Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Percentage Accurate: 97.8% → 97.8%

Time: 7.3s

Alternatives: 10

Speedup: 1.0×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. +-commutative 98.8%

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

   2. fma-define 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

   \[\leadsto \mathsf{fma}\left(y - x, \frac{z}{t}, x\right) \]
6. Add Preprocessing

Alternative 2: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -2e+155)
     t_1
     (if (<= (/ z t) -1e+110)
       (* x (/ z (- t)))
       (if (or (<= (/ z t) -1000.0) (not (<= (/ z t) 5e-20))) t_1 x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -2e+155) {
		tmp = t_1;
	} else if ((z / t) <= -1e+110) {
		tmp = x * (z / -t);
	} else if (((z / t) <= -1000.0) || !((z / t) <= 5e-20)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-2d+155)) then
        tmp = t_1
    else if ((z / t) <= (-1d+110)) then
        tmp = x * (z / -t)
    else if (((z / t) <= (-1000.0d0)) .or. (.not. ((z / t) <= 5d-20))) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -2e+155) {
		tmp = t_1;
	} else if ((z / t) <= -1e+110) {
		tmp = x * (z / -t);
	} else if (((z / t) <= -1000.0) || !((z / t) <= 5e-20)) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -2e+155:
		tmp = t_1
	elif (z / t) <= -1e+110:
		tmp = x * (z / -t)
	elif ((z / t) <= -1000.0) or not ((z / t) <= 5e-20):
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -2e+155)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e+110)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif ((Float64(z / t) <= -1000.0) || !(Float64(z / t) <= 5e-20))
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -2e+155)
		tmp = t_1;
	elseif ((z / t) <= -1e+110)
		tmp = x * (z / -t);
	elseif (((z / t) <= -1000.0) || ~(((z / t) <= 5e-20)))
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -2e+155], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e+110], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-20]], $MachinePrecision]], t$95$1, x]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -2.00000000000000001e155 or -1e110 < (/.f64 z t) < -1e3 or 4.9999999999999999e-20 < (/.f64 z t)

   1. Initial program 98.2%

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

   3. Taylor expanded in z around inf 86.8%

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

      1. *-commutative 86.8%

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

      2. sub-div 92.1%

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

      3. associate-/r/ 97.0%

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

   5. Applied egg-rr 97.0%

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

      1. associate-/r/ 92.1%

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

   7. Applied egg-rr 92.1%

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

   8. Taylor expanded in y around inf 60.0%

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

      1. associate-/l* 65.7%

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

      2. *-commutative 65.7%

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

   10. Simplified 65.7%

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

   if -2.00000000000000001e155 < (/.f64 z t) < -1e110

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-/l* 71.5%

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

      3. associate-*r* 71.5%

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

      4. *-commutative 71.5%

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

      5. associate-*r/ 71.5%

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

      6. neg-mul-1 71.5%

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

   8. Simplified 71.5%

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

   if -1e3 < (/.f64 z t) < 4.9999999999999999e-20

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 82.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;\frac{z}{t} \leq -1000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ t_2 := x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))) (t_2 (* x (- 1.0 (/ z t)))))
   (if (<= y -5e+207)
     t_1
     (if (<= y -5.2e+43)
       t_2
       (if (<= y -6.4e-27) (* z (/ y t)) (if (<= y 5e+109) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double t_2 = x * (1.0 - (z / t));
	double tmp;
	if (y <= -5e+207) {
		tmp = t_1;
	} else if (y <= -5.2e+43) {
		tmp = t_2;
	} else if (y <= -6.4e-27) {
		tmp = z * (y / t);
	} else if (y <= 5e+109) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (z / t)
    t_2 = x * (1.0d0 - (z / t))
    if (y <= (-5d+207)) then
        tmp = t_1
    else if (y <= (-5.2d+43)) then
        tmp = t_2
    else if (y <= (-6.4d-27)) then
        tmp = z * (y / t)
    else if (y <= 5d+109) then
        tmp = t_2
    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 = y * (z / t);
	double t_2 = x * (1.0 - (z / t));
	double tmp;
	if (y <= -5e+207) {
		tmp = t_1;
	} else if (y <= -5.2e+43) {
		tmp = t_2;
	} else if (y <= -6.4e-27) {
		tmp = z * (y / t);
	} else if (y <= 5e+109) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	t_2 = x * (1.0 - (z / t))
	tmp = 0
	if y <= -5e+207:
		tmp = t_1
	elif y <= -5.2e+43:
		tmp = t_2
	elif y <= -6.4e-27:
		tmp = z * (y / t)
	elif y <= 5e+109:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	t_2 = Float64(x * Float64(1.0 - Float64(z / t)))
	tmp = 0.0
	if (y <= -5e+207)
		tmp = t_1;
	elseif (y <= -5.2e+43)
		tmp = t_2;
	elseif (y <= -6.4e-27)
		tmp = Float64(z * Float64(y / t));
	elseif (y <= 5e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	t_2 = x * (1.0 - (z / t));
	tmp = 0.0;
	if (y <= -5e+207)
		tmp = t_1;
	elseif (y <= -5.2e+43)
		tmp = t_2;
	elseif (y <= -6.4e-27)
		tmp = z * (y / t);
	elseif (y <= 5e+109)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+207], t$95$1, If[LessEqual[y, -5.2e+43], t$95$2, If[LessEqual[y, -6.4e-27], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+109], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999999e207 or 5.0000000000000001e109 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. sub-div 67.2%

