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

Percentage Accurate: 97.7% → 97.2%

Time: 7.5s

Alternatives: 10

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: 97.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.25e-171) (+ x (* (- y x) (/ z t))) (+ x (/ z (/ t (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z / (t / (y - 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 <= 1.25d-171) then
        tmp = x + ((y - x) * (z / t))
    else
        tmp = x + (z / (t / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z / (t / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.25e-171:
		tmp = x + ((y - x) * (z / t))
	else:
		tmp = x + (z / (t / (y - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.25e-171)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.25e-171)
		tmp = x + ((y - x) * (z / t));
	else
		tmp = x + (z / (t / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.25e-171], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.24999999999999998e-171

   1. Initial program 99.2%

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

   if 1.24999999999999998e-171 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

      4. associate-*r/ 80.7%

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

      5. associate-/l* 84.7%

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

      6. distribute-rgt-out-- 93.8%

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

      7. associate-*l/ 92.7%

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

      8. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-188} \lor \neg \left(z \leq 1.2 \cdot 10^{-171}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e-188) (not (<= z 1.2e-171)))
   (+ x (* z (/ (- y x) t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e-188) || !(z <= 1.2e-171)) {
		tmp = x + (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 <= (-5.1d-188)) .or. (.not. (z <= 1.2d-171))) then
        tmp = x + (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 <= -5.1e-188) || !(z <= 1.2e-171)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e-188) or not (z <= 1.2e-171):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e-188) || !(z <= 1.2e-171))
		tmp = Float64(x + 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 <= -5.1e-188) || ~((z <= 1.2e-171)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e-188], N[Not[LessEqual[z, 1.2e-171]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.10000000000000009e-188 or 1.19999999999999993e-171 < z

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

      4. associate-*r/ 85.4%

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

      5. associate-/l* 90.9%

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

      6. distribute-rgt-out-- 96.4%

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

      7. associate-*l/ 91.3%

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

      8. associate-/l* 98.8%

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

   5. Simplified 98.8%

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

   if -5.10000000000000009e-188 < z < 1.19999999999999993e-171

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 92.8%

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

      1. associate-*r/ 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-188} \lor \neg \left(z \leq 1.2 \cdot 10^{-171}\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+27} \lor \neg \left(y \leq 1.5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e+27) (not (<= y 1.5e-29)))
   (+ x (* y (/ z t)))
   (* x (/ (- t z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+27) || !(y <= 1.5e-29)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - 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 <= (-2.5d+27)) .or. (.not. (y <= 1.5d-29))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * ((t - 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 <= -2.5e+27) || !(y <= 1.5e-29)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e+27) or not (y <= 1.5e-29):
		tmp = x + (y * (z / t))
	else:
		tmp = x * ((t - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e+27) || !(y <= 1.5e-29))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(t - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e+27) || ~((y <= 1.5e-29)))
		tmp = x + (y * (z / t));
	else
		tmp = x * ((t - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e+27], N[Not[LessEqual[y, 1.5e-29]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999999e27 or 1.5000000000000001e-29 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 88.5%

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

      1. associate-*r/ 93.9%

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

   5. Simplified 93.9%

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

   if -2.4999999999999999e27 < y < 1.5000000000000001e-29

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

      4. associate-*r/ 85.7%

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

      5. associate-/l* 91.1%

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

      6. distribute-rgt-out-- 95.5%

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

      7. associate-*l/ 93.6%

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

      8. associate-/l* 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in y around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

