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

Percentage Accurate: 97.7% → 97.7%

Time: 6.2s

Alternatives: 11

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

2. Taylor expanded in y around 0 89.8%

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

   1. +-commutative 89.8%

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

   2. mul-1-neg 89.8%

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

   3. sub-neg 89.8%

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

   4. associate-/l* 89.2%

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

   5. associate-/l* 90.9%

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

   6. div-sub 98.7%

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

4. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+64} \lor \neg \left(\frac{z}{t} \leq 2000000000000\right):\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -2e+64) (not (<= (/ z t) 2000000000000.0)))
   (* z (- (/ y t) (/ x t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -2e+64) || !((z / t) <= 2000000000000.0)) {
		tmp = z * ((y / t) - (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+64)) .or. (.not. ((z / t) <= 2000000000000.0d0))) then
        tmp = z * ((y / t) - (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+64) || !((z / t) <= 2000000000000.0)) {
		tmp = z * ((y / t) - (x / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -2e+64) or not ((z / t) <= 2000000000000.0):
		tmp = z * ((y / t) - (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+64) || !(Float64(z / t) <= 2000000000000.0))
		tmp = Float64(z * Float64(Float64(y / t) - Float64(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+64) || ~(((z / t) <= 2000000000000.0)))
		tmp = z * ((y / t) - (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+64], N[Not[LessEqual[N[(z / t), $MachinePrecision], 2000000000000.0]], $MachinePrecision]], N[(z * N[(N[(y / t), $MachinePrecision] - N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -2.00000000000000004e64 or 2e12 < (/.f64 z t)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 92.4%

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

   if -2.00000000000000004e64 < (/.f64 z t) < 2e12

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. associate-*r/ 93.0%

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

   4. Simplified 93.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -2 \cdot 10^{+64} \lor \neg \left(\frac{z}{t} \leq 2000000000000\right):\\ \;\;\;\;z \cdot \left(\frac{y}{t} - \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 3: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ z t) -10000000.0) (not (<= (/ z t) 0.5))) (* x (/ (- z) t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000.0) || !((z / t) <= 0.5)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z / t) <= (-10000000.0d0)) .or. (.not. ((z / t) <= 0.5d0))) then
        tmp = x * (-z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z / t) <= -10000000.0) || !((z / t) <= 0.5)) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z / t) <= -10000000.0) or not ((z / t) <= 0.5):
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z / t) <= -10000000.0) || !(Float64(z / t) <= 0.5))
		tmp = Float64(x * Float64(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) <= -10000000.0) || ~(((z / t) <= 0.5)))
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -10000000.0], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.5]], $MachinePrecision]], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 z t) < -1e7 or 0.5 < (/.f64 z t)

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in z around inf 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-frac-neg 51.9%

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

   7. Simplified 51.9%

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

   if -1e7 < (/.f64 z t) < 0.5

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 73.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -10000000 \lor \neg \left(\frac{z}{t} \leq 0.5\right):\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 40.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) (- INFINITY))
   (* x (/ z t))
   (if (<= (/ z t) 500000000000.0) x (* z (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -((double) INFINITY)) {
		tmp = x * (z / t);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = x * (z / t);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = x * (z / t)
	elif (z / t) <= 500000000000.0:
		tmp = x
	else:
		tmp = z * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(x * Float64(z / t));
	elseif (Float64(z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = x * (z / t);
	elseif ((z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = z * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 500000000000.0], x, N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-frac-neg 67.2%

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

   7. Simplified 67.2%

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

      1. distribute-frac-neg 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

      3. distribute-lft-neg-in 67.2%

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

      4. associate-*r/ 60.3%

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

      5. *-commutative 60.3%

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

      6. associate-/l* 60.3%

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

      7. add-sqr-sqrt 14.8%

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

      8. sqrt-unprod 19.5%

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

      9. sqr-neg 19.5%

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

      10. sqrt-unprod 5.2%

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

      11. add-sqr-sqrt 10.4%

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

   9. Applied egg-rr 10.4%

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

       1. associate-/r/ 23.8%

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

   11. Applied egg-rr 23.8%

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

   if -inf.0 < (/.f64 z t) < 5e11

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 53.5%

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

   if 5e11 < (/.f64 z t)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-frac-neg 57.1%

