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

Percentage Accurate: 97.4% → 97.4%

Time: 5.4s

Alternatives: 9

Speedup: 1.0×

• 25.0% 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: 97.4% 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: 97.4% 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 97.6%

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

   1. +-commutative 97.6%

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

   2. fma-def 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 2: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t}\\ \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z t))))
   (if (<= (/ z t) -5e-50)
     t_1
     (if (<= (/ z t) 1e-87) x (if (<= (/ z t) 5e+54) t_1 (* x (/ (- z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e-50) {
		tmp = t_1;
	} else if ((z / t) <= 1e-87) {
		tmp = x;
	} else if ((z / t) <= 5e+54) {
		tmp = t_1;
	} else {
		tmp = x * (-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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / t)
    if ((z / t) <= (-5d-50)) then
        tmp = t_1
    else if ((z / t) <= 1d-87) then
        tmp = x
    else if ((z / t) <= 5d+54) then
        tmp = t_1
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / t);
	double tmp;
	if ((z / t) <= -5e-50) {
		tmp = t_1;
	} else if ((z / t) <= 1e-87) {
		tmp = x;
	} else if ((z / t) <= 5e+54) {
		tmp = t_1;
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / t)
	tmp = 0
	if (z / t) <= -5e-50:
		tmp = t_1
	elif (z / t) <= 1e-87:
		tmp = x
	elif (z / t) <= 5e+54:
		tmp = t_1
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / t))
	tmp = 0.0
	if (Float64(z / t) <= -5e-50)
		tmp = t_1;
	elseif (Float64(z / t) <= 1e-87)
		tmp = x;
	elseif (Float64(z / t) <= 5e+54)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / t);
	tmp = 0.0;
	if ((z / t) <= -5e-50)
		tmp = t_1;
	elseif ((z / t) <= 1e-87)
		tmp = x;
	elseif ((z / t) <= 5e+54)
		tmp = t_1;
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z / t), $MachinePrecision], -5e-50], t$95$1, If[LessEqual[N[(z / t), $MachinePrecision], 1e-87], x, If[LessEqual[N[(z / t), $MachinePrecision], 5e+54], t$95$1, N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -4.99999999999999968e-50 or 1.00000000000000002e-87 < (/.f64 z t) < 5.00000000000000005e54

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. sub-div 77.6%

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

      3. associate-/r/ 85.2%

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

   4. Applied egg-rr 85.2%

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

   5. Taylor expanded in y around inf 50.0%

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

      1. associate-*r/ 57.0%

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

   7. Simplified 57.0%

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

   if -4.99999999999999968e-50 < (/.f64 z t) < 1.00000000000000002e-87

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 82.0%

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

   if 5.00000000000000005e54 < (/.f64 z t)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 89.2%

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

   3. Taylor expanded in y around 0 89.2%

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

      1. neg-mul-1 89.2%

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

      2. +-commutative 89.2%

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

      3. sub-neg 89.2%

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

      4. div-sub 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 62.0%

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

      1. associate-*r/ 62.0%

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

      2. mul-1-neg 62.0%

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

      3. distribute-rgt-neg-in 62.0%

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

      4. associate-*r/ 68.5%

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

   8. Simplified 68.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;\frac{z}{t} \leq 5 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]

Alternative 3: 83.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-7} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-67}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -1e-7) (not (<= (/ z t) 4e-67))) (* z (/ (- y x) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -1e-7) || !((z / t) <= 4e-67)) {
		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-7)) .or. (.not. ((z / t) <= 4d-67))) 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-7) || !((z / t) <= 4e-67)) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -1e-7) or not ((z / t) <= 4e-67):
		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-7) || !(Float64(z / t) <= 4e-67))
		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-7) || ~(((z / t) <= 4e-67)))
		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-7], N[Not[LessEqual[N[(z / t), $MachinePrecision], 4e-67]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -9.9999999999999995e-8 or 3.99999999999999977e-67 < (/.f64 z t)

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 84.9%

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

   3. Taylor expanded in y around 0 84.9%

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

      1. neg-mul-1 84.9%

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

      2. +-commutative 84.9%

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

      3. sub-neg 84.9%

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

      4. div-sub 88.6%

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

   5. Simplified 88.6%

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

   if -9.9999999999999995e-8 < (/.f64 z t) < 3.99999999999999977e-67

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 78.6%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -1 \cdot 10^{-7} \lor \neg \left(\frac{z}{t} \leq 4 \cdot 10^{-67}\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+67} \lor \neg \left(\frac{z}{t} \leq 50000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -4e+67) (not (<= (/ z t) 50000.0)))
   (* z (/ (- y x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -4e+67) || !((z / t) <= 50000.0)) {
		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) <= (-4d+67)) .or. (.not. ((z / t) <= 50000.0d0))) 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) <= -4e+67) || !((z / t) <= 50000.0)) {
		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) <= -4e+67) or not ((z / t) <= 50000.0):
		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) <= -4e+67) || !(Float64(z / t) <= 50000.0))
		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) <= -4e+67) || ~(((z / t) <= 50000.0)))
		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], -4e+67], N[Not[LessEqual[N[(z / t), $MachinePrecision], 50000.0]], $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) < -3.99999999999999993e67 or 5e4 < (/.f64 z t)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 90.1%