   8. Simplified 86.3%

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

      1. associate-*r/ 84.0%

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

      2. distribute-frac-neg2 84.0%

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

      3. add-sqr-sqrt 45.4%

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

      4. sqrt-unprod 58.6%

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

      5. sqr-neg 58.6%

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

      6. sqrt-unprod 20.4%

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

      7. add-sqr-sqrt 47.0%

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

      8. associate-*r/ 47.7%

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

      9. sub-neg 47.7%

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

      10. add-sqr-sqrt 22.7%

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

      11. sqrt-unprod 59.8%

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

      12. sqr-neg 59.8%

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

      13. sqrt-unprod 44.6%

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

      14. add-sqr-sqrt 86.3%

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

   10. Applied egg-rr 86.3%

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

   11. Taylor expanded in t around 0 73.3%

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

       1. *-commutative 73.3%

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

       2. distribute-rgt-out-- 73.4%

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

       3. associate-/l* 86.5%

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

   13. Simplified 86.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+27} \lor \neg \left(y \leq 1.5 \cdot 10^{-29}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-22} \lor \neg \left(z \leq 5.8 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.2e-22) (not (<= z 5.8e+21))) (* x (/ z (- t))) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.2e-22) || !(z <= 5.8e+21)) {
		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 <= (-9.2d-22)) .or. (.not. (z <= 5.8d+21))) 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 <= -9.2e-22) || !(z <= 5.8e+21)) {
		tmp = x * (z / -t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.2e-22) or not (z <= 5.8e+21):
		tmp = x * (z / -t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.2e-22) || !(z <= 5.8e+21))
		tmp = Float64(x * Float64(z / Float64(-t)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.2e-22) || ~((z <= 5.8e+21)))
		tmp = x * (z / -t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.2e-22], N[Not[LessEqual[z, 5.8e+21]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999992e-22 or 5.8e21 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 82.1%

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

      1. +-commutative 82.1%

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

      2. mul-1-neg 82.1%

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

      3. unsub-neg 82.1%

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

      4. associate-*r/ 79.7%

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

      5. associate-/l* 87.7%

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

      6. distribute-rgt-out-- 95.6%

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

      7. associate-*l/ 87.5%

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

      8. associate-/l* 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in y around 0 58.7%

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

      1. neg-mul-1 58.7%

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

      2. distribute-neg-frac2 58.7%

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

   8. Simplified 58.7%

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

      1. associate-*r/ 53.5%

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

      2. distribute-frac-neg2 53.5%

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

      3. add-sqr-sqrt 30.3%

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

      4. sqrt-unprod 29.8%

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

      5. sqr-neg 29.8%

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

      6. sqrt-unprod 4.0%

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

      7. add-sqr-sqrt 14.9%

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

      8. associate-*r/ 17.2%

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

      9. sub-neg 17.2%

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

      10. add-sqr-sqrt 6.9%

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

      11. sqrt-unprod 33.2%

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

      12. sqr-neg 33.2%

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

      13. sqrt-unprod 31.1%

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

      14. add-sqr-sqrt 58.7%

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

   10. Applied egg-rr 58.7%

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

   11. Taylor expanded in z around inf 42.3%

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

       1. mul-1-neg 42.3%

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

       2. associate-*r/ 43.8%

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

       3. distribute-rgt-neg-in 43.8%

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

       4. distribute-neg-frac2 43.8%

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

   13. Simplified 43.8%

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

   if -9.1999999999999992e-22 < z < 5.8e21

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 66.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-22} \lor \neg \left(z \leq 5.8 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e-25)
   (* x (/ z (- t)))
   (if (<= z 1.85e+21) x (/ (* x (- z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-25) {
		tmp = x * (z / -t);
	} else if (z <= 1.85e+21) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-7.2d-25)) then
        tmp = x * (z / -t)
    else if (z <= 1.85d+21) then
        tmp = x
    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 tmp;
	if (z <= -7.2e-25) {
		tmp = x * (z / -t);
	} else if (z <= 1.85e+21) {
		tmp = x;
	} else {
		tmp = (x * -z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e-25:
		tmp = x * (z / -t)
	elif z <= 1.85e+21:
		tmp = x
	else:
		tmp = (x * -z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e-25)
		tmp = Float64(x * Float64(z / Float64(-t)));
	elseif (z <= 1.85e+21)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.2e-25)
		tmp = x * (z / -t);
	elseif (z <= 1.85e+21)
		tmp = x;
	else
		tmp = (x * -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e-25], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+21], x, N[(N[(x * (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.1999999999999998e-25

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. mul-1-neg 84.3%

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

      3. unsub-neg 84.3%

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

      4. associate-*r/ 85.6%

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

      5. associate-/l* 95.4%

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

      6. distribute-rgt-out-- 98.5%

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

      7. associate-*l/ 85.8%

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

      8. associate-/l* 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 63.3%

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

      1. neg-mul-1 63.3%

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

      2. distribute-neg-frac2 63.3%

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

   8. Simplified 63.3%

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

      1. associate-*r/ 56.1%

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

      2. distribute-frac-neg2 56.1%

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

      3. add-sqr-sqrt 33.4%

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

      4. sqrt-unprod 29.9%

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

      5. sqr-neg 29.9%

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

      6. sqrt-unprod 2.4%

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

      7. add-sqr-sqrt 11.0%

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

      8. associate-*r/ 15.1%

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

      9. sub-neg 15.1%

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

      10. add-sqr-sqrt 6.6%

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

      11. sqrt-unprod 34.7%

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

      12. sqr-neg 34.7%

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

      13. sqrt-unprod 34.8%

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

      14. add-sqr-sqrt 63.3%

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

   10. Applied egg-rr 63.3%

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

   11. Taylor expanded in z around inf 46.3%

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

       1. mul-1-neg 46.3%

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

       2. associate-*r/ 52.2%

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

       3. distribute-rgt-neg-in 52.2%

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

       4. distribute-neg-frac2 52.2%

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

   13. Simplified 52.2%

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

   if -7.1999999999999998e-25 < z < 1.85e21

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 66.9%

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

   if 1.85e21 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in t around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. *-commutative 50.5%

