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

Percentage Accurate: 84.3% → 96.4%

Time: 11.1s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 96.4

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

4. Applied rewrites 96.4%

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

Alternative 2: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{z - t}\\ t_2 := \mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x (- z t)))) (t_2 (fma x (- (/ y z)) x)))
   (if (<= z -2.7e+110)
     t_2
     (if (<= z -8e-34)
       t_1
       (if (<= z 0.035) (* x (/ y (- t z))) (if (<= z 4.2e+68) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / (z - t));
	double t_2 = fma(x, -(y / z), x);
	double tmp;
	if (z <= -2.7e+110) {
		tmp = t_2;
	} else if (z <= -8e-34) {
		tmp = t_1;
	} else if (z <= 0.035) {
		tmp = x * (y / (t - z));
	} else if (z <= 4.2e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / Float64(z - t)))
	t_2 = fma(x, Float64(-Float64(y / z)), x)
	tmp = 0.0
	if (z <= -2.7e+110)
		tmp = t_2;
	elseif (z <= -8e-34)
		tmp = t_1;
	elseif (z <= 0.035)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 4.2e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-N[(y / z), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[z, -2.7e+110], t$95$2, If[LessEqual[z, -8e-34], t$95$1, If[LessEqual[z, 0.035], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+68], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7000000000000001e110 or 4.20000000000000002e68 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 7.1

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

   5. Applied rewrites 7.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 62.5

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

   8. Applied rewrites 62.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 84.1%

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

   if -2.7000000000000001e110 < z < -7.99999999999999942e-34 or 0.035000000000000003 < z < 4.20000000000000002e68

   1. Initial program 95.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/r/ N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

      26. associate--r+ N/A

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

   6. Applied rewrites 93.3%

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

   7. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 71.6

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

   9. Applied rewrites 71.6%

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

   if -7.99999999999999942e-34 < z < 0.035000000000000003

   1. Initial program 93.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{z - t}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+137}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{elif}\;z \leq 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x (- z t)))))
   (if (<= z -1.45e+137)
     (* x 1.0)
     (if (<= z -1.9e-134)
       t_1
       (if (<= z 1.65e-51) (/ (* y x) t) (if (<= z 1e+198) t_1 (* x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / (z - t));
	double tmp;
	if (z <= -1.45e+137) {
		tmp = x * 1.0;
	} else if (z <= -1.9e-134) {
		tmp = t_1;
	} else if (z <= 1.65e-51) {
		tmp = (y * x) / t;
	} else if (z <= 1e+198) {
		tmp = t_1;
	} else {
		tmp = x * 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) :: t_1
    real(8) :: tmp
    t_1 = z * (x / (z - t))
    if (z <= (-1.45d+137)) then
        tmp = x * 1.0d0
    else if (z <= (-1.9d-134)) then
        tmp = t_1
    else if (z <= 1.65d-51) then
        tmp = (y * x) / t
    else if (z <= 1d+198) then
        tmp = t_1
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / (z - t));
	double tmp;
	if (z <= -1.45e+137) {
		tmp = x * 1.0;
	} else if (z <= -1.9e-134) {
		tmp = t_1;
	} else if (z <= 1.65e-51) {
		tmp = (y * x) / t;
	} else if (z <= 1e+198) {
		tmp = t_1;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / (z - t))
	tmp = 0
	if z <= -1.45e+137:
		tmp = x * 1.0
	elif z <= -1.9e-134:
		tmp = t_1
	elif z <= 1.65e-51:
		tmp = (y * x) / t
	elif z <= 1e+198:
		tmp = t_1
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (z <= -1.45e+137)
		tmp = Float64(x * 1.0);
	elseif (z <= -1.9e-134)
		tmp = t_1;
	elseif (z <= 1.65e-51)
		tmp = Float64(Float64(y * x) / t);
	elseif (z <= 1e+198)
		tmp = t_1;
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / (z - t));
	tmp = 0.0;
	if (z <= -1.45e+137)
		tmp = x * 1.0;
	elseif (z <= -1.9e-134)
		tmp = t_1;
	elseif (z <= 1.65e-51)
		tmp = (y * x) / t;
	elseif (z <= 1e+198)
		tmp = t_1;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+137], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, -1.9e-134], t$95$1, If[LessEqual[z, 1.65e-51], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1e+198], t$95$1, N[(x * 1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999992e137 or 1.00000000000000002e198 < z