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

      3. associate-/r/ 77.8%

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

   5. Applied egg-rr 77.8%

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

      1. associate-/r/ 67.2%

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

   7. Applied egg-rr 67.2%

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

   8. Taylor expanded in y around inf 72.5%

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

      1. associate-/l* 77.8%

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

      2. *-commutative 77.8%

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

   10. Simplified 77.8%

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

   if -4.9999999999999999e207 < y < -5.20000000000000042e43 or -6.39999999999999982e-27 < y < 5.0000000000000001e109

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. unsub-neg 83.4%

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

   5. Simplified 83.4%

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

   if -5.20000000000000042e43 < y < -6.39999999999999982e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.0%

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

   4. Taylor expanded in y around inf 82.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+207}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-27}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 10^{+14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e+27) (not (<= (/ z t) 1e+14)))
   (* z (/ (- y x) t))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 1e+14)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1d+27)) .or. (.not. ((z / t) <= 1d+14))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x * (1.0d0 - (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e+27) || !((z / t) <= 1e+14)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e+27) or not ((z / t) <= 1e+14):
		tmp = z * ((y - x) / t)
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e+27) || !(Float64(z / t) <= 1e+14))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e+27) || ~(((z / t) <= 1e+14)))
		tmp = z * ((y - x) / t);
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e+14]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e27 or 1e14 < (/.f64 z t)

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 87.9%

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

   4. Taylor expanded in y around 0 87.9%

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

      1. mul-1-neg 87.9%

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

      2. distribute-frac-neg2 87.9%

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

      3. +-commutative 87.9%

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

      4. distribute-frac-neg2 87.9%

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

      5. sub-neg 87.9%

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

      6. div-sub 93.1%

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

   6. Simplified 93.1%

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

   if -1e27 < (/.f64 z t) < 1e14

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+27} \lor \neg \left(\frac{z}{t} \leq 10^{+14}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000000000.0) (not (<= (/ z t) 5e+15)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000000.0) || !((z / t) <= 5e+15)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-10000000000000.0d0)) .or. (.not. ((z / t) <= 5d+15))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000000.0) || !((z / t) <= 5e+15)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -10000000000000.0) or not ((z / t) <= 5e+15):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10000000000000.0) || !(Float64(z / t) <= 5e+15))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -10000000000000.0) || ~(((z / t) <= 5e+15)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10000000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e+15]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e13 or 5e15 < (/.f64 z t)

