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

Percentage Accurate: 97.7% → 97.7%

Time: 5.5s

Alternatives: 9

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: 97.7% 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: 97.7% 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 96.5%

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

   1. +-commutative 96.5%

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

   2. fma-def 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+305}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ z t)))))
   (if (<= (/ z t) -1e+305)
     (* z (/ y t))
     (if (<= (/ z t) -4e+42)
       t_1
       (if (<= (/ z t) -1e-30) (* y (/ z t)) (if (<= (/ z t) 0.2) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -(z / t);
	double tmp;
	if ((z / t) <= -1e+305) {
		tmp = z * (y / t);
	} else if ((z / t) <= -4e+42) {
		tmp = t_1;
	} else if ((z / t) <= -1e-30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 0.2) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -(z / t)
    if ((z / t) <= (-1d+305)) then
        tmp = z * (y / t)
    else if ((z / t) <= (-4d+42)) then
        tmp = t_1
    else if ((z / t) <= (-1d-30)) then
        tmp = y * (z / t)
    else if ((z / t) <= 0.2d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -(z / t);
	double tmp;
	if ((z / t) <= -1e+305) {
		tmp = z * (y / t);
	} else if ((z / t) <= -4e+42) {
		tmp = t_1;
	} else if ((z / t) <= -1e-30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 0.2) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -(z / t)
	tmp = 0
	if (z / t) <= -1e+305:
		tmp = z * (y / t)
	elif (z / t) <= -4e+42:
		tmp = t_1
	elif (z / t) <= -1e-30:
		tmp = y * (z / t)
	elif (z / t) <= 0.2:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-Float64(z / t)))
	tmp = 0.0
	if (Float64(z / t) <= -1e+305)
		tmp = Float64(z * Float64(y / t));
	elseif (Float64(z / t) <= -4e+42)
		tmp = t_1;
	elseif (Float64(z / t) <= -1e-30)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 0.2)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -(z / t);
	tmp = 0.0;
	if ((z / t) <= -1e+305)
		tmp = z * (y / t);
	elseif ((z / t) <= -4e+42)
		tmp = t_1;
	elseif ((z / t) <= -1e-30)
		tmp = y * (z / t);
	elseif ((z / t) <= 0.2)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-N[(z / t), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -1e+305], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], -4e+42], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], -1e-30], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.2], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 z t) < -9.9999999999999994e304

   1. Initial program 73.5%

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

   2. Taylor expanded in z around inf 92.6%

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

   3. Taylor expanded in y around inf 68.3%

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

   if -9.9999999999999994e304 < (/.f64 z t) < -4.00000000000000018e42 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 88.7%

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

      1. sub-div 92.4%

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

      2. associate-/r/ 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*r/ 66.6%

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

      3. associate-*r* 66.6%

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

      4. neg-mul-1 66.6%

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

      5. *-commutative 66.6%

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

   7. Simplified 66.6%

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

   if -4.00000000000000018e42 < (/.f64 z t) < -1e-30

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 64.0%

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

      1. associate-*r/ 85.5%

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

   4. Simplified 85.5%

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

      1. +-commutative 85.5%

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

      2. *-commutative 85.5%

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

      3. fma-def 85.5%

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

   6. Applied egg-rr 85.5%

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

   7. Taylor expanded in z around inf 61.4%

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

      1. associate-*r/ 77.3%

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

   9. Simplified 77.3%

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

   if -1e-30 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0 70.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{+305}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq -4 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \mathbf{elif}\;\frac{z}{t} \leq -1 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{z}{t}\right)\\ \end{array} \]

Alternative 3: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-30} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e-30) (not (<= (/ z t) 2e-20))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e-30) || !((z / t) <= 2e-20)) {
		tmp = z * ((y - x) / 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) <= (-1d-30)) .or. (.not. ((z / t) <= 2d-20))) then
        tmp = z * ((y - x) / 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) <= -1e-30) || !((z / t) <= 2e-20)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e-30) or not ((z / t) <= 2e-20):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -1e-30) || !(Float64(z / t) <= 2e-20))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -1e-30) || ~(((z / t) <= 2e-20)))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -1e-30], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e-30 or 1.99999999999999989e-20 < (/.f64 z t)

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 86.0%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. +-commutative 86.0%

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

      3. sub-neg 86.0%

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

      4. div-sub 89.5%

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

   5. Simplified 89.5%

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

   if -1e-30 < (/.f64 z t) < 1.99999999999999989e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 71.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-30} \lor \neg \left(\frac{z}{t} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+31} \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e+31) (not (<= (/ z t) 0.2)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e+31) || !((z / t) <= 0.2)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-2d+31)) .or. (.not. ((z / t) <= 0.2d0))) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e+31) || !((z / t) <= 0.2)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e+31) or not ((z / t) <= 0.2):
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -2e+31) || !(Float64(z / t) <= 0.2))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z / t) <= -2e+31) || ~(((z / t) <= 0.2)))
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -2e+31], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.2]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1.9999999999999999e31 or 0.20000000000000001 < (/.f64 z t)