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

   7. Simplified 57.1%

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

      1. distribute-frac-neg 57.1%

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

      2. distribute-rgt-neg-in 57.1%

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

      3. distribute-lft-neg-in 57.1%

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

      4. associate-*r/ 52.6%

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

      5. *-commutative 52.6%

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

      6. associate-/l* 48.2%

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

      7. add-sqr-sqrt 25.5%

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

      8. sqrt-unprod 28.0%

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

      9. sqr-neg 28.0%

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

      10. sqrt-unprod 5.4%

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

      11. add-sqr-sqrt 9.2%

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

   9. Applied egg-rr 9.2%

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

       1. clear-num 9.2%

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

       2. associate-/r/ 9.2%

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

       3. clear-num 9.2%

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

   11. Applied egg-rr 9.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 5: 40.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) (- INFINITY))
   (/ x (/ t z))
   (if (<= (/ z t) 500000000000.0) x (* z (/ x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -((double) INFINITY)) {
		tmp = x / (t / z);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (t / z);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = x / (t / z)
	elif (z / t) <= 500000000000.0:
		tmp = x
	else:
		tmp = z * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(x / Float64(t / z));
	elseif (Float64(z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = x / (t / z);
	elseif ((z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = z * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 500000000000.0], x, N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-frac-neg 67.2%

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

   7. Simplified 67.2%

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

      1. distribute-frac-neg 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

      3. distribute-lft-neg-in 67.2%

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

      4. add-sqr-sqrt 19.3%

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

      5. sqrt-unprod 19.0%

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

      6. sqr-neg 19.0%

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

      7. sqrt-unprod 9.5%

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

      8. add-sqr-sqrt 23.8%

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

      9. associate-*r/ 10.4%

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

      10. associate-/l* 23.9%

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

   9. Applied egg-rr 23.9%

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

   if -inf.0 < (/.f64 z t) < 5e11

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 53.5%

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

   if 5e11 < (/.f64 z t)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-frac-neg 57.1%

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

   7. Simplified 57.1%

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

      1. distribute-frac-neg 57.1%

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

      2. distribute-rgt-neg-in 57.1%

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

      3. distribute-lft-neg-in 57.1%

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

      4. associate-*r/ 52.6%

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

      5. *-commutative 52.6%

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

      6. associate-/l* 48.2%

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

      7. add-sqr-sqrt 25.5%

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

      8. sqrt-unprod 28.0%

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

      9. sqr-neg 28.0%

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

      10. sqrt-unprod 5.4%

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

      11. add-sqr-sqrt 9.2%

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

   9. Applied egg-rr 9.2%

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

       1. clear-num 9.2%

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

       2. associate-/r/ 9.2%

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

       3. clear-num 9.2%

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

   11. Applied egg-rr 9.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \end{array} \]

Alternative 6: 40.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ z t) (- INFINITY))
   (/ x (/ t z))
   (if (<= (/ z t) 500000000000.0) x (/ z (/ t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -((double) INFINITY)) {
		tmp = x / (t / z);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z / (t / x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z / t) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (t / z);
	} else if ((z / t) <= 500000000000.0) {
		tmp = x;
	} else {
		tmp = z / (t / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z / t) <= -math.inf:
		tmp = x / (t / z)
	elif (z / t) <= 500000000000.0:
		tmp = x
	else:
		tmp = z / (t / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z / t) <= Float64(-Inf))
		tmp = Float64(x / Float64(t / z));
	elseif (Float64(z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = Float64(z / Float64(t / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z / t) <= -Inf)
		tmp = x / (t / z);
	elseif ((z / t) <= 500000000000.0)
		tmp = x;
	else
		tmp = z / (t / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z / t), $MachinePrecision], (-Infinity)], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z / t), $MachinePrecision], 500000000000.0], x, N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 z t) < -inf.0

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   4. Simplified 67.2%

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

   5. Taylor expanded in z around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-frac-neg 67.2%

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

   7. Simplified 67.2%

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

      1. distribute-frac-neg 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

      3. distribute-lft-neg-in 67.2%

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

      4. add-sqr-sqrt 19.3%

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

      5. sqrt-unprod 19.0%

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

      6. sqr-neg 19.0%

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

      7. sqrt-unprod 9.5%

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

      8. add-sqr-sqrt 23.8%

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

      9. associate-*r/ 10.4%

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

      10. associate-/l* 23.9%

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

   9. Applied egg-rr 23.9%

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

   if -inf.0 < (/.f64 z t) < 5e11

   1. Initial program 98.7%

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

   2. Taylor expanded in z around 0 53.5%

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

   if 5e11 < (/.f64 z t)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. unsub-neg 57.1%