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

   3. Taylor expanded in y around 0 90.1%

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

      1. neg-mul-1 90.1%

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

      2. +-commutative 90.1%

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

      3. sub-neg 90.1%

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

      4. div-sub 94.7%

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

   5. Simplified 94.7%

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

   if -3.99999999999999993e67 < (/.f64 z t) < 5e4

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 91.5%

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

      1. associate-*r/ 94.8%

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

   4. Simplified 94.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -4 \cdot 10^{+67} \lor \neg \left(\frac{z}{t} \leq 50000\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 5: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 50000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -400.0)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 50000.0) (+ x (* y (/ z t))) (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -400.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 50000.0) {
		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) <= (-400.0d0)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 50000.0d0) 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) <= -400.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 50000.0) {
		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) <= -400.0:
		tmp = z / (t / (y - x))
	elif (z / t) <= 50000.0:
		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) <= -400.0)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 50000.0)
		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) <= -400.0)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 50000.0)
		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], -400.0], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 50000.0], 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) < -400

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 85.9%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. neg-mul-1 85.9%

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

      2. +-commutative 85.9%

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

      3. sub-neg 85.9%

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

      4. div-sub 90.8%

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

   5. Simplified 90.8%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l* 93.5%

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

   7. Applied egg-rr 93.5%

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

   if -400 < (/.f64 z t) < 5e4

   1. Initial program 98.4%

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

   2. Taylor expanded in y around inf 95.1%

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

      1. associate-*r/ 97.2%

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

   4. Simplified 97.2%

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

   if 5e4 < (/.f64 z t)

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 89.0%

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

   3. Taylor expanded in y around 0 89.0%

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

      1. neg-mul-1 89.0%

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

      2. +-commutative 89.0%

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

      3. sub-neg 89.0%

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

      4. div-sub 92.2%

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

   5. Simplified 92.2%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 50000:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 6: 95.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.4:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) -400.0)
   (/ z (/ t (- y x)))
   (if (<= (/ z t) 0.4) (+ x (* y (/ z t))) (/ (- y x) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -400.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.4) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) / (t / z);
	}
	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) <= (-400.0d0)) then
        tmp = z / (t / (y - x))
    else if ((z / t) <= 0.4d0) then
        tmp = x + (y * (z / t))
    else
        tmp = (y - x) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -400.0) {
		tmp = z / (t / (y - x));
	} else if ((z / t) <= 0.4) {
		tmp = x + (y * (z / t));
	} else {
		tmp = (y - x) / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -400.0:
		tmp = z / (t / (y - x))
	elif (z / t) <= 0.4:
		tmp = x + (y * (z / t))
	else:
		tmp = (y - x) / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= -400.0)
		tmp = Float64(z / Float64(t / Float64(y - x)));
	elseif (Float64(z / t) <= 0.4)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(y - x) / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -400.0)
		tmp = z / (t / (y - x));
	elseif ((z / t) <= 0.4)
		tmp = x + (y * (z / t));
	else
		tmp = (y - x) / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], -400.0], N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 0.4], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -400

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 85.9%

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

   3. Taylor expanded in y around 0 85.9%

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

      1. neg-mul-1 85.9%

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

      2. +-commutative 85.9%

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

      3. sub-neg 85.9%

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

      4. div-sub 90.8%

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

   5. Simplified 90.8%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l* 93.5%

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

   7. Applied egg-rr 93.5%

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

   if -400 < (/.f64 z t) < 0.40000000000000002

   1. Initial program 98.3%

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

   2. Taylor expanded in y around inf 95.0%

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

      1. associate-*r/ 97.2%

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

   4. Simplified 97.2%

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

   if 0.40000000000000002 < (/.f64 z t)

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. sub-div 90.9%

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

      3. associate-/r/ 98.0%

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

   4. Applied egg-rr 98.0%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -400:\\ \;\;\;\;\frac{z}{\frac{t}{y - x}}\\ \mathbf{elif}\;\frac{z}{t} \leq 0.4:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{\frac{t}{z}}\\ \end{array} \]

Alternative 7: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-50} \lor \neg \left(\frac{z}{t} \leq 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -5e-50) (not (<= (/ z t) 1e-87))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -5e-50) || !((z / t) <= 1e-87)) {
		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-50)) .or. (.not. ((z / t) <= 1d-87))) 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-50) || !((z / t) <= 1e-87)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -5e-50) or not ((z / t) <= 1e-87):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -5e-50) || !(Float64(z / t) <= 1e-87))
		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-50) || ~(((z / t) <= 1e-87)))
		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-50], N[Not[LessEqual[N[(z / t), $MachinePrecision], 1e-87]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -4.99999999999999968e-50 or 1.00000000000000002e-87 < (/.f64 z t)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. sub-div 83.3%

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

      3. associate-/r/ 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in y around inf 49.0%

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

      1. associate-*r/ 54.8%

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

   7. Simplified 54.8%

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

   if -4.99999999999999968e-50 < (/.f64 z t) < 1.00000000000000002e-87

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 82.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -5 \cdot 10^{-50} \lor \neg \left(\frac{z}{t} \leq 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 97.4% 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 9: 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 39.4%

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

3. Final simplification 39.4%

   \[\leadsto x \]

Developer target: 97.1% 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 2023290 
(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))))