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

Percentage Accurate: 97.8% → 97.8%

Time: 6.4s

Alternatives: 6

Speedup: 1.0×

• 25.1% 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, 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 97.2%

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

Alternative 2: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e-27) (not (<= (/ z t) 5e-47))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e-27) || !((z / t) <= 5e-47)) {
		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) <= (-4d-27)) .or. (.not. ((z / t) <= 5d-47))) 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) <= -4e-27) || !((z / t) <= 5e-47)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -4e-27) or not ((z / t) <= 5e-47):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -4e-27) || !(Float64(z / t) <= 5e-47))
		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) <= -4e-27) || ~(((z / t) <= 5e-47)))
		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], -4e-27], N[Not[LessEqual[N[(z / t), $MachinePrecision], 5e-47]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.0000000000000002e-27 or 5.00000000000000011e-47 < (/.f64 z t)

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. remove-double-neg 74.8%

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

      3. mul-1-neg 74.8%

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

      4. distribute-neg-in 74.8%

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

      5. *-commutative 74.8%

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

      6. times-frac 83.9%

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

      7. distribute-rgt-out 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in z around 0 89.2%

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

      1. associate-*r/ 89.2%

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

      2. associate-*r* 89.2%

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

      3. sub-neg 89.2%

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

      4. metadata-eval 89.2%

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

      5. associate-*r/ 89.8%

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

      6. associate-*l/ 91.1%

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

      7. *-commutative 91.1%

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

      8. neg-mul-1 91.1%

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

      9. distribute-rgt-neg-in 91.1%

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

      10. distribute-lft-neg-in 91.1%

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

      11. cancel-sign-sub-inv 91.1%

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

      12. *-commutative 91.1%

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

      13. associate-*l/ 89.8%

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

      14. associate-/l* 86.3%

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

      15. associate-*r* 85.9%

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

      16. *-commutative 85.9%

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

      17. +-commutative 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in x around 0 57.5%

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

       1. associate-/l* 60.2%

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

   11. Simplified 60.2%

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

   if -4.0000000000000002e-27 < (/.f64 z t) < 5.00000000000000011e-47

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 73.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{-27} \lor \neg \left(\frac{z}{t} \leq 5 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-15} \lor \neg \left(x \leq 2.2 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.65e-15) (not (<= x 2.2e+91)))
   (/ x (/ t (- t z)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.65e-15) || !(x <= 2.2e+91)) {
		tmp = x / (t / (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 ((x <= (-1.65d-15)) .or. (.not. (x <= 2.2d+91))) then
        tmp = x / (t / (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 ((x <= -1.65e-15) || !(x <= 2.2e+91)) {
		tmp = x / (t / (t - z));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.65e-15) or not (x <= 2.2e+91):
		tmp = x / (t / (t - z))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.65e-15) || !(x <= 2.2e+91))
		tmp = Float64(x / Float64(t / 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 ((x <= -1.65e-15) || ~((x <= 2.2e+91)))
		tmp = x / (t / (t - z));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.65e-15], N[Not[LessEqual[x, 2.2e+91]], $MachinePrecision]], N[(x / N[(t / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-15 or 2.19999999999999999e91 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around 0 88.1%

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

      1. clear-num 88.1%

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

      2. un-div-inv 88.2%

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

   8. Applied egg-rr 88.2%

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

   if -1.65e-15 < x < 2.19999999999999999e91

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 86.8%

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

      1. associate-*r/ 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-15} \lor \neg \left(x \leq 2.2 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{\frac{t}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-17} \lor \neg \left(x \leq 1.2 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.2e-17) (not (<= x 1.2e+91)))
   (* x (- 1.0 (/ z t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.2e-17) || !(x <= 1.2e+91)) {
		tmp = x * (1.0 - (z / 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 ((x <= (-8.2d-17)) .or. (.not. (x <= 1.2d+91))) then
        tmp = x * (1.0d0 - (z / 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 ((x <= -8.2e-17) || !(x <= 1.2e+91)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.2e-17) or not (x <= 1.2e+91):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.2e-17) || !(x <= 1.2e+91))
		tmp = Float64(x * Float64(1.0 - Float64(z / 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 ((x <= -8.2e-17) || ~((x <= 1.2e+91)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.2e-17], N[Not[LessEqual[x, 1.2e+91]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000001e-17 or 1.19999999999999991e91 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   if -8.2000000000000001e-17 < x < 1.19999999999999991e91

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf 86.8%

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

      1. associate-*r/ 87.2%

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

   5. Simplified 87.2%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-17} \lor \neg \left(x \leq 1.2 \cdot 10^{+91}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-226} \lor \neg \left(x \leq 3.4 \cdot 10^{-115}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.8e-226) (not (<= x 3.4e-115)))
   (* x (- 1.0 (/ z t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e-226) || !(x <= 3.4e-115)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (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 ((x <= (-4.8d-226)) .or. (.not. (x <= 3.4d-115))) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = (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 ((x <= -4.8e-226) || !(x <= 3.4e-115)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.8e-226) or not (x <= 3.4e-115):
		tmp = x * (1.0 - (z / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.8e-226) || !(x <= 3.4e-115))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.8e-226) || ~((x <= 3.4e-115)))
		tmp = x * (1.0 - (z / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.8e-226], N[Not[LessEqual[x, 3.4e-115]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999999e-226 or 3.3999999999999998e-115 < x

   1. Initial program 98.8%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   5. Simplified 75.9%

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

   if -4.7999999999999999e-226 < x < 3.3999999999999998e-115

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. remove-double-neg 80.5%

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

      3. mul-1-neg 80.5%

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

      4. distribute-neg-in 80.5%

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

      5. *-commutative 80.5%

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

      6. times-frac 88.1%

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

      7. distribute-rgt-out 93.3%

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

   5. Simplified 93.3%

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

   6. Taylor expanded in z around 0 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-*r* 94.6%

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

      3. sub-neg 94.6%

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

      4. metadata-eval 94.6%

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

      5. associate-*r/ 93.3%

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

      6. associate-*l/ 93.3%

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

      7. *-commutative 93.3%

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

      8. neg-mul-1 93.3%

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

      9. distribute-rgt-neg-in 93.3%

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

      10. distribute-lft-neg-in 93.3%

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

      11. cancel-sign-sub-inv 93.3%

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

      12. *-commutative 93.3%

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

      13. associate-*l/ 93.3%

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

      14. associate-/l* 92.0%

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

      15. associate-*r* 91.4%

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

      16. *-commutative 91.4%

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

      17. +-commutative 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in x around 0 76.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-226} \lor \neg \left(x \leq 3.4 \cdot 10^{-115}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in z around 0 36.5%

   \[\leadsto \color{blue}{x} \]
4. 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 2024091 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (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))))