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

      4. distribute-lft-neg-in 50.5%

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

      5. distribute-rgt-out 50.6%

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

   8. Simplified 50.6%

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

   9. Taylor expanded in t around 0 37.9%

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

       1. mul-1-neg 37.9%

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

       2. distribute-lft-neg-out 37.9%

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

       3. *-commutative 37.9%

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

   11. Simplified 37.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.25e-171) (+ x (* (- y x) (/ z t))) (+ x (* z (/ (- y x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (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 <= 1.25d-171) then
        tmp = x + ((y - x) * (z / t))
    else
        tmp = x + (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 <= 1.25e-171) {
		tmp = x + ((y - x) * (z / t));
	} else {
		tmp = x + (z * ((y - x) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.25e-171:
		tmp = x + ((y - x) * (z / t))
	else:
		tmp = x + (z * ((y - x) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.25e-171)
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z / t)));
	else
		tmp = Float64(x + 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 <= 1.25e-171)
		tmp = x + ((y - x) * (z / t));
	else
		tmp = x + (z * ((y - x) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.25e-171], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.24999999999999998e-171

   1. Initial program 99.2%

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

   if 1.24999999999999998e-171 < z

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

      4. associate-*r/ 80.7%

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

      5. associate-/l* 84.7%

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

      6. distribute-rgt-out-- 93.8%

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

      7. associate-*l/ 92.7%

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

      8. associate-/l* 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.25 \cdot 10^{-171}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 97.3%

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

   1. clear-num 96.9%

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

   2. un-div-inv 97.9%

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

4. Applied egg-rr 97.9%

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

5. Final simplification 97.9%

   \[\leadsto x + \frac{y - x}{\frac{t}{z}} \]
6. Add Preprocessing

Alternative 8: 66.0% 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 97.3%

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

3. Taylor expanded in x around inf 66.3%

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

   1. mul-1-neg 66.3%

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

   2. unsub-neg 66.3%

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

5. Simplified 66.3%

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

6. Final simplification 66.3%

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

Alternative 9: 66.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in y around 0 90.5%

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

   1. +-commutative 90.5%

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

   2. mul-1-neg 90.5%

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

   3. unsub-neg 90.5%

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

   4. associate-*r/ 89.2%

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

   5. associate-/l* 93.3%

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

   6. distribute-rgt-out-- 97.3%

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

   7. associate-*l/ 93.2%

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

   8. associate-/l* 93.3%

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

5. Simplified 93.3%

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

6. Taylor expanded in y around 0 63.7%

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

   1. neg-mul-1 63.7%

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

   2. distribute-neg-frac2 63.7%

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

8. Simplified 63.7%

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

   1. associate-*r/ 63.6%

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

   2. distribute-frac-neg2 63.6%

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

   3. add-sqr-sqrt 32.1%

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

   4. sqrt-unprod 48.6%

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

   5. sqr-neg 48.6%

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

   6. sqrt-unprod 19.7%

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

   7. add-sqr-sqrt 40.4%

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

   8. associate-*r/ 39.6%

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

   9. sub-neg 39.6%

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

   10. add-sqr-sqrt 20.4%

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

   11. sqrt-unprod 48.5%

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

   12. sqr-neg 48.5%

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

   13. sqrt-unprod 31.4%

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

   14. add-sqr-sqrt 63.7%

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

10. Applied egg-rr 63.7%

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

11. Taylor expanded in t around 0 54.7%

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

    1. *-commutative 54.7%

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

    2. distribute-rgt-out-- 55.2%

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

    3. associate-/l* 66.4%

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

13. Simplified 66.4%

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

14. Final simplification 66.4%

    \[\leadsto x \cdot \frac{t - z}{t} \]
15. Add Preprocessing

Alternative 10: 39.1% 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 97.3%

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

3. Taylor expanded in z around 0 41.4%

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

4. Final simplification 41.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 97.5% accurate, 0.3× 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 2024079 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :alt
  (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))))