (<= z 4.2e-70) (* y (/ x (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -1.55e+22) {
		tmp = t_1;
	} else if (z <= 4.2e-70) {
		tmp = y * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - (t / z))
    if (z <= (-1.55d+22)) then
        tmp = t_1
    else if (z <= 4.2d-70) then
        tmp = y * (x / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (1.0 - (t / z));
	double tmp;
	if (z <= -1.55e+22) {
		tmp = t_1;
	} else if (z <= 4.2e-70) {
		tmp = y * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (1.0 - (t / z))
	tmp = 0
	if z <= -1.55e+22:
		tmp = t_1
	elif z <= 4.2e-70:
		tmp = y * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(1.0 - Float64(t / z)))
	tmp = 0.0
	if (z <= -1.55e+22)
		tmp = t_1;
	elseif (z <= 4.2e-70)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (1.0 - (t / z));
	tmp = 0.0;
	if (z <= -1.55e+22)
		tmp = t_1;
	elseif (z <= 4.2e-70)
		tmp = y * (x / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+22], t$95$1, If[LessEqual[z, 4.2e-70], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e22 or 4.2000000000000002e-70 < z

   1. Initial program 77.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\left(1 + -1 \cdot \frac{t}{z}\right) - -1 \cdot \frac{y}{z}\right)}\right) \]
   6. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \color{blue}{\left(-1 \cdot \frac{t}{z} - -1 \cdot \frac{y}{z}\right)}\right)\right) \]

      2. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \color{blue}{\left(\frac{t}{z} - \frac{y}{z}\right)}\right)\right) \]

      3. div-sub N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + -1 \cdot \frac{t - y}{\color{blue}{z}}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{t - y}{z}\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(1 - \color{blue}{\frac{t - y}{z}}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t - y}{z}\right)}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(t - y\right), \color{blue}{z}\right)\right)\right) \]

      8. --lowering--.f64 83.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), z\right)\right)\right) \]

   7. Simplified 83.6%

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

   8. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 - \frac{t}{z}\right)}\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{t}{z}\right)}\right)\right) \]

      3. /-lowering-/.f64 83.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   10. Simplified 83.5%

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

   if -1.5500000000000001e22 < z < 4.2000000000000002e-70

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      5. --lowering--.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 78.6%

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

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= t -1.7e+47) t_1 (if (<= t 4.3e+14) (* x (- 1.0 (/ y z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (t <= -1.7e+47) {
		tmp = t_1;
	} else if (t <= 4.3e+14) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    if (t <= (-1.7d+47)) then
        tmp = t_1
    else if (t <= 4.3d+14) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (t <= -1.7e+47) {
		tmp = t_1;
	} else if (t <= 4.3e+14) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if t <= -1.7e+47:
		tmp = t_1
	elif t <= 4.3e+14:
		tmp = x * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (t <= -1.7e+47)
		tmp = t_1;
	elseif (t <= 4.3e+14)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (t <= -1.7e+47)
		tmp = t_1;
	elseif (t <= 4.3e+14)
		tmp = x * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+47], t$95$1, If[LessEqual[t, 4.3e+14], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e47 or 4.3e14 < t

   1. Initial program 84.3%

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

   3. Taylor expanded in t around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - z}{t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - z\right), \color{blue}{t}\right)\right) \]

      4. --lowering--.f64 77.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right)\right) \]

   5. Simplified 77.7%

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

   if -1.6999999999999999e47 < t < 4.3e14

   1. Initial program 83.9%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 81.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -4.5e-44) t_1 (if (<= z 7.2e-37) (/ (* x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -4.5e-44) {
		tmp = t_1;
	} else if (z <= 7.2e-37) {
		tmp = (x * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-4.5d-44)) then
        tmp = t_1
    else if (z <= 7.2d-37) then
        tmp = (x * y) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -4.5e-44) {
		tmp = t_1;
	} else if (z <= 7.2e-37) {
		tmp = (x * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -4.5e-44:
		tmp = t_1
	elif z <= 7.2e-37:
		tmp = (x * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.5e-44)
		tmp = t_1;
	elseif (z <= 7.2e-37)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.5e-44)
		tmp = t_1;
	elseif (z <= 7.2e-37)
		tmp = (x * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e-44], t$95$1, If[LessEqual[z, 7.2e-37], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999999e-44 or 7.20000000000000014e-37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 67.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 67.9%

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

   if -4.4999999999999999e-44 < z < 7.20000000000000014e-37

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 71.4%

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

Alternative 7: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e-44) x (if (<= z 7.6e-37) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e-44) {
		tmp = x;
	} else if (z <= 7.6e-37) {
		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 <= (-5d-44)) then
        tmp = x
    else if (z <= 7.6d-37) 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 <= -5e-44) {
		tmp = x;
	} else if (z <= 7.6e-37) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5e-44:
		tmp = x
	elif z <= 7.6e-37:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e-44)
		tmp = x;
	elseif (z <= 7.6e-37)
		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 <= -5e-44)
		tmp = x;
	elseif (z <= 7.6e-37)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e-44], x, If[LessEqual[z, 7.6e-37], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000039e-44 or 7.6000000000000008e-37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 53.7%

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

   if -5.00000000000000039e-44 < z < 7.6000000000000008e-37

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 71.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 71.4%

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

Alternative 8: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-37}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e-45) x (if (<= z 8.6e-37) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-45) {
		tmp = x;
	} else if (z <= 8.6e-37) {
		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 <= (-5.5d-45)) then
        tmp = x
    else if (z <= 8.6d-37) 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 <= -5.5e-45) {
		tmp = x;
	} else if (z <= 8.6e-37) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e-45:
		tmp = x
	elif z <= 8.6e-37:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e-45)
		tmp = x;
	elseif (z <= 8.6e-37)
		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 <= -5.5e-45)
		tmp = x;
	elseif (z <= 8.6e-37)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e-45], x, If[LessEqual[z, 8.6e-37], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000003e-45 or 8.59999999999999936e-37 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 53.7%

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

   if -5.5000000000000003e-45 < z < 8.59999999999999936e-37

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{t - z}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{\left(t - z\right)}\right)\right) \]

      5. --lowering--.f64 79.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 79.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{t}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 71.3%

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

Alternative 9: 34.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.1%

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

3. Taylor expanded in z around inf

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

5. Simplified 37.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 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 2024161 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

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