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

Percentage Accurate: 97.6% → 97.6%

Time: 5.1s

Alternatives: 8

Speedup: 1.0×

• 24.7% 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: 97.6% 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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - x) / (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 - x) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. clear-num 97.6%

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

   2. un-div-inv 97.7%

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

3. Applied egg-rr 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-45) (not (<= (/ z t) 2e-15))) (* (- y x) (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-45) || !((z / t) <= 2e-15)) {
		tmp = (y - x) * (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) <= (-5d-45)) .or. (.not. ((z / t) <= 2d-15))) then
        tmp = (y - x) * (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) <= -5e-45) || !((z / t) <= 2e-15)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-45) or not ((z / t) <= 2e-15):
		tmp = (y - x) * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-45) || !(Float64(z / t) <= 2e-15))
		tmp = Float64(Float64(y - x) * 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) <= -5e-45) || ~(((z / t) <= 2e-15)))
		tmp = (y - x) * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-45], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-15]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999976e-45 or 2.0000000000000002e-15 < (/.f64 z t)

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. sub-div 88.0%

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

      2. associate-/r/ 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in y around 0 78.0%

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

      1. fma-def 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r/ 76.1%

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

      4. fma-def 76.1%

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

      5. neg-mul-1 76.1%

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

      6. +-commutative 76.1%

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

      7. sub-neg 76.1%

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

      8. associate-*r/ 78.0%

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

      9. associate-/l* 76.1%

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

      10. associate-/l* 73.8%

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

      11. div-sub 93.7%

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

      12. associate-/l* 90.6%

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

      13. associate-*r/ 93.6%

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

   7. Simplified 93.6%

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

   if -4.99999999999999976e-45 < (/.f64 z t) < 2.0000000000000002e-15

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 85.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.1\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 0.1)))
   (* (- y x) (/ z t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 0.1)) {
		tmp = (y - x) * (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 (((z / t) <= (-2.0d0)) .or. (.not. ((z / t) <= 0.1d0))) then
        tmp = (y - x) * (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 (((z / t) <= -2.0) || !((z / t) <= 0.1)) {
		tmp = (y - x) * (z / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2.0) or not ((z / t) <= 0.1):
		tmp = (y - x) * (z / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2.0) || !(Float64(z / t) <= 0.1))
		tmp = Float64(Float64(y - x) * 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 (((z / t) <= -2.0) || ~(((z / t) <= 0.1)))
		tmp = (y - x) * (z / 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], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.1]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z / 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) < -2 or 0.10000000000000001 < (/.f64 z t)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. sub-div 92.2%

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

      2. associate-/r/ 96.8%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in y around 0 80.5%

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

      1. fma-def 80.5%

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

      2. *-commutative 80.5%

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

      3. associate-*r/ 77.5%

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

      4. fma-def 77.5%

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

      5. neg-mul-1 77.5%

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

      6. +-commutative 77.5%

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

      7. sub-neg 77.5%

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

      8. associate-*r/ 80.5%

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

      9. associate-/l* 77.6%

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

      10. associate-/l* 75.0%

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

      11. div-sub 96.8%

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

      12. associate-/l* 94.2%

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

      13. associate-*r/ 96.7%

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

   7. Simplified 96.7%

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

   if -2 < (/.f64 z t) < 0.10000000000000001

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 93.9%

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

      1. associate-*r/ 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.1\right):\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.1\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2.0) (not (<= (/ z t) 0.1)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2.0) || !((z / t) <= 0.1)) {
		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) <= (-2.0d0)) .or. (.not. ((z / t) <= 0.1d0))) 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) <= -2.0) || !((z / t) <= 0.1)) {
		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) <= -2.0) or not ((z / t) <= 0.1):
		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) <= -2.0) || !(Float64(z / t) <= 0.1))
		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) <= -2.0) || ~(((z / t) <= 0.1)))
		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], -2.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.1]], $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) < -2 or 0.10000000000000001 < (/.f64 z t)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. sub-div 92.2%

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

      2. associate-/r/ 96.8%

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

   4. Applied egg-rr 96.8%

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

   if -2 < (/.f64 z t) < 0.10000000000000001

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf 93.9%

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

      1. associate-*r/ 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \lor \neg \left(\frac{z}{t} \leq 0.1\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-45) (not (<= (/ z t) 2e-15))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-45) || !((z / t) <= 2e-15)) {
		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) <= (-5d-45)) .or. (.not. ((z / t) <= 2d-15))) 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) <= -5e-45) || !((z / t) <= 2e-15)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-45) or not ((z / t) <= 2e-15):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-45) || !(Float64(z / t) <= 2e-15))
		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) <= -5e-45) || ~(((z / t) <= 2e-15)))
		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], -5e-45], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-15]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999976e-45 or 2.0000000000000002e-15 < (/.f64 z t)

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. sub-div 88.0%

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

      2. associate-/r/ 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 62.0%

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

   7. Simplified 62.0%

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

   if -4.99999999999999976e-45 < (/.f64 z t) < 2.0000000000000002e-15

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 85.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-45) (not (<= (/ z t) 2e-15))) (/ y (/ t z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-45) || !((z / t) <= 2e-15)) {
		tmp = y / (t / z);
	} 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) <= (-5d-45)) .or. (.not. ((z / t) <= 2d-15))) then
        tmp = y / (t / z)
    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) <= -5e-45) || !((z / t) <= 2e-15)) {
		tmp = y / (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-45) or not ((z / t) <= 2e-15):
		tmp = y / (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-45) || !(Float64(z / t) <= 2e-15))
		tmp = Float64(y / Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -5e-45) || ~(((z / t) <= 2e-15)))
		tmp = y / (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-45], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-15]], $MachinePrecision]], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999976e-45 or 2.0000000000000002e-15 < (/.f64 z t)

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 81.4%

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

      1. sub-div 88.0%

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

      2. associate-/r/ 93.7%

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

   4. Applied egg-rr 93.7%

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

   5. Taylor expanded in y around inf 57.8%

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

      1. associate-*r/ 62.0%

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

   7. Simplified 62.0%

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

      1. clear-num 61.9%

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

      2. div-inv 62.0%

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

   9. Applied egg-rr 62.0%

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

   if -4.99999999999999976e-45 < (/.f64 z t) < 2.0000000000000002e-15

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 85.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-45} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 97.6% 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 97.6%

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

2. Final simplification 97.6%

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

Alternative 8: 38.8% 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 97.6%

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

2. Taylor expanded in z around 0 42.7%

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

3. Final simplification 42.7%

   \[\leadsto x \]

Developer target: 97.4% accurate, 0.4× 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 2023181 
(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))))