   1. Initial program 68.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 85.0%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -1.44999999999999992e137 < z < -1.90000000000000001e-134 or 1.64999999999999986e-51 < z < 1.00000000000000002e198

   1. Initial program 92.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.0

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

   4. Applied rewrites 99.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/r/ N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

      26. associate--r+ N/A

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

   6. Applied rewrites 92.1%

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

   7. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 61.9

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

   9. Applied rewrites 61.9%

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

   if -1.90000000000000001e-134 < z < 1.64999999999999986e-51

   1. Initial program 91.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 77.8

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

   5. Applied rewrites 77.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+137}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-134}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{elif}\;z \leq 10^{+198}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (- (/ y z)) x)))
   (if (<= z -5.6e-72)
     t_1
     (if (<= z 1.65e-51)
       (/ (* y x) t)
       (if (<= z 4.2e+68) (* z (/ x (- z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, -(y / z), x);
	double tmp;
	if (z <= -5.6e-72) {
		tmp = t_1;
	} else if (z <= 1.65e-51) {
		tmp = (y * x) / t;
	} else if (z <= 4.2e+68) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(-Float64(y / z)), x)
	tmp = 0.0
	if (z <= -5.6e-72)
		tmp = t_1;
	elseif (z <= 1.65e-51)
		tmp = Float64(Float64(y * x) / t);
	elseif (z <= 4.2e+68)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-N[(y / z), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[z, -5.6e-72], t$95$1, If[LessEqual[z, 1.65e-51], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 4.2e+68], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5999999999999996e-72 or 4.20000000000000002e68 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 14.7

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

   5. Applied rewrites 14.7%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 59.0

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

   8. Applied rewrites 59.0%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 73.8%

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

   if -5.5999999999999996e-72 < z < 1.64999999999999986e-51

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 74.8

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

   5. Applied rewrites 74.8%

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

   if 1.64999999999999986e-51 < z < 4.20000000000000002e68

   1. Initial program 99.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/r/ N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

      26. associate--r+ N/A

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

   6. Applied rewrites 91.9%

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

   7. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 68.3

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

   9. Applied rewrites 68.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-51}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e-30)
   (* x 1.0)
   (if (<= z -6.4e-72)
     (* (/ x z) (- y))
     (if (<= z 0.065) (/ (* y x) t) (* x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-30) {
		tmp = x * 1.0;
	} else if (z <= -6.4e-72) {
		tmp = (x / z) * -y;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 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 <= (-4.5d-30)) then
        tmp = x * 1.0d0
    else if (z <= (-6.4d-72)) then
        tmp = (x / z) * -y
    else if (z <= 0.065d0) then
        tmp = (y * x) / t
    else
        tmp = x * 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 <= -4.5e-30) {
		tmp = x * 1.0;
	} else if (z <= -6.4e-72) {
		tmp = (x / z) * -y;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5e-30:
		tmp = x * 1.0
	elif z <= -6.4e-72:
		tmp = (x / z) * -y
	elif z <= 0.065:
		tmp = (y * x) / t
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e-30)
		tmp = Float64(x * 1.0);
	elseif (z <= -6.4e-72)
		tmp = Float64(Float64(x / z) * Float64(-y));
	elseif (z <= 0.065)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.5e-30)
		tmp = x * 1.0;
	elseif (z <= -6.4e-72)
		tmp = (x / z) * -y;
	elseif (z <= 0.065)
		tmp = (y * x) / t;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e-30], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, -6.4e-72], N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 0.065], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999967e-30 or 0.065000000000000002 < z

   1. Initial program 82.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 58.8%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -4.49999999999999967e-30 < z < -6.39999999999999998e-72