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 88.7%

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

   4. Taylor expanded in y around 0 88.7%

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

      1. mul-1-neg 88.7%

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

      2. distribute-frac-neg2 88.7%

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

      3. +-commutative 88.7%

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

      4. distribute-frac-neg2 88.7%

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

      5. sub-neg 88.7%

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

      6. div-sub 93.9%

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

   6. Simplified 93.9%

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

   if -1e13 < (/.f64 z t) < 5e15

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 92.8%

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

      1. associate-*r/ 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000000 \lor \neg \left(\frac{z}{t} \leq 0.0002\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000000000.0) (not (<= (/ z t) 0.0002)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000000.0) || !((z / t) <= 0.0002)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-10000000000000.0d0)) .or. (.not. ((z / t) <= 0.0002d0))) then
        tmp = (y - x) / (t / z)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000000000.0) || !((z / t) <= 0.0002)) {
		tmp = (y - x) / (t / z);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -10000000000000.0) or not ((z / t) <= 0.0002):
		tmp = (y - x) / (t / z)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10000000000000.0) || !(Float64(z / t) <= 0.0002))
		tmp = Float64(Float64(y - x) / Float64(t / z));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -10000000000000.0) || ~(((z / t) <= 0.0002)))
		tmp = (y - x) / (t / z);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10000000000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e13 or 2.0000000000000001e-4 < (/.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. sub-div 91.7%

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

      3. associate-/r/ 97.2%

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

   5. Applied egg-rr 97.2%

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

   if -1e13 < (/.f64 z t) < 2.0000000000000001e-4

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 95.5%

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

      1. associate-*r/ 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000000000 \lor \neg \left(\frac{z}{t} \leq 0.0002\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1000.0) (not (<= (/ z t) 5e-20))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000.0) || !((z / t) <= 5e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-1000.0d0)) .or. (.not. ((z / t) <= 5d-20))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1000.0) || !((z / t) <= 5e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1000.0) or not ((z / t) <= 5e-20):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1000.0) || !(Float64(z / t) <= 5e-20))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1000.0) || ~(((z / t) <= 5e-20)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-20]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e3 or 4.9999999999999999e-20 < (/.f64 z t)

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. sub-div 91.1%

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

      3. associate-/r/ 97.2%

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

   5. Applied egg-rr 97.2%

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

      1. associate-/r/ 91.1%

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

   7. Applied egg-rr 91.1%

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

   8. Taylor expanded in y around inf 57.3%

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

      1. associate-/l* 62.5%

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

      2. *-commutative 62.5%

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

   10. Simplified 62.5%

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

   if -1e3 < (/.f64 z t) < 4.9999999999999999e-20

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 82.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1000 \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-18} \lor \neg \left(z \leq 9.5 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e-18) (not (<= z 9.5e+60))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-18) || !(z <= 9.5e+60)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5d-18)) .or. (.not. (z <= 9.5d+60))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-18) || !(z <= 9.5e+60)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e-18) or not (z <= 9.5e+60):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e-18) || !(z <= 9.5e+60))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5e-18) || ~((z <= 9.5e+60)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e-18], N[Not[LessEqual[z, 9.5e+60]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000036e-18 or 9.49999999999999988e60 < z

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 79.6%

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

   4. Taylor expanded in y around inf 58.8%

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

   if -5.00000000000000036e-18 < z < 9.49999999999999988e60

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 62.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-18} \lor \neg \left(z \leq 9.5 \cdot 10^{+60}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x) * (z / t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 10: 38.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in z around 0 43.2%

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

4. Final simplification 43.2%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{z}{t}\\ t_2 := x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{if}\;t\_1 < -1013646692435.8867:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 < 0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
   (if (< t_1 -1013646692435.8867)
     t_2
     (if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - x) * (z / t)
    t_2 = x + ((y - x) / (t / z))
    if (t_1 < (-1013646692435.8867d0)) then
        tmp = t_2
    else if (t_1 < 0.0d0) then
        tmp = x + (((y - x) * z) / t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (z / t);
	double t_2 = x + ((y - x) / (t / z));
	double tmp;
	if (t_1 < -1013646692435.8867) {
		tmp = t_2;
	} else if (t_1 < 0.0) {
		tmp = x + (((y - x) * z) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (z / t)
	t_2 = x + ((y - x) / (t / z))
	tmp = 0
	if t_1 < -1013646692435.8867:
		tmp = t_2
	elif t_1 < 0.0:
		tmp = x + (((y - x) * z) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(z / t))
	t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z)))
	tmp = 0.0
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (z / t);
	t_2 = x + ((y - x) / (t / z));
	tmp = 0.0;
	if (t_1 < -1013646692435.8867)
		tmp = t_2;
	elseif (t_1 < 0.0)
		tmp = x + (((y - x) * z) / t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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