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

   4. Simplified 57.1%

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

   5. Taylor expanded in z around inf 57.1%

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

      1. mul-1-neg 57.1%

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

      2. distribute-frac-neg 57.1%

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

   7. Simplified 57.1%

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

      1. distribute-frac-neg 57.1%

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

      2. distribute-rgt-neg-in 57.1%

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

      3. distribute-lft-neg-in 57.1%

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

      4. associate-*r/ 52.6%

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

      5. *-commutative 52.6%

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

      6. associate-/l* 48.2%

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

      7. add-sqr-sqrt 25.5%

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

      8. sqrt-unprod 28.0%

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

      9. sqr-neg 28.0%

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

      10. sqrt-unprod 5.4%

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

      11. add-sqr-sqrt 9.2%

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

   9. Applied egg-rr 9.2%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;\frac{z}{t} \leq 500000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 7: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-80} \lor \neg \left(y \leq 4.8 \cdot 10^{-101}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e-80) (not (<= y 4.8e-101)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-80) || !(y <= 4.8e-101)) {
		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 <= (-2.2d-80)) .or. (.not. (y <= 4.8d-101))) 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 <= -2.2e-80) || !(y <= 4.8e-101)) {
		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 <= -2.2e-80) or not (y <= 4.8e-101):
		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 <= -2.2e-80) || !(y <= 4.8e-101))
		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 <= -2.2e-80) || ~((y <= 4.8e-101)))
		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, -2.2e-80], N[Not[LessEqual[y, 4.8e-101]], $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 < -2.2000000000000001e-80 or 4.8e-101 < y

   1. Initial program 98.0%

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

   2. Taylor expanded in y around inf 86.0%

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

      1. associate-*r/ 89.5%

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

   4. Simplified 89.5%

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

   if -2.2000000000000001e-80 < y < 4.8e-101

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   4. Simplified 90.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-80} \lor \neg \left(y \leq 4.8 \cdot 10^{-101}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \end{array} \]

Alternative 8: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-78)
   (+ x (* y (/ z t)))
   (if (<= y 4.9e-101) (* x (- 1.0 (/ z t))) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-78) {
		tmp = x + (y * (z / t));
	} else if (y <= 4.9e-101) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (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 (y <= (-5d-78)) then
        tmp = x + (y * (z / t))
    else if (y <= 4.9d-101) then
        tmp = x * (1.0d0 - (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-78) {
		tmp = x + (y * (z / t));
	} else if (y <= 4.9e-101) {
		tmp = x * (1.0 - (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5e-78:
		tmp = x + (y * (z / t))
	elif y <= 4.9e-101:
		tmp = x * (1.0 - (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-78)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (y <= 4.9e-101)
		tmp = Float64(x * Float64(1.0 - Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-78)
		tmp = x + (y * (z / t));
	elseif (y <= 4.9e-101)
		tmp = x * (1.0 - (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5e-78], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-101], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e-78

   1. Initial program 97.2%

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

   2. Taylor expanded in y around inf 83.8%

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

      1. associate-*r/ 87.5%

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

   4. Simplified 87.5%

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

   if -4.9999999999999996e-78 < y < 4.9e-101

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

   4. Simplified 90.0%

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

   if 4.9e-101 < y

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 87.9%

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

      1. associate-*r/ 91.2%

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

   4. Simplified 91.2%

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

      1. associate-*r/ 87.9%

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

      2. associate-/l* 92.3%

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

   6. Applied egg-rr 92.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 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 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: 65.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{t}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - (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 * (1.0d0 - (z / t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - (z / t));
}

Python

def code(x, y, z, t):
	return x * (1.0 - (z / t))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - Float64(z / t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - (z / t));
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

2. Taylor expanded in x around inf 63.6%

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

   1. mul-1-neg 63.6%

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

   2. unsub-neg 63.6%

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

4. Simplified 63.6%

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

5. Final simplification 63.6%

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

Alternative 11: 38.1% 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 36.3%

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

3. Final simplification 36.3%

   \[\leadsto x \]

Developer target: 97.5% 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 2023310 
(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))))