   1. Initial program 94.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 94.5

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

   4. Applied rewrites 94.5%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. associate-/r/ N/A

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

      7. frac-2neg N/A

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

      8. associate-/r/ N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

      26. associate--r+ N/A

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 68.1

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

   9. Applied rewrites 68.1%

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

   10. Taylor expanded in z around 0

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

       1. mul-1-neg N/A

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

       2. lower-neg.f64 62.0

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

   12. Applied rewrites 62.0%

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

   if -6.39999999999999998e-72 < z < 0.065000000000000002

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-134}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.65e+110)
   (* x 1.0)
   (if (<= z -1.9e-134)
     (/ (* x (- z)) t)
     (if (<= z 0.065) (/ (* y x) t) (* x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.65e+110) {
		tmp = x * 1.0;
	} else if (z <= -1.9e-134) {
		tmp = (x * -z) / t;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 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 <= (-2.65d+110)) then
        tmp = x * 1.0d0
    else if (z <= (-1.9d-134)) then
        tmp = (x * -z) / t
    else if (z <= 0.065d0) then
        tmp = (y * x) / t
    else
        tmp = x * 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 <= -2.65e+110) {
		tmp = x * 1.0;
	} else if (z <= -1.9e-134) {
		tmp = (x * -z) / t;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.65e+110:
		tmp = x * 1.0
	elif z <= -1.9e-134:
		tmp = (x * -z) / t
	elif z <= 0.065:
		tmp = (y * x) / t
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.65e+110)
		tmp = Float64(x * 1.0);
	elseif (z <= -1.9e-134)
		tmp = Float64(Float64(x * Float64(-z)) / t);
	elseif (z <= 0.065)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.65e+110)
		tmp = x * 1.0;
	elseif (z <= -1.9e-134)
		tmp = (x * -z) / t;
	elseif (z <= 0.065)
		tmp = (y * x) / t;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.65e+110], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, -1.9e-134], N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 0.065], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6499999999999999e110 or 0.065000000000000002 < z

   1. Initial program 79.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 65.9%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -2.6499999999999999e110 < z < -1.90000000000000001e-134

   1. Initial program 94.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \left(-1 \cdot z\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.8%

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

   if -1.90000000000000001e-134 < z < 0.065000000000000002

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 73.4

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

   5. Applied rewrites 73.4%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+110}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-134}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+192}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+137)
   (fma x (- (/ y z)) x)
   (if (<= z 6.2e+192) (* (- y z) (/ x (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+137) {
		tmp = fma(x, -(y / z), x);
	} else if (z <= 6.2e+192) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+137)
		tmp = fma(x, Float64(-Float64(y / z)), x);
	elseif (z <= 6.2e+192)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+137], N[(x * (-N[(y / z), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[z, 6.2e+192], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000009e137

   1. Initial program 62.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 6.9

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

   5. Applied rewrites 6.9%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 59.3

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

   8. Applied rewrites 59.3%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 94.3%

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

   if -1.60000000000000009e137 < z < 6.1999999999999997e192

   1. Initial program 92.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.0

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

   4. Applied rewrites 91.0%

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

   if 6.1999999999999997e192 < z

   1. Initial program 83.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 99.9

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

   7. Applied rewrites 99.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+137}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+192}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -8e-33) t_1 (if (<= z 0.035) (/ (* y x) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -8e-33) {
		tmp = t_1;
	} else if (z <= 0.035) {
		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 * (z / (z - t))
    if (z <= (-8d-33)) then
        tmp = t_1
    else if (z <= 0.035d0) 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 * (z / (z - t));
	double tmp;
	if (z <= -8e-33) {
		tmp = t_1;
	} else if (z <= 0.035) {
		tmp = (y * x) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -8e-33:
		tmp = t_1
	elif z <= 0.035:
		tmp = (y * x) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -8e-33)
		tmp = t_1;
	elseif (z <= 0.035)
		tmp = Float64(Float64(y * x) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -8e-33)
		tmp = t_1;
	elseif (z <= 0.035)
		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[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-33], t$95$1, If[LessEqual[z, 0.035], N[(N[(y * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000004e-33 or 0.035000000000000003 < z

   1. Initial program 82.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 78.0

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

   7. Applied rewrites 78.0%

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

   if -8.0000000000000004e-33 < z < 0.035000000000000003

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 78.7

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

   5. Applied rewrites 78.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 0.035:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) t)))
   (if (<= t -6.8e+44) t_1 (if (<= t 1.06e+51) (fma x (- (/ y z)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / t;
	double tmp;
	if (t <= -6.8e+44) {
		tmp = t_1;
	} else if (t <= 1.06e+51) {
		tmp = fma(x, -(y / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / t)
	tmp = 0.0
	if (t <= -6.8e+44)
		tmp = t_1;
	elseif (t <= 1.06e+51)
		tmp = fma(x, Float64(-Float64(y / z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -6.8e+44], t$95$1, If[LessEqual[t, 1.06e+51], N[(x * (-N[(y / z), $MachinePrecision]) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8e44 or 1.06000000000000004e51 < t

