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

Percentage Accurate: 97.9% → 97.9%

Time: 6.3s

Alternatives: 10

Speedup: 1.0×

• 24.9% 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: 97.9% 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: 97.9% 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 98.4%

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

   1. +-commutative 98.4%

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

   2. fma-def 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -4e+174)
   (* x (/ (- z) t))
   (if (or (<= (/ z t) -5e-67) (not (<= (/ z t) 1e-35))) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -4e+174) {
		tmp = x * (-z / t);
	} else if (((z / t) <= -5e-67) || !((z / t) <= 1e-35)) {
		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+174)) then
        tmp = x * (-z / t)
    else if (((z / t) <= (-5d-67)) .or. (.not. ((z / t) <= 1d-35))) 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+174) {
		tmp = x * (-z / t);
	} else if (((z / t) <= -5e-67) || !((z / t) <= 1e-35)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -4e+174:
		tmp = x * (-z / t)
	elif ((z / t) <= -5e-67) or not ((z / t) <= 1e-35):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -4e+174)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif ((Float64(z / t) <= -5e-67) || !(Float64(z / t) <= 1e-35))
		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+174)
		tmp = x * (-z / t);
	elseif (((z / t) <= -5e-67) || ~(((z / t) <= 1e-35)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -4e+174], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-67], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-35]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.00000000000000028e174

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in z around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg 65.2%

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

   7. Simplified 65.2%

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

   if -4.00000000000000028e174 < (/.f64 z t) < -4.9999999999999999e-67 or 1.00000000000000001e-35 < (/.f64 z t)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 82.3%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. clear-num 53.1%

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

      2. un-div-inv 53.4%

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

   5. Applied egg-rr 53.4%

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

      1. associate-/r/ 59.3%

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

   7. Applied egg-rr 59.3%

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

   if -4.9999999999999999e-67 < (/.f64 z t) < 1.00000000000000001e-35

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 80.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 64.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -4e+174)
   (* z (/ (- x) t))
   (if (or (<= (/ z t) -5e-67) (not (<= (/ z t) 1e-35))) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -4e+174) {
		tmp = z * (-x / t);
	} else if (((z / t) <= -5e-67) || !((z / t) <= 1e-35)) {
		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+174)) then
        tmp = z * (-x / t)
    else if (((z / t) <= (-5d-67)) .or. (.not. ((z / t) <= 1d-35))) 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+174) {
		tmp = z * (-x / t);
	} else if (((z / t) <= -5e-67) || !((z / t) <= 1e-35)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -4e+174:
		tmp = z * (-x / t)
	elif ((z / t) <= -5e-67) or not ((z / t) <= 1e-35):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -4e+174)
		tmp = Float64(z * Float64(Float64(-x) / t));
	elseif ((Float64(z / t) <= -5e-67) || !(Float64(z / t) <= 1e-35))
		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+174)
		tmp = z * (-x / t);
	elseif (((z / t) <= -5e-67) || ~(((z / t) <= 1e-35)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -4e+174], N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(z / t), $MachinePrecision], -5e-67], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-35]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.00000000000000028e174

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 96.3%

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

   3. Taylor expanded in y around 0 68.5%

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

      1. neg-mul-1 68.5%

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

      2. distribute-neg-frac 68.5%

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

   5. Simplified 68.5%

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

   if -4.00000000000000028e174 < (/.f64 z t) < -4.9999999999999999e-67 or 1.00000000000000001e-35 < (/.f64 z t)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 82.3%

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

   3. Taylor expanded in y around inf 54.1%

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

      1. clear-num 53.1%

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

      2. un-div-inv 53.4%

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

   5. Applied egg-rr 53.4%

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

      1. associate-/r/ 59.3%

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

   7. Applied egg-rr 59.3%

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

   if -4.9999999999999999e-67 < (/.f64 z t) < 1.00000000000000001e-35

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 80.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 96.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5.0) (not (<= (/ z t) 0.2)))
   (/ (- y x) (/ t z))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5.0) || !((z / t) <= 0.2)) {
		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) <= (-5.0d0)) .or. (.not. ((z / t) <= 0.2d0))) 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) <= -5.0) || !((z / t) <= 0.2)) {
		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) <= -5.0) or not ((z / t) <= 0.2):
		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) <= -5.0) || !(Float64(z / t) <= 0.2))
		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) <= -5.0) || ~(((z / t) <= 0.2)))
		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], -5.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.2]], $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) < -5 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf 90.3%

