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

Percentage Accurate: 84.6% → 97.1%

Time: 7.9s

Alternatives: 10

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: 84.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% 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]

Derivation

1. Initial program 84.0%

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

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.1

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

4. Applied rewrites 97.1%

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

Alternative 2: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t} \cdot x\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-42}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- y z) t) x)))
   (if (<= t -7.5e+186)
     t_1
     (if (<= t -4.8e-61)
       (* (/ z (- z t)) x)
       (if (<= t 9.4e-42) (fma (- x) (/ y z) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y - z) / t) * x;
	double tmp;
	if (t <= -7.5e+186) {
		tmp = t_1;
	} else if (t <= -4.8e-61) {
		tmp = (z / (z - t)) * x;
	} else if (t <= 9.4e-42) {
		tmp = fma(-x, (y / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - z) / t) * x)
	tmp = 0.0
	if (t <= -7.5e+186)
		tmp = t_1;
	elseif (t <= -4.8e-61)
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	elseif (t <= 9.4e-42)
		tmp = fma(Float64(-x), Float64(y / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t, -7.5e+186], t$95$1, If[LessEqual[t, -4.8e-61], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 9.4e-42], N[((-x) * N[(y / z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.4999999999999998e186 or 9.4000000000000001e-42 < t

   1. Initial program 82.6%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 95.8

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

   4. Applied rewrites 95.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 95.7%

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

   7. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. distribute-frac-neg N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-neg-in N/A

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

      6. remove-double-neg N/A

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

      7. sub-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 84.7

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

   9. Applied rewrites 84.7%

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

   if -7.4999999999999998e186 < t < -4.8000000000000002e-61

   1. Initial program 87.9%

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

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

      3. lower-*.f64 33.1

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

   5. Applied rewrites 33.1%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 65.6

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

   8. Applied rewrites 65.6%

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

   if -4.8000000000000002e-61 < t < 9.4000000000000001e-42

   1. Initial program 83.8%

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

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-lft-out N/A

         \[\leadsto 0 - \color{blue}{\left(x \cdot \frac{y}{z} + x \cdot -1\right)} \]

      9. associate-/l* N/A

         \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + x \cdot -1\right) \]

      10. *-commutative N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{-1 \cdot x}\right) \]

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 83.4

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

   5. Applied rewrites 83.4%

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

   7. Applied rewrites 84.4%

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

Alternative 3: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -0.02:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -0.02)
     t_1
     (if (<= z 1.22e-123)
       (/ (* (- y z) x) t)
       (if (<= z 9.5e+89) (* (/ x (- t z)) y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -0.02) {
		tmp = t_1;
	} else if (z <= 1.22e-123) {
		tmp = ((y - z) * x) / t;
	} else if (z <= 9.5e+89) {
		tmp = (x / (t - z)) * y;
	} 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 = (z / (z - t)) * x
    if (z <= (-0.02d0)) then
        tmp = t_1
    else if (z <= 1.22d-123) then
        tmp = ((y - z) * x) / t
    else if (z <= 9.5d+89) then
        tmp = (x / (t - z)) * y
    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 = (z / (z - t)) * x;
	double tmp;
	if (z <= -0.02) {
		tmp = t_1;
	} else if (z <= 1.22e-123) {
		tmp = ((y - z) * x) / t;
	} else if (z <= 9.5e+89) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (z - t)) * x
	tmp = 0
	if z <= -0.02:
		tmp = t_1
	elif z <= 1.22e-123:
		tmp = ((y - z) * x) / t
	elif z <= 9.5e+89:
		tmp = (x / (t - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -0.02)
		tmp = t_1;
	elseif (z <= 1.22e-123)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	elseif (z <= 9.5e+89)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / (z - t)) * x;
	tmp = 0.0;
	if (z <= -0.02)
		tmp = t_1;
	elseif (z <= 1.22e-123)
		tmp = ((y - z) * x) / t;
	elseif (z <= 9.5e+89)
		tmp = (x / (t - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -0.02], t$95$1, If[LessEqual[z, 1.22e-123], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 9.5e+89], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0200000000000000004 or 9.5000000000000003e89 < z