   1. Initial program 90.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot \left(-1 \cdot z\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 44.3%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 79.5%

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

   if -6.8e44 < t < 1.06000000000000004e51

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 24.1

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

   5. Applied rewrites 24.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 66.6

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

   8. Applied rewrites 66.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.0%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))))
   (if (<= t -6.8e+44) t_1 (if (<= t 1.06e+51) (fma x (- (/ y z)) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (t <= -6.8e+44) {
		tmp = t_1;
	} else if (t <= 1.06e+51) {
		tmp = fma(x, -(y / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	tmp = 0.0
	if (t <= -6.8e+44)
		tmp = t_1;
	elseif (t <= 1.06e+51)
		tmp = fma(x, Float64(-Float64(y / z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+44], t$95$1, If[LessEqual[t, 1.06e+51], N[(x * (-N[(y / z), $MachinePrecision]) + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.8e44 or 1.06000000000000004e51 < t

   1. Initial program 90.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   7. Applied rewrites 74.7%

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

   if -6.8e44 < t < 1.06000000000000004e51

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 24.1

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

   5. Applied rewrites 24.1%

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

   6. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 66.6

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

   8. Applied rewrites 66.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 77.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(x, -\frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e-7) (* x 1.0) (if (<= z 0.065) (/ (* y x) t) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e-7) {
		tmp = x * 1.0;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 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 <= (-1.8d-7)) then
        tmp = x * 1.0d0
    else if (z <= 0.065d0) then
        tmp = (y * x) / t
    else
        tmp = x * 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 <= -1.8e-7) {
		tmp = x * 1.0;
	} else if (z <= 0.065) {
		tmp = (y * x) / t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e-7:
		tmp = x * 1.0
	elif z <= 0.065:
		tmp = (y * x) / t
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e-7)
		tmp = Float64(x * 1.0);
	elseif (z <= 0.065)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.8e-7)
		tmp = x * 1.0;
	elseif (z <= 0.065)
		tmp = (y * x) / t;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e-7], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 0.065], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999997e-7 or 0.065000000000000002 < z

   1. Initial program 81.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 60.3%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -1.79999999999999997e-7 < z < 0.065000000000000002

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 63.0

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

   5. Applied rewrites 63.0%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 0.065:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 0.017:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e-7) (* x 1.0) (if (<= z 0.017) (* y (/ x t)) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e-7) {
		tmp = x * 1.0;
	} else if (z <= 0.017) {
		tmp = y * (x / t);
	} else {
		tmp = x * 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 <= (-1.75d-7)) then
        tmp = x * 1.0d0
    else if (z <= 0.017d0) then
        tmp = y * (x / t)
    else
        tmp = x * 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 <= -1.75e-7) {
		tmp = x * 1.0;
	} else if (z <= 0.017) {
		tmp = y * (x / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e-7:
		tmp = x * 1.0
	elif z <= 0.017:
		tmp = y * (x / t)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e-7)
		tmp = Float64(x * 1.0);
	elseif (z <= 0.017)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.75e-7)
		tmp = x * 1.0;
	elseif (z <= 0.017)
		tmp = y * (x / t);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e-7], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 0.017], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.74999999999999992e-7 or 0.017000000000000001 < z

   1. Initial program 81.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.9%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -1.74999999999999992e-7 < z < 0.017000000000000001

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 62.7

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

   5. Applied rewrites 62.7%

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

   7. Applied rewrites 59.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 0.017:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x \cdot 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x 1.0))

C

double code(double x, double y, double z, double t) {
	return x * 1.0;
}

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 * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * 1.0;
}

Python

def code(x, y, z, t):
	return x * 1.0

Julia

function code(x, y, z, t)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * 1.0), $MachinePrecision]

Derivation

1. Initial program 87.4%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 96.4

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

4. Applied rewrites 96.4%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 35.9%

   \[\leadsto \color{blue}{1} \cdot x \]

8. Final simplification 35.9%

   \[\leadsto x \cdot 1 \]
9. Add Preprocessing

Developer Target 1: 96.6% accurate, 0.8× 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 2024238 
(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)))