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

      1. *-commutative 90.3%

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

      2. sub-div 92.6%

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

      3. associate-/r/ 96.7%

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

   4. Applied egg-rr 96.7%

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

   if -5 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 99.1%

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

   2. Taylor expanded in y around inf 94.5%

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

      1. associate-*r/ 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-67) (not (<= (/ z t) 1e-35))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-67) || !((z / t) <= 1e-35)) {
		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-67)) .or. (.not. ((z / t) <= 1d-35))) 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-67) || !((z / t) <= 1e-35)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-67) or not ((z / t) <= 1e-35):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-67) || !(Float64(z / t) <= 1e-35))
		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-67) || ~(((z / t) <= 1e-35)))
		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-67], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-35]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.9999999999999999e-67 or 1.00000000000000001e-35 < (/.f64 z t)

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 85.0%

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

   3. Taylor expanded in y around inf 51.5%

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

      1. clear-num 50.7%

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

      2. un-div-inv 50.9%

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

   5. Applied egg-rr 50.9%

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

      1. associate-/r/ 57.0%

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

   7. Applied egg-rr 57.0%

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

   if -4.9999999999999999e-67 < (/.f64 z t) < 1.00000000000000001e-35

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 80.0%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-67} \lor \neg \left(\frac{z}{t} \leq 10^{-35}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-63} \lor \neg \left(x \leq 2.76 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.9e-63) (not (<= x 2.76e-132)))
   (* x (- 1.0 (/ z t)))
   (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.9e-63) || !(x <= 2.76e-132)) {
		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 <= (-4.9d-63)) .or. (.not. (x <= 2.76d-132))) 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 <= -4.9e-63) || !(x <= 2.76e-132)) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.9e-63) or not (x <= 2.76e-132):
		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 <= -4.9e-63) || !(x <= 2.76e-132))
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.9e-63) || ~((x <= 2.76e-132)))
		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, -4.9e-63], N[Not[LessEqual[x, 2.76e-132]], $MachinePrecision]], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.90000000000000015e-63 or 2.76e-132 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 82.5%

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

      1. mul-1-neg 82.5%

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

      2. unsub-neg 82.5%

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

   4. Simplified 82.5%

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

   if -4.90000000000000015e-63 < x < 2.76e-132

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 73.2%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. clear-num 66.3%

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

      2. un-div-inv 66.7%

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

   5. Applied egg-rr 66.7%

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

      1. associate-/r/ 71.6%

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

   7. Applied egg-rr 71.6%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-63} \lor \neg \left(x \leq 2.76 \cdot 10^{-132}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 7: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-167} \lor \neg \left(y \leq 2.6 \cdot 10^{-127}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.6e-167) (not (<= y 2.6e-127)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.6e-167) || !(y <= 2.6e-127)) {
		tmp = x + (y * (z / 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 ((y <= (-2.6d-167)) .or. (.not. (y <= 2.6d-127))) then
        tmp = x + (y * (z / 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 ((y <= -2.6e-167) || !(y <= 2.6e-127)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.6e-167) or not (y <= 2.6e-127):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.6e-167) || !(y <= 2.6e-127))
		tmp = Float64(x + Float64(y * Float64(z / 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 ((y <= -2.6e-167) || ~((y <= 2.6e-127)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.6e-167], N[Not[LessEqual[y, 2.6e-127]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5999999999999999e-167 or 2.59999999999999991e-127 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 85.4%

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

      1. associate-*r/ 89.0%

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

   4. Simplified 89.0%

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

   if -2.5999999999999999e-167 < y < 2.59999999999999991e-127

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. unsub-neg 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-167} \lor \neg \left(y \leq 2.6 \cdot 10^{-127}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.12e-29) x (if (<= t 4e-57) (* z (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.12e-29) {
		tmp = x;
	} else if (t <= 4e-57) {
		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 (t <= (-1.12d-29)) then
        tmp = x
    else if (t <= 4d-57) 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 (t <= -1.12e-29) {
		tmp = x;
	} else if (t <= 4e-57) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.12e-29:
		tmp = x
	elif t <= 4e-57:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.12e-29)
		tmp = x;
	elseif (t <= 4e-57)
		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 (t <= -1.12e-29)
		tmp = x;
	elseif (t <= 4e-57)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.12e-29], x, If[LessEqual[t, 4e-57], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.11999999999999995e-29 or 3.99999999999999982e-57 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 61.2%

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

   if -1.11999999999999995e-29 < t < 3.99999999999999982e-57

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 79.7%

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

   3. Taylor expanded in y around inf 49.2%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-29}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 97.9% 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 98.4%

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

2. Final simplification 98.4%

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

Alternative 10: 38.0% 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 98.4%

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

2. Taylor expanded in z around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto x \]

Developer target: 97.7% 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 2023322 
(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))))