   1. Initial program 71.9%

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

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

      3. lower-*.f64 11.6

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

   5. Applied rewrites 11.6%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 84.1

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

   8. Applied rewrites 84.1%

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

   if -0.0200000000000000004 < z < 1.22e-123

   1. Initial program 95.3%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if 1.22e-123 < z < 9.5000000000000003e89

   1. Initial program 84.9%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 69.6

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

   5. Applied rewrites 69.6%

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

Alternative 4: 69.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+213}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -24000000000000:\\ \;\;\;\;\frac{x}{z - t} \cdot z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+213)
   (* 1.0 x)
   (if (<= z -24000000000000.0)
     (* (/ x (- z t)) z)
     (if (<= z 1.4e+93) (* (/ x (- t z)) y) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+213) {
		tmp = 1.0 * x;
	} else if (z <= -24000000000000.0) {
		tmp = (x / (z - t)) * z;
	} else if (z <= 1.4e+93) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.45d+213)) then
        tmp = 1.0d0 * x
    else if (z <= (-24000000000000.0d0)) then
        tmp = (x / (z - t)) * z
    else if (z <= 1.4d+93) then
        tmp = (x / (t - z)) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+213) {
		tmp = 1.0 * x;
	} else if (z <= -24000000000000.0) {
		tmp = (x / (z - t)) * z;
	} else if (z <= 1.4e+93) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+213:
		tmp = 1.0 * x
	elif z <= -24000000000000.0:
		tmp = (x / (z - t)) * z
	elif z <= 1.4e+93:
		tmp = (x / (t - z)) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+213)
		tmp = Float64(1.0 * x);
	elseif (z <= -24000000000000.0)
		tmp = Float64(Float64(x / Float64(z - t)) * z);
	elseif (z <= 1.4e+93)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.45e+213)
		tmp = 1.0 * x;
	elseif (z <= -24000000000000.0)
		tmp = (x / (z - t)) * z;
	elseif (z <= 1.4e+93)
		tmp = (x / (t - z)) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+213], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -24000000000000.0], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 1.4e+93], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45000000000000015e213 or 1.39999999999999994e93 < z

   1. Initial program 72.2%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 82.0%

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

   if -1.45000000000000015e213 < z < -2.4e13

   1. Initial program 69.2%

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

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

      3. lower-*.f64 21.7

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

   5. Applied rewrites 21.7%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 71.4

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

   8. Applied rewrites 71.4%

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

   10. Applied rewrites 71.2%

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

   if -2.4e13 < z < 1.39999999999999994e93

   1. Initial program 92.1%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

Alternative 5: 90.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+213}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{y}{z}, x\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+213)
   (fma (- x) (/ y z) x)
   (if (<= z 6e+146) (* (/ x (- t z)) (- y z)) (* (/ z (- z t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+213) {
		tmp = fma(-x, (y / z), x);
	} else if (z <= 6e+146) {
		tmp = (x / (t - z)) * (y - z);
	} else {
		tmp = (z / (z - t)) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+213)
		tmp = fma(Float64(-x), Float64(y / z), x);
	elseif (z <= 6e+146)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(y - z));
	else
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+213], N[((-x) * N[(y / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 6e+146], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999996e213

   1. Initial program 66.9%

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

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

         \[\leadsto 0 - \color{blue}{x \cdot \frac{y - z}{z}} \]

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto 0 - x \cdot \left(\frac{y}{z} + \color{blue}{-1}\right) \]

      8. distribute-lft-out N/A

         \[\leadsto 0 - \color{blue}{\left(x \cdot \frac{y}{z} + x \cdot -1\right)} \]

      9. associate-/l* N/A

         \[\leadsto 0 - \left(\color{blue}{\frac{x \cdot y}{z}} + x \cdot -1\right) \]

      10. *-commutative N/A

          \[\leadsto 0 - \left(\frac{x \cdot y}{z} + \color{blue}{-1 \cdot x}\right) \]

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   7. Applied rewrites 95.2%