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 89.3%

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

   3. Taylor expanded in y around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. +-commutative 89.3%

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

      3. sub-neg 89.3%

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

      4. div-sub 93.3%

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

   5. Simplified 93.3%

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

   if -1.9999999999999999e31 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 91.9%

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

      1. associate-*r/ 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+31} \lor \neg \left(\frac{z}{t} \leq 0.2\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -4e+42)
   (/ (* (- y x) z) t)
   (if (<= (/ z t) 0.2) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -4e+42) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 0.2) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / 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) <= (-4d+42)) then
        tmp = ((y - x) * z) / t
    else if ((z / t) <= 0.2d0) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / 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) <= -4e+42) {
		tmp = ((y - x) * z) / t;
	} else if ((z / t) <= 0.2) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -4e+42:
		tmp = ((y - x) * z) / t
	elif (z / t) <= 0.2:
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -4e+42)
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	elseif (Float64(z / t) <= 0.2)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -4e+42)
		tmp = ((y - x) * z) / t;
	elseif ((z / t) <= 0.2)
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -4e+42], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.2], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.00000000000000018e42

   1. Initial program 93.9%

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

   2. Taylor expanded in z around inf 89.1%

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

   3. Taylor expanded in t around inf 96.8%

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

   if -4.00000000000000018e42 < (/.f64 z t) < 0.20000000000000001

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. associate-*r/ 95.8%

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

   4. Simplified 95.8%

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

   if 0.20000000000000001 < (/.f64 z t)

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 89.1%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. neg-mul-1 89.1%

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

      2. +-commutative 89.1%

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

      3. sub-neg 89.1%

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

      4. div-sub 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.2:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 6: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -3 \cdot 10^{-34} \lor \neg \left(\frac{z}{t} \leq 2.4 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -3e-34) (not (<= (/ z t) 2.4e-16))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -3e-34) || !((z / t) <= 2.4e-16)) {
		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) <= (-3d-34)) .or. (.not. ((z / t) <= 2.4d-16))) 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) <= -3e-34) || !((z / t) <= 2.4e-16)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -3e-34) or not ((z / t) <= 2.4e-16):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -3e-34) || !(Float64(z / t) <= 2.4e-16))
		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) <= -3e-34) || ~(((z / t) <= 2.4e-16)))
		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], -3e-34], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2.4e-16]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -3e-34 or 2.40000000000000005e-16 < (/.f64 z t)

   1. Initial program 95.4%

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

   2. Taylor expanded in y around inf 50.5%

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

      1. associate-*r/ 52.2%

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

   4. Simplified 52.2%

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

      1. +-commutative 52.2%

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

      2. *-commutative 52.2%

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

      3. fma-def 52.2%

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

   6. Applied egg-rr 52.2%

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

   7. Taylor expanded in z around inf 49.8%

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

      1. associate-*r/ 50.7%

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

   9. Simplified 50.7%

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

   if -3e-34 < (/.f64 z t) < 2.40000000000000005e-16

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 71.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -3 \cdot 10^{-34} \lor \neg \left(\frac{z}{t} \leq 2.4 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -1e-30)
   (* y (/ z t))
   (if (<= (/ z t) 2e-20) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-20) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z / t) <= (-1d-30)) then
        tmp = y * (z / t)
    else if ((z / t) <= 2d-20) then
        tmp = x
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -1e-30) {
		tmp = y * (z / t);
	} else if ((z / t) <= 2e-20) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -1e-30:
		tmp = y * (z / t)
	elif (z / t) <= 2e-20:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -1e-30)
		tmp = Float64(y * Float64(z / t));
	elseif (Float64(z / t) <= 2e-20)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -1e-30)
		tmp = y * (z / t);
	elseif ((z / t) <= 2e-20)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -1e-30], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 2e-20], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -1e-30

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 50.6%

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

      1. associate-*r/ 52.4%

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

   4. Simplified 52.4%

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

      1. +-commutative 52.4%

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

      2. *-commutative 52.4%

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

      3. fma-def 52.4%

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

   6. Applied egg-rr 52.4%

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

   7. Taylor expanded in z around inf 49.1%

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

      1. associate-*r/ 49.7%

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

   9. Simplified 49.7%

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

   if -1e-30 < (/.f64 z t) < 1.99999999999999989e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 71.2%

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

   if 1.99999999999999989e-20 < (/.f64 z t)

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf 87.9%

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

   3. Taylor expanded in y around inf 52.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 97.7% 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 96.5%

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

2. Final simplification 96.5%

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

Alternative 9: 38.5% 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 96.5%

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

2. Taylor expanded in z around 0 33.4%

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

3. Final simplification 33.4%

   \[\leadsto x \]

Developer target: 97.6% 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 2023224 
(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))))