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

   if -1.69999999999999996e213 < z < 6.00000000000000005e146

   1. Initial program 87.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 90.7

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

   4. Applied rewrites 90.7%

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

   if 6.00000000000000005e146 < z

   1. Initial program 74.4%

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

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

      3. lower-*.f64 4.6

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

   5. Applied rewrites 4.6%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 96.9

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

   8. Applied rewrites 96.9%

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

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -24000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -24000000000000.0)
     t_1
     (if (<= z 9.5e+89) (* (/ x (- t z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -24000000000000.0) {
		tmp = t_1;
	} else if (z <= 9.5e+89) {
		tmp = (x / (t - z)) * y;
	} 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 = (z / (z - t)) * x
    if (z <= (-24000000000000.0d0)) then
        tmp = t_1
    else if (z <= 9.5d+89) then
        tmp = (x / (t - z)) * y
    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 = (z / (z - t)) * x;
	double tmp;
	if (z <= -24000000000000.0) {
		tmp = t_1;
	} else if (z <= 9.5e+89) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (z - t)) * x
	tmp = 0
	if z <= -24000000000000.0:
		tmp = t_1
	elif z <= 9.5e+89:
		tmp = (x / (t - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -24000000000000.0)
		tmp = t_1;
	elseif (z <= 9.5e+89)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / (z - t)) * x;
	tmp = 0.0;
	if (z <= -24000000000000.0)
		tmp = t_1;
	elseif (z <= 9.5e+89)
		tmp = (x / (t - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -24000000000000.0], t$95$1, If[LessEqual[z, 9.5e+89], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e13 or 9.5000000000000003e89 < z

   1. Initial program 71.1%

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

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

      3. lower-*.f64 10.8

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

   5. Applied rewrites 10.8%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. lower-*.f64 N/A

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

      6. distribute-neg-frac2 N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. mul-1-neg N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 84.6

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

   8. Applied rewrites 84.6%

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

   if -2.4e13 < z < 9.5000000000000003e89

   1. Initial program 92.1%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 72.9

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

   5. Applied rewrites 72.9%

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

Alternative 7: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+106}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.42e+106)
   (* 1.0 x)
   (if (<= z 1.4e+93) (* (/ x (- t z)) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+106) {
		tmp = 1.0 * x;
	} else if (z <= 1.4e+93) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.42d+106)) then
        tmp = 1.0d0 * x
    else if (z <= 1.4d+93) then
        tmp = (x / (t - z)) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+106) {
		tmp = 1.0 * x;
	} else if (z <= 1.4e+93) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.42e+106:
		tmp = 1.0 * x
	elif z <= 1.4e+93:
		tmp = (x / (t - z)) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.42e+106)
		tmp = Float64(1.0 * x);
	elseif (z <= 1.4e+93)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.42e+106)
		tmp = 1.0 * x;
	elseif (z <= 1.4e+93)
		tmp = (x / (t - z)) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.42e+106], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 1.4e+93], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4200000000000001e106 or 1.39999999999999994e93 < z

   1. Initial program 68.2%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 74.7%

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

   if -1.4200000000000001e106 < z < 1.39999999999999994e93

   1. Initial program 91.2%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 69.6

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

   5. Applied rewrites 69.6%

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

Alternative 8: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+51}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.9e+51) (* 1.0 x) (if (<= z 9.5e+92) (* (/ y t) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+51) {
		tmp = 1.0 * x;
	} else if (z <= 9.5e+92) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.9d+51)) then
        tmp = 1.0d0 * x
    else if (z <= 9.5d+92) then
        tmp = (y / t) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+51) {
		tmp = 1.0 * x;
	} else if (z <= 9.5e+92) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.9e+51:
		tmp = 1.0 * x
	elif z <= 9.5e+92:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.9e+51)
		tmp = Float64(1.0 * x);
	elseif (z <= 9.5e+92)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.9e+51)
		tmp = 1.0 * x;
	elseif (z <= 9.5e+92)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.9e+51], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 9.5e+92], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.89999999999999983e51 or 9.4999999999999995e92 < z

   1. Initial program 67.9%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. clear-num N/A

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

      7. lower-*.f64 N/A

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 70.4%

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

   if -4.89999999999999983e51 < z < 9.4999999999999995e92

   1. Initial program 92.5%

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

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

      3. lower-*.f64 62.3

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

   5. Applied rewrites 62.3%

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

   7. Applied rewrites 63.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+51}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% 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 84.0%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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 96.5

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

4. Applied rewrites 96.5%

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

Alternative 10: 35.3% accurate, 3.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.0%

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

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.1

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

4. Applied rewrites 97.1%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lift--.f64 N/A

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

   5. lift-/.f64 N/A

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

   6. clear-num N/A

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

   7. lower-*.f64 N/A

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

6. Applied rewrites 96.5%

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

7. Taylor expanded in z around inf

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

9. Applied rewrites 33.4%

   \[\leadsto \color{blue}{1} \cdot x \]
10. Add Preprocessing

Developer Target 1: 97.1% 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 2024270 
(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)))